Download Financial Management

Basics of Financial Management
By
Muhammad Arif
Member Visiting Faculty Sheikh
Zayed Sultan Institute University
of Karachi and Biztek
According to the course and syllabus prescribed
in all universities in Pakistan
1
Thanks and acknowledgements are for Muhammad Al Souki
my student in Sheikh Zayed Sultan Institute, University of
Karachi for his help and review in preparation of this book
2
Contents
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
3
Financial Management - 4
Definitions
Present value of Bonds
9
and Equities
NPV leads to better 14
investment decisions
Cash Flows/Financial
Statements
Managerial Finance
Financial Markets
Risk and opportunities
Interest Rate
Management
Foreign Exchange
Markets
Derivatives
Credit Derivatives and
their role in global
financial crisis
Capital Budgeting and
Risks
17
A project is not a black
box
Pay out policy
Financial analysis and
Planning
About Finance
Exercises
Bibliography
Index
Profile about writer
84
20
23
30
40
44
49
75
80
93
103
108
110
115
116
117
Chapter 1
Financial Management -Definitions
Finance is the social science that deals with the funds management. The general areas of
finance are business (Corporate) finance, personal finance, and (Government) public
finance. Finance includes saving money and often includes lending money. The field of finance
deals with the concepts of time, money and risk and how they are interrelated. It also deals with
how money is spent and budgeted.
Financial management means:•
•
Managerial finance, the branch of finance that concerns itself with the managerial
significance of financial techniques &
Corporate finance i.e. an area of finance that deals with the corporate financial decisions
In addition Conventional financial management tagged with Shriah rulings is termed as Islamic
financial management. In this case data used whether historical or current and evaluation
process for valuation of any asset remains the same, However investment strategy differs in
some ways.
1. Managerial finance
It is the branch of finance that concerns itself with the managerial significance of financial
techniques. It is focused on assessment rather than techniques. Why! because it is better to be
approximately right rather than precisely wrong.
In this respect first of all management would want to know what the figures mean.
Than they might compare the returns with other businesses in the industry and ask the
question, why we are performing better or worse than others? If so, than what can be the source
of the problem? Do we have the same profit margins? If not than why? Do we have the same
expenses or are we paying more for something than others?
They may also look at changes in asset balances looking for red flags that indicate problems
with bill collection or bad debts.
They will tend to analyze working capital to anticipate future cash flow problems.
Managerial finance is an interdisciplinary approach that borrows from both managerial
accounting and corporate finance.
2. Corporate finance
It is an area of finance that deals with the financial decisions corporations make and the tools
and analysis they use to make these decisions. The primary goal of corporate finance is to
maximize corporate value while managing the firm's financial risks. Although it is in principle
different from managerial finance which studies the financial decisions of other firms as well
rather than the corporation itself and alone.
The main concept in the study of corporate finance is the applicability and resolution of financial
problems that all kinds of firms do have.
This discipline can be divided into long-term and short-term decisions and techniques. Capital
investment decisions are long-term choices about which projects receive investment, whether to
finance that investment with equity or debt, and when or whether to pay dividends to
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shareholders. On the other hand, the short term decisions can be grouped under the heading
"Working capital management“, the focus here is on managing cash, inventories, and short-term
borrowing and lending (such as the terms on credit extended to customers).
3. Public finance
It is a field of economics concerned with paying for collective or governmental activities, and
with the administration and design of those activities. The field is often divided into questions of
what the government or collective organizations should do or are doing, and questions of how to
pay for those activities. The broader term, public economics, and the narrower term,
government finance, are also often used.
Collection of sufficient resources from the economy in an appropriate manner along with
allocating and use of these resources efficiently and effectively constitute good financial
management. Resource generation, resource allocation and expenditure management
(resource utilization) are the essential components of a public financial management system.
Public Finance Management (PFM) basically deals with all aspects of resource mobilization and
expenditure management in government. Just as managing finances is a critical function of
management in any organization, similarly public finance management is an essential part of
the governance process. Public finance management includes resource mobilization,
prioritization of programmes, the budgetary process, efficient management of resources and
exercising controls. Rising aspirations of people are placing more demands on financial
resources. At the same time, the emphasis of the citizenry is on value for money, thus making
public finance management increasingly vital.
Government expenditures are financed in two ways:


Government revenue
o Taxes
o Non-tax revenue (revenue from government-owned corporations, sovereign
wealth funds, sales of assets, or Seigniorage
Government borrowing
How a government chooses to finance its activities can have important effects on the
distribution of income and wealth (income redistribution) and on the efficiency of markets (effect
of taxes on market prices and efficiency). The issue of how taxes affect income distribution is
closely related to tax incidence, which examines the distribution of tax burdens after market
adjustments are taken into account. Public finance research also analyzes effects of the various
types of taxes and types of borrowing as well as administrative concerns, such as tax
enforcement.
3. Personal Finance
It deals with the Credit i.e is the provision of resources (such as granting a loan) by one party
to another party where that second party does not reimburse the first party immediately, thereby
generating a debt, and instead arranges either to repay or return those resources (or material(s)
of equal value) at a later date. It is any form of deferred payment. The first party is called a
creditor, also known as a lender, while the second party is called a debtor, also known as a
borrower.
Movements of financial capital are normally dependent on either credit or equity transfers.
Credit is in turn dependent on the reputation or creditworthiness of the entity which takes
responsibility for the funds.
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Credit need not necessarily be based on formal monetary systems. The credit concept can be
applied in barter economies based on the direct exchange of goods and services, and some
would go so far as to suggest that the true nature of money is best described as a
representation of the credit-debt relationships that exist in society.
Credit is denominated by a unit of account. Unlike money (by a strict definition), credit itself
cannot act as a unit of account. However, many forms of credit can readily act as a medium of
exchange. As such, various forms of credit are frequently referred to as money and are included
in estimates of the money supply.
Credit is also traded in the market. The purest form is the credit default swap market, which is
essentially a traded market in credit insurance. A credit default swap represents the price at
which two parties exchange this risk – the protection "seller" takes the risk of default of the
credit in return for a payment, commonly denoted in basis points (one basis point is 1/100 of a
percent) of the notional amount to be referenced, while the protection "buyer" pays this premium
and in the case of default of the underlying (a loan, bond or other receivable), delivers this
receivable to the protection seller and receives from the seller the par amount (that is, is made
whole).
Main steps in carrying out Financial Management Decisions
1. Capital investment decisions: - They are long-term corporate financial decisions
relating to fixed assets and capital structure. Capital investment decisions thus comprise
an investment decision, a financing decision, and a dividend decision.
2. Project valuation:- each project's value is estimated using a discounted cash flow
(DCF) valuation, and the opportunity with the highest value, as measured by the
resultant net present value (NPV)
3. Estimating the size and timing of all of the incremental cash flows resulting from the
project and then discounting these cash flows to determine their present value.
4. These present values are then summed, and this sum net of the initial investment outlay
becomes the NPV.
5. The NPV is greatly affected by the discount rate. Thus identifying the proper discount
rate—the project "hurdle rate"—is critical in making the right decision. The hurdle rate is
the minimum acceptable return on an investment—i.e. the project appropriate discount
rate. The hurdle rate should reflect the riskiness of the investment, typically measured by
volatility of cash flows, and must take into account the financing mix. Managers use
models such as the Capital Asset Pricing Model (CAPM) or the Arbitrage Pricing
Techniques (APT) to estimate a discount rate appropriate for a particular project, and
use the weighted average cost of capital (WACC) to reflect the financing mix selected.
6. In conjunction with NPV, there are several other measures used as (secondary)
selection criteria in corporate finance. These are visible from the DCF and include
discounted payback period, IRR, Modified IRR (The internal rate of return (IRR) is a
rate of return used in capital budgeting to measure and compare the profitability of
investments, equivalent annuity, capital efficiency), and ROI In finance, (rate of return
(ROR), also known as return on investment (ROI), rate of profit or sometimes just
return, is the ratio of money gained or lost (whether realized or unrealized) on an
investment relative to the amount of money invested);
Present value (PV)
PV is the value on a given date of a future payment or series of future payments,
discounted to reflect the time value of money and other factors such as investment risk. Present
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value calculations are widely used in business and economics to provide a means to compare
cash flows at different times on a meaningful "like to like" basis.


Formula :-present value= discount factor x (C1 i.e. expected cash flow at time t)
Discount factor= 1/1+r
Example: - if you anticipate to receive Rs 100000/- at the end of year. Suppose the
rate of interest is 10% than you would have to invest 100000/1.1=Rs 90909 This
means that the present value today of Rs 100000/- onward one year is Rs 90909/-
Net present value (NPV)
(NPV) or net present worth (NPW) is defined as the total present value (PV) of a time series of
cash flows. It is a standard method for using the time value of money to appraise long-term
projects. Used for capital budgeting, and widely throughout economics, it measures the excess
or shortfall of cash flows, in present value terms, once financing charges are met.
According to last example today's worth of cash flow in future was Rs 90900/- but it is not
necessary that you may have invested in some project Rs 90909/- today. It may be Rs 75000/
therefore your net present value may be Rs15909 i.e. NPV=PV-required investment or NPV=
Co+C1/1+r i.e. -75000+ (100000/1.1) = Rs 15909
What NPV Means
If NPV > 0 the investment would add value to the firm than the project may be accepted. NPV <
0 the investment would subtract value from the firm than the project should be rejected. NPV =
0 the investment would neither gain nor lose value for the firm. However, NPV = 0 does not
mean that a project is only expected to break even, in the sense of undiscounted profit or loss
(earnings) it can show net total positive cash flow and earnings over its life.
Present values and rate of return
It is the return on the capital invested as proportion of initial outlay= profit/investment = 10000075000/75000= 33%.
These findings devise some decision rules for the capital investment i.e.
(a) Accept investments that have positive present value
(b) Accept investments that offer rates of return in excess of their opportunity cost of the capital
Trade off between investing in spot/future markets.
Suppose you have some cash in hand and some cash to be received after one year. By
investing on spot through cash or through borrowing you can increase your consumption today.
On the contrary by using your future cash flows or through lending you can increase your
consumption in tomorrow. This requires a trade off by using following assumptions.
Net present value rule: - invest so as to maximize the net present value of the investment. This
is the difference between the discounted, or present, value of the future income and the amount
of the initial investment.
Rate of return rule: - invest up to the point at which the marginal return on the investment is
equal to the rate of return on the equal investments in the capital market. This is the point of
tangency between the interest rate line and the investment opportunities line
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Example of tradeoff
Suppose you have Rs 100 and Rs 200 as cash to be received after one year. In case you do
not consume today than you would invest Rs 100 at 10%. This would make your investment as
Rs 110+200=Rs 310. On the contrary if you borrow Rs 200 against your future cash flow. It
would cost you as 200/1.1= Rs181 thus making total cash in hand as Rs 281. if you again invest
this amount at 10% you would get Rs 310. However while investing in real assets other than
financial assets rule of diminishing return or marginal returns come in to play making the payoff
curve flat in the last. In economics, diminishing returns (also called diminishing marginal
returns) refers to how the marginal contribution of a factor of production usually decreases as
more of the factor is used. According to this relationship, in a production system with fixed and
variable inputs (say factory size and labor), beyond some point, each additional unit of the
variable input yields smaller and smaller increases in output. Conversely, producing one more
unit of output costs more and more in variable inputs.
This concept is also known as the law of diminishing marginal returns, the law of increasing
relative cost, or the law of increasing opportunity cost
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Chapter - 2
Present value of Bonds and Equities
A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought
at a price lower than its face value, with the face value repaid at the time of maturity. It does not
make periodic interest payments, or have so-called "coupons," hence it is termed as zerocoupon bond.
A coupon bearing bond is a debt security, in which the authorized issuer owes the holders a
debt and, depending on the terms of the bond, is obliged to pay interest (the coupon) and/or to
repay the principal at a later date, termed as maturity.
Perpetuity is an annuity that has no definite end, or a stream of cash payments that continues
forever. There are few actual perpetuities in existence (although the British government has
issued them in the past, and they are known and still trade. A number of types of investments
are effectively perpetuities, such as real estate and preferred stock, and techniques for valuing
perpetuity can be applied to establish their prices. Perpetuities are but one of the time value
of money methods for valuing financial assets
Annuity refers to any terminating stream of fixed payments over a specified period of time.
Their usage is most commonly seen in valuation of the stream of payments, taking into account
time value of money concepts such as interest rate and future value. Examples of annuities are
regular deposits to a savings account, monthly home mortgage payments and monthly
insurance payments. Annuities are classified by payment dates.
Market Capitalization rate (or "cap rate") is a measure of the ratio between the net operating
income produced by an asset (usually real estate) and its capital cost (the original price paid to
buy the asset) or alternatively its current market value. The rate is calculated in a simple fashion
as follows:
For example, if a building is purchased for Rs 1,000,000 sale price and it produces Rs 100,000
in positive net operating income (the amount left over after fixed costs and variable costs are
subtracted from gross lease income) during one year, then:
$100,000 / $1,000,000 = 0.10 = 10%
The asset's capitalization rate is ten percent.
The dividend yield or the dividend-price ratio on a company stock is the company's annual
dividend payments divided by its market cap, or the dividend per share divided by the price per
share. It is often expressed as a percentage. Its reciprocal is the Price/Dividend ratio.
Dividend payout ratio is the fraction of net income a firm pays to its stockholders in dividends:
The part of the earnings not paid to investors is left for investment to provide for future earnings
growth. Investors seeking high current income and limited capital growth prefer companies with
high Dividend payout ratio. However investors seeking capital growth may prefer lower payout
ratio because capital gains are taxed at a lower rate. High growth firms in early life generally
have low or zero payout ratios. As they mature, they tend to return more of the earnings back to
investors
Plow back ratio shows the proportion of earnings not paid out as dividends, which is plowed
back into the business. The formula is: = (100 - Dividend Payout Ratio) or = (Retained Profit PS
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/ EPS-basic) * 100. If a company had losses during the period under review, Plowback ratio is
not defined.
Earnings per share (EPS) are the earnings returned on the initial investment amount. Diluted
Earnings Per Share (diluted EPS) is a company's earnings per share (EPS) calculated using
fully diluted shares outstanding (i.e. including the impact of stock option grants and convertible
bonds).
Earnings growth rate is the Annual rate of growth of earnings from investments. Generally, the
greater the earnings growth, the better. When the dividend payout ratio is the same, the
dividend growth rate is equal to the earnings growth rate. Earnings growth rate is a key value
that is needed when the DCF model is used for stock valuation.
Free cash flow (FCF) is cash flow available for distribution among all the securities holders of
an organization. They include equity holders, debt holders, preferred stock holders, convertible
security holders, and so on.
The P/E ratio (price-to-earnings ratio) of a stock (also called its "P/E", "PER", "earnings
multiple," or simply "multiple") is a measure of the price paid for a share relative to the annual
net income or profit earned by the firm per share. It is a financial ratio used for valuation: a
higher P/E ratio means that investors are paying more for each unit of net income, so the stock
is more expensive compared to one with lower P/E ratio. The P/E ratio has units of years, which
can be interpreted as "number of years of earnings to pay back purchase price", ignoring the
time value of money. In other words, P/E ratio shows current investor demand for a company
share. The reciprocal of the PE ratio is known as the earnings yield. The earnings yield is an
estimate of expected return to be earned from holding the stock.
Long means: - An obligation to buy a financial instrument.
Short: means - An obligation to sell a financial instrument.
Valuing present value of long dated assets
Zero coupon instruments (Treasury Bills/Commercial papers) PV=DF x C= C/1+r suppose on
investment of Rs 100 the return is 10% per year than 100/1.1= Rs 90.90. In second year if
extended the formula would be 100/ (1.1)². In this case first year would bring no cash flow as
zero coupon instruments the payment is done on cumulative basis.
For extended period of coupon bearing instruments the formula would be PV=∑ Ct/ (1+rt) t. For
example at the end of first year Rs 100 would fetch Rs 110 at the same rate in the 2nd year.
The sum of all corresponding years would get you the PV for the period under review.
Term structure of interest rate is an important element in the decision making under financial
management which is the series of interest rate prevailing in a market subject to different time
horizons. This develops yield curve in the market that can be flat, humped, inverted or steep.
Valuing present value of Perpetuities and Annuities
Perpetuities: - The formula is Return=Cash flow/present value or r=C/PV. Suppose a person
wants to endow a fund with cash flow of Rs 100000/ per year than according to this formula he
has to provide Rs 1,000,000/- with an interest rate of 10 i.e. = present value of perpetuity = C/r
= 100000/.10 = Rs 1,000,000. Suppose another benefactor wants to provide Rs 100,000/- in a
year with a growth of 4% on yearly basis. I.e. in a fashion that in the first year Rs 100,000/-
10
would be provided with 1.04 and so on. In this case the formula would be PV=C/r-g i.e.
100000/.10-.04. So accordingly he has to spare Rs 1,666,667.
Annuities: - The PV of an annuity is the difference between the values of two perpetuities i.e.
PV of perpetuity (first payment year) is = C/r whereas PV of perpetuity (first payment year t+1) is
C/r (1+r) t, hence PV of annuity from year 1 to year t = C (1/r-1/r(1+r)t). Suppose in case of our
benefactor to endow Rs 100,000/ for 20 years he would have to spare 100000 x (1/.10-1/.10
(1.10)20) = Rs 851,400
As you can see, the mathematics of this can be a little cumbersome especially when the time
involved gets larger. To make these calculations a little easier, there is another formula:
Total = Amount x {(1+r) ⁿ+1)-1/r} – amount, where the AMOUNT is the annual amount invested
each year, 'n' is the number of years and 'r' is the annual rate of the investment
However before we use the annuity formula, let's solve a short 3 year example the "long way".
First we need the compound interest formula which is: Total = Principal × (1 + Rate) years..
Now let's say the amount that we invest annually is PKR 2,000 per year and the interest rate is
8%.
The PKR 2,000 invested 3 years ago has become PKR 2, 000 * (1.08)3 = PKR 2,000 * 1.259712
= PKR2, 519.424 after 3 years.
The PKR 2,000 invested 2 years ago has become PKR 2,000 * (1.08)2 = PKR 2,000 * 1.1664 =
PKR 2,332.80 after 2 years.
The PKR 2,000 invested 1 year ago becomes PKR2, 000 * (1.08)1 = PKR 2, 000 * 1.08 = PKR
2, 160.00 after 1 year. Adding up all 3 yearly amounts, we obtain PKR 7, 012.22
By using the formula we also get the same amount i.e.
2,000 * { [(1 + .08) (3 + 1) -1] ÷ .08 } — 2,000
2,000 * { [1.36048896 -1] ÷ .08 } — 2,000
2,000 * {.36048896 ÷ .08} — 2,000
2,000 * {4.506112} — 2,000
9,012.224 -2,000
7,012.22
Simple and compound interest rate
The distinction between simple and compound interest rates is that when money is invested in
compound interest, each interest payment is reinvested to earn more interest in subsequent
periods. In contrast the opportunity to earn interest on interest is not provided by an investment
that pays only simple interest.
By looking in to the curve path of simple and compound interests it transpires that path of
compound interest payments remains steep whereas in case of simple interest rate it flattens in
the latter period. Accordingly discounting process also travels in straight line so in fact
discounting of any cash flow incorporates with compounding impact
Valuing present value of Bonds
Bonds are normally more than of one year tenor and are subject to periodical profit payments on
annual, semiannual or on quarterly basis. Their profit payments can be fixed or floating based
11
on some credible benchmark. To know about their PV one needs to discount the prospective
stream of its cash flows. On maturity the cash flow includes principal amount. The formula is
PV= ∑ Ct/ (1+r)t . In case of 3 years PIBs worth Rs 100,000/- with 10% return on semiannual
basis the formula would be =
5,000/1.10/2+5000/(1.10/2)2+5,000/(1.10/2)3+5,000/(1.10/2)4+5,000/(1.10/2)5+105,000/(1.10/2)6
Valuing Stocks
Cash payoffs on stock are in two forms i.e. (1) cash dividend and (2) capital gain or losses. The rate of
return on share thus is = expected return or market capitalization rate=r=Div1+P1 (expected price at the
year end) - P0 (current price)/P0 or 5+110-100/100=.15 = 15%.Correspondingly price can be calculated
as P0 = Div1+P1/1+r = 5+110/1.15 = 100.
Assumption:-All securities in an equivalent risk class are priced to offer the same expected return.
Going forward one can look in to future by using this formula:- P0=∑ Div1/(1+r)t + PH/(1+r)H.
Suppose in above case the dividend for the next year is 5.5 and the price is Rs 121 than for two
years forecast the today's price would be (5-0/1.15)+(5.5+121/(1.15)²)=100
Present price can also be known by using this formula P0 = Div1/r-g. In this case g is the
anticipated growth rate for company's, dividends, however g should be lesser than r. Why
because if g approaches r than stock price would become infinite. Alternatively the formula can
be used to obtain an estimate of market capitalization rate r from Div1, P0, and g. i.e.
r=Div1/P0+g.
However hard part is to get g because it also depends on pay out and plows back ratios. This
impacts return on equity and book equity per share. ROE can be calculated as EPS1/book
equity per share.
Dividend growth rate=g=Plow back ratio x ROE
Valuing present value of Stocks-Case of growth and Income Stocks
Income stocks are like perpetual bonds so its price can be calculated as
P0=Div1/r=EPS1/r=10.0/.10=100. In this case NPV per share comes out as =-10+1/.10=0.
However since it is assumed that increase in value caused by the extra dividends in later years
would once again make the market capitalization rate equals the earnings price ratio = r=
EPS1/P0=10/100=.10 or 10%. In general one can think of stock price as the capitalized value of
average earnings under a no growth policy plus present value of growth opportunities = P0 =
EPS1/r + PVGO. The EPR therefore = EPS1/P0= r (1- PVGO/P0). If PVGO is positive than r
has been underestimated and if PVGO is negative than r has been overestimated
Example: - Suppose a company is expected to pay Rs 5 as dividend and the dividend has to
increase by 10% a year indefinitely. The capitalization rate r is 15%. Further suppose EPS is Rs
8.3. Ratio of earnings to book equity is i.e. ROE= .25. Than first:P0=Div1/r-g= 5/.15-.10=Rs 100
Payout ratio= Div1/EPS1= 5.0/8.33= .6
This reflects that company is plowing back = 1-.6= .40
Growth rate= g = plowback ratio x ROE = .4 x .25 = .10
The capitalized value of company's EPS if it had no growth policy would be EPS1/r = 8.33/.15 =
Rs 55.56. However since share price is Rs 100 so Rs 44.44 is the amount for growth
opportunities
12
Another version of using DCF formula is to use free cash flows instead of Dividend which is =
revenue – cost – investment. Or P0 = ∑ (Free cash flow per share) t/ (1+r) t
NPV leads to better investment decisions
Analysis of proposed investment in a project
1.
2.
3.
4.
Forecast the cash flows generated by project X over its economic life.
Appropriate opportunity cost of the capital to be determined.
Use the opportunity cost of capital to discount the future cash flows. This would give PV.
Calculate the NPV.
Invest if NPV is greater than zero
Points to remember:Stock prices are equal to the PV of forecasted dividends
The discount rate is the opportunity cost of investing in the project rather than in the capital
market. The opportunity concept makes sense only if assets of equivalent risk are compared. In
general we should identify the financial assets with risks equivalent to the project, estimate the
expected rate of return on these assets and use this rate as opportunity cost.
13
Chapter 3
NPV leads to better investment decisions
Alternates to the NPV rule can be
1.
2.
3.
4.
Payback rule
Average return on book value rule
Internal rate of return rule
Profitability index rule
Pay back rule:-Companies require that the initial outlay on any project should be recoverable
within some specified period. The payback period of a project is found by counting the number
of years it takes before cumulative forecasted cash flows equal the initial investment.
Example
Project
C01
d stands for
discounted
C1
C2
C3
NPV at 10%
A
-2000
+1000
909.09 (d)
+1000
826.44 (d)
+5000
3492
3756.57 (d)
2
B
-2000
0
+2000
1652 (d)
+5000
3409
3756.57 (d)
2
C
-2000
+1000
909.09 (d)
+1000
826.44 (d)
+100000
75131 (d)
2
74867
Payback period
Pay back alternate:
Pay back assumptions:1. Appropriate cut of date.
2. Appropriate cut off dates can be ascertained only if you know the pattern of cash flows
that is not possible most of the time- so in result it is better to use NPV rule.
Some companies use discounted cash flows to arrive at payback period and some
companies do not. It is somewhat better than undiscounted payback.
Average rate of return on book value:Some companies judge an investment project by looking at its book rate of return, which is
derived by dividing the average forecasted profits of the project after depreciation and taxes by
the average book value of the investment. The ratio is than measured against the book rate of
return of some benchmark.
14
Computation of average book of return on an investment of 9000 is as follows
Y1
Y2
Y3
Rev
12000
10000
8000
Out of pocket 6000
cost
Cash flow
6000
5000
4000
5000
4000
depreciation
3000
3000
3000
Net income
3000
2000
1000
Average rate of return= average annual income/average annual investment =
2,000/4500= .44
Care: - Average annual investment has to account for depreciation i.e. average net book value
of investment= 4500
Y0
Y1
Y2
Y3
Book V of Inv
9000
9000
9000
9000
Accumu Dep
0
3000
6000
9000
6000
3000
0
Net book Value of 9000
investment
Average return on book value depends on average return on book investments and ignores
immediate receipts that have more value whereas payback valuation gives no weight to the
distant flows. In average return sometime current book return is used as a yardstick. In this case
companies with high rate of return on their existing business may be led to reject good projects
and companies with low rate of return may be led to accept bad ones.
Internal Rate of Return (IRR)
We know the rule that accept investment opportunities offering rates of return in excess of their
opportunity costs of capital.
In its application first we have to find out that when NPV becomes 0. The formula would remain
the same:NPV=C0+ C1/1+discount rate=0 or
Discount rate= C1/-C0 –1
So internal rate of return or discounted cash flow rate of return means that rate which makes
NPV = 0
For finding IRR we have to use trial and error method because it is directly related with NPV. If
IRR is greater than the opportunity cost of the capital than it results in to positive NPV.
Example- Suppose we have cash flows of - 4000, +2000 and +4000 as C0, C1 and C2. In case
we use 0 as discount rate than the result would be:-
15
NPV=-4000 + 2000/1.0 + 4000/ (1.0)²= +2000
In case we use the discount rate as 50% than the result would be:NPV = -4000 + 2000/1.50 + 4000/ (1.50)²= - 889
So for getting zero the discount rate should be above 0 but below 50.
i.e. NPV = -4000 + 2000/1.28 + 4000/ (1.28)² = 0
Normally firms calculate IRR thorough computerized programmed systems or plotting it with
NPV on vertical and discount rate in % on vertical
However there are some pitfalls in using IRR. They are:1. It does not account for the fact that money used as investment in form of lending or
borrowing should have different rate of return as normally borrowing is done by trying to use
cheaper rate whereas in case of lending one tries to use higher rate.
2. One project can have different IRRs depending on its variable cash flows. Even in some
cases no IRR is required since on all rates their NPV = 0. Example:- incase of cash flows of
+1000 ( CO), -3000 (C1), +2500 (C3) with discount rate at 10%
3. In mutually exclusive projects like one project is handled manually and one is computerized
the IRR can be misleading. In this one project with less NPV can have higher IRR whereas
other project with less IRR can have better NPV? Here the decision would rests on
incremental expenditure.
4. It does not account for the term structure of the interest rate. Normally short term rates are
different from long term. So in this case for C1, C2, C3 and so forth different IRR would be
required and for reaching upon overall IRR weighted average of these rates would be
required to be computed
Profitability Index
Another alternate can be to use profitability index or benefit cost ratio. It is the present value of
the future cash flows divided by the initial investment.
•
•
Profitability index = NPV/- C0
The rule tells that all projects with an index greater than 1 may be accepted.
However in this case the results can be misleading in case of mutually exclusive investments.
In ultimate in this case as well other, the greater the NPV in rule form remains decisive
Making investment decisions with NPV rule
The task is three fold in making decisions under NPV rule
1. One is to know about what should be discounted.
2. The second one is to explain how the NPV rule should be used when there are project
interactions.
3. The third task is to develop procedures for coping with capital rationing or other
situations in which resources are strictly limited
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Chapter 4
Cash flows/ Financial Statements
In estimating NPV
1. Only cash flows are relevant
2. Cash flows have to be estimated on incremental basis.
3. One has to be consistent in treatment of inflation.
Cash flows means Rupees in and rupees out and they are recorded only when they occur.
Further they are required to be estimated on after tax basis.
Estimating cash flows on incremental basis means that not averages but incremental pay offs to
be accounted for by including all incidental effects. Further working capital requirements are to
be ascertained, sunk costs to be forgotten, opportunity costs to be accounted for and one
should be beware of allocated overhead costs. Further inflation needs to be considered on
consistent manner to arrive at nominal or real cash flows. If this consistency prevails than
nominal or real cash flows would bring the same results. However to forecast nominal cash
flows nominal rates are used whereas for forecasting real cash flows real rates are used
Depreciation is a non cash expense but it provides a shield from taxes = Tax shield =
depreciation x tax rate. In common, straight line depreciation is used for stock holders and
accelerated for the tax books. Straight line depreciation means investment - salvage value
depreciated in life period.
Project interactions are involved in deciding capital expenditures i.e. either or at choice. So it
depends on timings and on capital rationing that can be soft or hard. In this case projects can be
ranked by their profitability index and top most are selected until funds are exhausted. The
solution can also be found through linear or integer programming. Hard and soft rationing
depends on free or less access to the capital market
Financial Statements
Financial statements are pieces of paper with numbers written on them reflecting real assets
and liabilities that lie under these numbers.
Financial statement analysis involves (1) comparing the firm’s performance with other firms in
the same industry (2) Evaluating trends in the firm’s financial position over time.
However the real worth of the financial statements lies that they can be used to help future
earnings, dividends and firms cash flows.
Financial statements are most important for stockholders.
They comprise of:•
•
•
•
17
Balance sheet
Income statement
Statement of retained earnings.
Statement of cash flows.
Balance Sheet- Some tips
The common equity is a residual i.e. assets-liabilities-preferred stock= Common stock
The common equity is comprised of common equity + retained earnings.
Inventory accounting is mostly done under rising prices through FIFO (first in first out) and in
declining prices through LIFO (last in first out to show better profits).
Depreciation is some time charged less or at rapid basis for tax purposes.
The balance sheet is a snapshot at a point in time.
Income Statement-some tips
The income statements are reports on operation over a period of time
• Net sales
(-) Operating costs excluding depreciation and amortization
• Earnings before interest, depreciation and amortization (EBITDA))
• Depreciation
• Amortization
(-) Depreciation and amortization
• Earnings before interest and taxes (EBIT or operating income)
(-) Less interest.
• Earnings before taxes (EBT)
(-) Taxes
• Net income before preferred dividends
(-) Preferred dividends
• Net income
•
Common dividends
• Addition to retained earnings.
The data required in income statement can be explained as follows:•
•
•
•
•
Common stock price
Earnings per share (EPS) = Net income/common shares outstanding
Dividends per share (DPS) = Dividends paid to common stock holders/common shares
outstanding
Book value per share (BVPS)= Total common equity/common shares outstanding
Cash flow per share = Net income +Depreciation +Amortization/common shares
outstanding
Statement of Retained Earnings-Some tips
Changes in retained earnings between balance sheet dates are reported in a separate
statement
• Balance of retained earnings- date-year
• Add net income year
• Less dividends to common stock holders
• Balance of retained earnings-year
•
Firms primarily retain them to expand their business and they do not represent cash and
available for payments.
18
Statement of Cash flows-some tips
Statement of cash flows reports the effect of operating, investing, financing activities on cash
flows over an accounting period. Net cash flows differ from accounting profit because some of
the revenues and expenses reflected in the statement may not have been received or paid in
cash during the period.
Operating activities can be as follows
• Net income
Adjustments
• Non cash adjustments
(+) Depreciation
Due to changes in working capital
(-) Increase in accounts receivable
(-) Increase in inventories
(+) Increase in accounts payable
(+)Increase in accruals
• Net cash provided by operating activities
Long term investing activities
(-) Cash used to acquire fixed assets
 Financing activities
(+) Sale of short term investments
(+) Increase in notes payable
(+) Increase in bonds outstanding
(-) Payments of dividends
• Net cash provided by financing activities
Summary
•
•
•
19
Net change in cash
Cash at beginning of year
Cash at end of year
Chapter 5
Managerial Finance
Data required for managerial decisions
Operating current assets: - They are the current assets that are used to support operations
such as cash, inventory and accounts receivable.
Operating current liabilities:- They are the current liabilities that occur as a natural
consequence of operations such as accounts payable and accruals.
Net operating working capital: - It is the difference between operating current assets and
operating current liabilities.
Operating long term assets: - They are the long term assets used to support operation such
as net plant and equipment.
Total operating assets or capital: - It is the sum of net operating working capital and operating
long term assets. It is the capital required to run the business.
NOPAT: - It is the net operating profit after taxes. It excludes debt and any investment in non
operating investments.
Operating cash flow: - It is the difference between cash revenues and cash costs including
taxes on operating income. It is different from net cash flows as it does not recognize interest
income or interest expenses
Free cash Flow: - It is the amount of cash flow remaining after a company makes the assets
investment necessary to support operations.
Market value added (MVA):- It represents the difference between the total market value of a
firm and the total amount of investor supplied capital. If debt value and preferred stocks are
equal to their market value than MVA = difference between the market values of the firms
stocks and the amount of equity its stockholders have supplied.
Economic Value added EVA:- It is the difference between after tax operating profit and the
cost of capital including the cost of capital
Financial Ratios
They are the numbers that are designed to help evaluate financial statements.
Liquidity Ratios: - They reflect ability to meet short term obligations. A liquid asset is one that
trades in an active market and can be quickly converted to cash at the going market price.
Liquidity ratios are meant to throw light on the capability of a firm in this respect.

Current ratio = Current assets/current liabilities= time
Current assets include cash, marketable securities, accounts receivables and
inventories.
Current liabilities include accounts payable, short term notes payable, current maturities
of long term debt, accrued taxes and other accrued expenses (principally) wages

Quick or acid test ratios:- It is calculated by deducting inventories from current assets
since they are typically less liquid = Current assets-inventories/Current liabilities = times
Asset management ratios: - They measures how effectively the firm is managing its assets
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For evaluating inventories its turnover ratio is used i.e. Inventory turnover ratio =
Sales/inventories = times
For evaluating receivables, disposable outstanding (DSO) is used. DSO is also called averaging
collection period so it is mentioned in days = Receivables/Average sale*days
= Receivables/annual sale/360 = days
For evaluating fixed assets
Fixed turnover ratio is used. It measures how effectively the firm uses its plants and
equipment = Sales/net fixed assets = times
The total asset turnover ratio measures the turnover of all firms assets = Sales/Total assets =
times
To evaluate firm’s use of debt financing following ratios are used
Total Debt to total assets are used to measures the funds provided by the creditors = Total
Debt/Total assets = %
For measuring ability to pay interest Times interest earned (TIE) ratio is used =
EBIT/interest charges = times
To judge firms ability to reduce its debt or to accounts for depreciation and amortization
impacts EBITDA coverage ratio is used = EBITDA+Lease payments/Interest + principal
payments +Lease payments = times
Profitability ratios:- profitability is the net result of a number of policies and decisions. They
show the combined results of liquidity, asset management and debt on operating results.
Profit margin on sales ratio shows the profit on sales = net income available to common stock
holders/sales= times
Basic Earning power (BEP) ratio shows the raw earning power of the firms assets, before the
influence of the taxes and different degrees of financial leveraging = EBIT/ Total assets = times
Return on Total assets (ROA) measures the return on total assets = Net income available to
common stock holders/ total assets = times
Return on common equity (ROE):- It measures the return on common equity = Net income
available to common stock holders / common equity
Market value ratios relate the firms stock price to its earnings, cash flow and book value per
share. These ratios give management an indication of what investors think of the company’s
past and future prospects
Price earning ratio (P/E) multiple show how much investors are willing to pay against reported
profit = price per share/Earnings per share = times
Price/ cash flow ratio: - It measures that how much stock price is tied more closely to cash
flows = Price per share/ cash flow per share = times
Market Book ratio:- This measures the difference between equity having high return with those
having less return. In this first book value /share is calculated = common equity/shares
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outstanding. Than Market/Book Ratio is calculated = Market price per share/ Book value per
share
22
Chapter 6
Financial Markets
In economics, a financial market is a mechanism that allows people to buy and sell (trade) financial
securities (such as stocks and bonds), commodities (such as precious metals or agricultural goods), and
other fungible items of value at low transaction costs and at prices that reflect the efficient-market
hypothesis.
Financial markets have evolved significantly over several hundred years and are undergoing constant
innovation to improve liquidity.
It must be remembered that the world financial system is dominated by bank based system rather than
market based financial systems. US and UK are dominated by market based systems whereas Japan and
EU are dominated by bank based systems. Other than these, their exists family conglomerates (groups) as
well. Each has their strengths and weaknesses. Banking system suits for well established corporate.
Market based system demands transparency and allows free access to market transactions. Finally
conglomerates come in where businesses are at start or they are short of funds.
A business (also called a company, enterprise or firm) is a legally recognized organization designed to
provide goods and/or services to consumers. Businesses are predominant in capitalist economies, most
being privately owned and formed to earn profit that will increase the wealth of its owners and grow the
business itself. The owners and operators of a business have as one of their main objectives the receipt or
generation of a financial return in exchange for work and acceptance of risk. Notable exceptions include
cooperative enterprises and state-owned enterprises. Businesses can also be formed not-for-profit or be
state-owned.
Although forms of business ownership vary by jurisdiction, there are several common forms:
Sole proprietorship: A sole proprietorship is a business owned by one person. The owner may operate
on his or her own or may employ others. The owner of the business has personal liability of the debts
incurred by the business.
Partnership: A partnership is a form of business in which two or more people operate for the common
goal which is often making profit. In most forms of partnerships, each partner has personal liability of the
debts incurred by the business. There are three typical classifications of partnerships: general
partnerships, limited partnerships, and limited liability partnerships.
Corporation: A corporation is either a limited or unlimited liability entity that has a separate legal
personality from its members. A corporation can be organized for-profit or not-for-profit. A corporation is
owned by multiple shareholders and is overseen by a board of directors, which hires the business's
managerial staff. In addition to privately-owned corporate models, there are state-owned corporate
models.
Cooperative: Often referred to as a "co-op", a cooperative is a limited liability entity that can organize
for-profit or not-for-profit. A cooperative differs from a corporation in that it has members, as opposed to
shareholders, who share decision-making authority. Cooperatives are typically classified as either
consumer cooperatives or worker cooperatives. Cooperatives are fundamental to the ideology of
economic democracy.
Both general markets (where many commodities are traded) and specialized markets (where only one
commodity is traded) exist. Markets work by placing many interested buyers and sellers in one "place",
thus making it easier for them to find each other. An economy which relies primarily on interactions
between buyers and sellers to allocate resources is known as a market economy in contrast either to a
command economy or to a non-market economy such as a gift economy.
In finance, financial markets facilitate:
23
•
•
•
•
The procurement of short term funds and management of interest rate (Money Market)
The raising of capital (in the capital markets)
The transfer of risk (in the derivatives markets)
International trade (in the currency markets)
They are typically used to match those who want capital to those who have it.
Typically a borrower issues a receipt to the lender promising to pay back the capital. These receipts are
securities which may be freely bought or sold. In return for lending money to the borrower, the lender
will expect some compensation in the form of interest or dividends.
In mathematical finance, the concept of a financial market is defined in terms of a continuous-time
Brownian motion stochastic process.
Types of financial markets
The financial markets can be divided into different subtypes:
•
•
•
•
•
•
•
Capital markets which consist of:
• Stock markets, which provide financing through the issuance of shares or common stock,
and enable the subsequent trading thereof.
• Bond markets, which provide financing through the issuance of bonds, and enable the
subsequent trading thereof.
Commodity markets, which facilitate the trading of commodities.
Money markets, which provide short term debt financing and investment.
Derivatives markets, which provide instruments for the management of financial risk.
Futures markets, which provide standardized forward contracts for trading products at some
future date; see also forward market.
Insurance markets, which facilitate the redistribution of various risks
Foreign exchange markets, which facilitate the trading of foreign exchange.
The capital and Money markets consist of primary markets and secondary markets. Newly formed
(issued) securities are bought or sold in primary markets. Secondary markets allow investors to sell
securities that they hold or buy existing securities
Raising capital or Capital formation
To understand financial markets, let us look at what they are used for, i.e. what is their purpose?
Without financial markets, borrowers would have difficulty finding lenders themselves. Intermediaries
such as banks help in this process. Banks take deposits from those who have money to save. They can
then lend money from this pool of deposited money to those who seek to borrow. Banks popularly lend
money in the form of loans and mortgages.
More complex transactions than a simple bank deposit require markets where lenders and their agents can
meet borrowers and their agents, and where existing borrowing or lending commitments can be sold on to
other parties. A good example of a financial market is a stock exchange. A company can raise money by
selling shares to investors and its existing shares can be bought or sold.
Relationship
Lenders
•
24
Individuals
•
•
•
•
•
•
•
•
•
Many individuals are not aware that they are lenders, but almost everybody does lend money in
many ways. A person lends money when he or she:
puts money in a savings account at a bank;
contributes to a pension plan;
pays premiums to an insurance company;
invests in government bonds; or
Invests in company shares.
Companies
Companies tend to be borrowers of capital. When companies have surplus cash that is not needed
for a short period of time, they may seek to make money from their cash surplus by lending it via
short term markets called money markets.
There are a few companies that have very strong cash flows. These companies tend to be lenders
rather than borrowers. Such companies may decide to return cash to lenders (e.g. via a share
buyback.) Alternatively, they may seek to make more money on their cash by lending it (e.g.
investing in bonds and stocks.)
Borrowers
• Individuals borrow money via bankers' loans for short term needs or longer term mortgages to
help finance a house purchase.
• Companies borrow money to aid short term or long term cash flows. They also borrow to fund
modernization or future business expansion.
• Governments often find their spending requirements exceed their tax revenues. To make up this
difference, they need to borrow. Governments also borrow on behalf of nationalized industries,
municipalities, local authorities and other public sector bodies. In the UK, the total borrowing
requirement is often referred to as the Public sector net cash requirement (PSNCR).
• Governments borrow by issuing bonds. In the UK, the government also borrows from individuals
by offering bank accounts and Premium Bonds. Government debt seems to be permanent. Indeed
the debt seemingly expands rather than being paid off. One strategy used by governments to
reduce the value of the debt is to influence inflation.
• Municipalities and local authorities may borrow in their own name as well as receiving funding
from national governments. In the UK, this would cover an authority like Hampshire County
Council.
• Public Corporations typically include nationalized industries. These may include the postal
services, railway companies and utility companies.
• Many borrowers have difficulty raising money locally. They need to borrow internationally with
the aid of Foreign exchange markets.
•
Derivative products
During the 1980s and 1990s, a major growth sector in financial markets is the trade in so called
derivative products, or derivatives for short.
In the financial markets, stock prices, bond prices, currency rates, interest rates and dividends go up and
down, creating risk. Derivative products are financial products which are used to control risk or
paradoxically exploit risk. It is also called financial economics.
Currency markets
Seemingly, the most obvious buyers and sellers of currency are importers and exporters of goods. While
this may have been true in the distant past, when international trade created the demand for currency
markets, importers and exporters now represent only 1/32 of foreign exchange dealing, according to the
Bank for International Settlements.
25
The picture of foreign currency transactions today shows following players involved in the businesss:
•
•
•
•
•
Banks/Institutions
Speculators
Government spending (for example, military bases abroad)
Importers/Exporters
Tourists
Analysis of Financial markets
Much effort has gone into the study of financial markets and how prices vary with time. Charles Dow,
one of the founders of Dow Jones & Company and The Wall Street Journal, enunciated a set of ideas on
the subject which are now called Dow Theory. This is the basis of the so-called technical analysis method
of attempting to predict future changes. One of the tenets of "technical analysis" is that market trends give
an indication of the future, at least in the short term. The claims of the technical analysts are disputed by
many academics, who claim that the evidence points rather to the random walk hypothesis, which states
that the next change is not correlated to the last change.
The scale of changes in price over some unit of time is called the volatility. It was discovered by Benoît
Mandelbrot. The scale of change, or volatility, depends on the length of the time unit to a power a bit
more than 1/2. Large changes up or down are more likely than what one would calculate using a Gaussian
distribution with an estimated standard deviation.
A new area of concern is the proper analysis of international market effects. As connected as today's
global financial markets are, it is important to realize the there are both benefits and consequences to a
global financial network. As new opportunities appear due to integration, so do the possibilities of
contagion. This presents unique issues when attempting to analyze markets, as a problem can ripple
through the entire connected global network very quickly. For example, a bank failure in one country can
spread quickly to others, which proper analysis more difficult.
Money Market
In general terms, the money market is the market where liquid and short-term borrowing and lending take
place. The lending of funds in this market constitutes short-term investments. In a certain sense all bank
notes, current accounts, cheque accounts, etc. belong to the money market.
In financial market terms, the money market exists for the purpose of issuing and trading of short-term
instruments, that is, instruments where the term remaining from the date when trading takes place to the
date of redemption of the loan represented by die instrument (commonly referred to as the "term to
maturity"), is of a short-term nature. In theory, this term for classification as a money market instrument
is given as one year. In practice, however in some countries instruments with a term to maturity of three
years or less are normally classified as money market instruments although this is not a hard and fast rule.
Money market instruments are not traded through an exchange, but by means of informal telephone
trading and OTC (over the counter) trading. The money market is probably the most informal market in
Pakistan and does not use screen or electronic trading at this stage. E Bond trading recently introduced
may change the system in the time to come Physical trading documents and settlement procedures are
still used in this market.
The rates at which these instruments are issued and traded are quoted by the financial institutions in form
of KIBOR/PKRV via Reuters and can be seen on a computer screen which is linked to one of the
participating systems.
26
Institutions involved in MM transactions
There are quite a few active institutions in the market, and it probably has the most active participants of
all the financial markets. Individuals form an important and integral part of the market through cash
income and spending, investments and borrowings at banks and funds (e.g. unit trusts, pension funds,
etc.) and other short-term funds, which they invest and borrow.
In case of Pakistan the main players in the market are banks and primary Dealers appointed by the SBP to
acquire T-bill/PIB/Sukuk through auctions
The government is involved in the market through the MOF and the SBP. They interact with other
players in the market such as the commercial banks, the merchant banks, the funds and corporate
companies. Other financial institutions such as insurers, money market trusts, micro-lenders, etc. all play
a part to keep the money market vibrant and liquid.
Instruments
There are basically two types of instruments issued and traded in the money market, namely:
•
•
•
•
Instruments which pay interest on the amount invested, where the interest is normally paid to the
holder of the instrument (the lender), together with the redemption amount at redemption date.
Interim interest payments may be made in certain cases. These instruments are called interest
instruments. Instruments in this category include:
Negotiable certificates of deposit (NCDs)
Short-term government stock
Interest rate instruments issued by the private sector, with terms to maturity of three to eight
years.
Instruments that do not pay interest on the amount invested but are issued at a discount on the
nominal value (the redemption amount). These instruments are called discount instruments.
Instruments in this category include:
• Bankers' acceptances (BAs)
• Treasury bills (TBs)
• Commercial paper
• Negotiable certificates of deposit (NCDs)
A negotiable certificate of deposit is a certificate issued by a bank for a deposit made at the bank. This
deposit attracts a fixed rate of interest, which is normally payable to the holder of the instrument together
with the nominal amount invested, at redemption date. NCDs are bearer documents which mean that the
name of the owner (holder or depositor) does not appear on the document. The bearer or holder of the
document will receive the maturity value (the amount deposited plus interest) at maturity date.
Government stock and other short-term interest rate instruments
Government stock and other private sector instruments are normally issued for long-term periods with
more than one interest payment before redemption.
Further where the term to redemption of a government stock or other interest rate instrument has moved
into the money market category, and there is just one interest payment left, which falls on the same date
as the redemption payment, the same falls in the money market category.
A bankers' acceptance (BA) was invented to suit the needs of a party requiring temporary finance to
facilitate the trading of specific goods. The party needing finance would approach investors for this
temporary finance. The investors or lenders would then lend a certain amount to the borrower in
27
exchange for a document stating that the debt would be paid back on a certain date in the short-term
future. For this arrangement to be attractive to the lender, the amount paid back by the borrower (called
the nominal amount) would have to be more than the amount advanced by the lender. The difference
between the amount advanced and the amount paid back (the nominal amount) is known as the discount
on the nominal amount. The two parties would normally be brought together by a bank.
The redemption of the loan would have to be guaranteed by a bank, called the acceptance by the bank
making the arrangement or named as "bankers' acceptance".
The holder of the document i.e. BA may, at the redemption date approach the bank who will pay the
nominal amount to the holder. The bank will then claim the nominal amount from the borrower.
A bank acceptance can, in formal terms, be described as an unconditional order in writing
•
•
•
•
addressed and signed by a drawer (the lender)
to a bank which signs the document and becomes the acceptor
promising to pay a certain amount of money at a fixed date in the future
To the bearer or holder (the borrower) of the document (the acceptance).
Treasury bills
The government issues treasury bills .They are discount instruments issued for the short term, similar to
BAs. The issue and redemption of these instruments are handled by the SBP as depository on behalf of
the government. Treasury bills are issued through auction held on fortnightly basis in 3, 6 and 12 month
tenors to the appointed primary dealers who further distribute them to the end investors. The bearer or
holder of the instrument may present it for payment of the nominal amount at redemption date. SBP
would pay this amount into the holder's Subsidiary General Ledger account maintained with a bank on the
redemption date.
Tenders are submitted by parties in percentage form to two decimals at discount to Rs 100 treated as par
value. The auctions are held on at mutipriced basis i.e. bidders are due to get the amount at rate quoted by
them on acceptance from SBP.
Commercial paper and other discount instruments
Commercial paper refers to short-term unsecured promissory notes normally issued by the corporate
companies with a high credit rating. These instruments are also issued on a discount basis such as BAs.
Because they are unsecured, the risk involved will be higher than that of BAs, and therefore the issuing
institution must be financially strong and sound. Because of the risk attached to these instruments they
would normally be issued and traded at a higher discount than the prevailing BA rate. In Pakistan they
can be issued in tenors of 3, 6 and 9 months
Finance can be obtained by making use of various alternative kinds of discount instruments. Other
discount instruments that have been used in the international market are secured promissory notes and
asset backed commercial papers.
Segregation of Money Market in Pakistan
Money market in Pakistan can be segregated in to clean/call transaction or Repo transactions or
transactions done on outright basis
Call transactions refer to transactions within banking institutions without using any collateral.
28
Clean transactions are placement of deposits with non bank financial institutions like investment banks.
Repo is a collateralized transaction for raising of funds for a short period.
Outright transaction is sale and purchase of government securities or any other debt securities in the
market.
For pricing these transactions KIBOR rates and PKRV rates appearing on Reuters on daily basis are used.
KIBOR are the rates quoted by the banks against call transactions. The tenors of KIBOR are one week to
3 years.
PKRV rates are revaluations rates used in the market to price Repo or outright transaction. These rates
are quoted by the brokerage firms.
Capital market
It is a market for securities (debt or equity), where business enterprises (companies) and governments can
raise long-term funds. It is defined as a market in which money is provided for periods longer than a year,
as the raising of short-term funds takes place on other markets (e.g., the money market). The capital
market includes the stock market (equity securities) and the bond market (debt). Financial regulators, such
as the UK's Financial Services Authority (FSA) or the U.S. Securities and Exchange Commission (SEC),
oversee the capital markets in their designated jurisdictions to ensure that investors are protected against
fraud, among other duties. In Pakistan SECP is responsible to regulate this market
Capital markets as well Money Market may be classified as primary markets and secondary markets. In
primary markets, new stock or bond issues are sold to investors via a mechanism known as underwriting.
In the secondary markets, existing securities are sold and bought among investors or traders, usually on a
securities exchange, over-the-counter, or elsewhere.
The primary market consists of two areas . One is equity market that deals with new equity issues by
issuers and investors in such securities. Equity issues are made by the companies incorporated under the
Companies Act.
The primary debt market is the market for long term debt securities. Investment bankers play a key role
in issuance of these securities on behalf of corporate or non bank or banking financial institutions.
In case of government securities SBP is responsible to issue these securities through auction to the
primary dealers appointed by the SBP. Banks/Investment bank or a brokerage house can be the primary
dealer for the government securities.
NSS is another government institution to issue debt securities in scrip forms but they are not tradable.
Hence they are not considered part of capital market in true sense.
The government or corporate securities mostly exist in scrip or non scrip form. For non scrip form CDC is
depository for corporate securities whereas in case of government securities, SBP is the depository
Structure of Primary Market consists of primary issues, right issues and private placements, whereas
investors can be institutional, wholesale and retail. Issuers can be Government, companies other statutory
bodies and corporations. Instruments can be equity, preferred share, debt and convertibles. Intermediaries
can be Merchant bankers, underwriter and brokers.
Issuers can be government/ corporate/Public sector enterprises/Non bank or banking financial
institutions.
29
Investors can be government/banks/institutional/wholesale investor or retail investor.
Investors can further be segregated in to local or foreign investors. In Pakistan foreign investors are
allowed to invest in equity or debt securities through SCRA maintained on their behalf by any
commercial bank
Primary market intermediaries are commercial banks/ investment banks and brokers who play their
role in bringing the issues to the primary market investors.
Other intermediary can be registrar who performs the function of back office to an issue by providing
necessary infrastructure and automated processing capability.
Banks to an issue performs the function in providing remittance facilities to applicants in an issue
through their collecting branches.
Other support services can be stationery printers, advertisement agencies the press and financial
analysts.
Equity
Funds in capital market are raised through equity which is the residual claim or interest of the most
junior class of investors in an asset, after all liabilities are paid. If valuations placed on assets do not
exceed liabilities, negative equity exists. In an accounting context, Shareholders' equity (or stockholders'
equity, shareholders' funds, shareholders' capital or similar terms) represents the remaining interest in
assets of a company, spread among individual shareholders of common or preferred stock.
The common stock or capital stock of a business entity represents the original capital paid or invested
into the business by its founders. It serves as a security for the creditors of a business since it cannot be
withdrawn to the detriment of the creditors. Stock is distinct from the property and the assets of a business
which may fluctuate in quantity and value.
Preferred stock, also called preferred shares, preference shares, or simply preferred, is a special
equity security that resembles properties of both equity and a debt instrument and is generally considered
a hybrid instrument. Preferred are senior (i.e. higher ranking) to common stock, but are subordinate to
bonds.
Preferred stock usually carries no voting rights, but may carry priority over common stock in the payment
of dividends and upon liquidation. Preferred stock may carry a dividend that is paid out prior to any
dividends being paid to common stock holders.
Capital market in Pakistan is comprised of three stock exchanges and is regulated by the SECP.
Equity issuance can take place in the following forms:•
Initial public offers
•
Right issues
•
Follow on public issues
•
Depository Receipt issue
30
Debt Market/Fixed Income market
Debt is that which is owed; usually referencing assets owed, but the term can also cover moral obligations
and other interactions not requiring money. In the case of assets, debt is a mean of using future purchasing
power in the present before a summation has been earned. Some companies and corporations use debt as a
part of their overall corporate finance strategy. In Pakistan the main instruments in this regard are TFCs
and Pakistan Investment Bonds and Sukuk issued by the GOP
31
Chapter 7
Risk and Opportunities
Risk refers to the possibility that you will lose money (both principal and any earnings) or fail to make
money on an investment.
Every type of investment involves risk.
Investment objectives and its holdings are influential factors in determining how risky a fund is and how
you are managing your risk.
Call Risk. The possibility that falling interest rates will cause a bond issuer to redeem—or call—its highyielding bond before the bond's maturity date.
Country Risk. The possibility that political events (a war, national elections), financial problems (rising
inflation, government default), or natural disasters (an earthquake, a poor harvest) will weaken a country's
economy and cause investments in that country to decline.
Credit Risk. The possibility that a bond issuer will or counterparty would fail to repay interest and
principal in a timely manner. Also called default risk.
Currency Risk. The possibility that returns could be reduced for investing in foreign securities because
of a rise in the value of the foreign currencies. Also called exchange-rate risk.
Income Risk. The possibility that a fixed-income dividends will decline as a result of falling overall
interest rates.
Industry Risk or Unique Risk. The possibility that a group of stocks in a single industry will decline in
price due to developments in that industry.
Inflation Risk. The possibility that increases in the cost of living will reduce or eliminate a fund's real
inflation-adjusted returns.
Interest Rate Risk. The possibility that a fund will decline in value because of an increase in interest
rates.
Manager Risk. The possibility that an actively managed investment adviser will fail to execute the fund's
investment strategy effectively resulting in the failure of stated objectives.
Market Risk. The possibility that stocks or fixed income prices overall will decline over short or even
extended periods. Stock and bond markets tend to move in cycles, with periods when prices rise and other
periods when prices fall.
Principal Risk. The possibility that an investment will go down in value, or "lose money," from the
original or invested amount.
Major Requirements
32
1. The ability to derive above average returns for a given risk class.
2. The ability to completely diversify the portfolio to eliminate all unsystematic risk.
Requirement 1 can be achieved through better timing or superior security selection. For this one can
select high beta securities during a time when he thinks the market will perform well and low (or
negative) beta stocks at a time when he thinks the market will perform poorly.
Conversely one can try to select undervalued stocks or bonds for a given risk class.
Requirement 2 argues that one should be able to completely diversify away all unsystematic risk.
For this you have to measure the level of diversification by computing the correlation between the returns
of the portfolio and the market portfolio.
Risks on investments
They can arise on
1.
Portfolio of Government securities
2.
Portfolio of Government Bonds
3.
Corporate Debt Securitas
4.
Common stocks
Instrument
T-bill (6 month)
Gov. bonds (10 year)
Corporate Bonds (TFCs)
Common stocks
Return nominal %
12.44
14.00 (12.43)
16.00 (14.55)
18.00 ( 6.0)
Risk Premium
0
.2
.3
.5
Use of simple or compound average
Suppose a stock of Rs 100 has a equal chance of going Rs 90, Rs 110 or Rs 130 at the end of year. This
would draw average return of -10%, 10% or 30%’
By simple arithmetic average the return would be -10+10+30/3=10%
By average compound annual return the position would be (.9x1.1x1.3) is to power1/3 =.088 or 8.8%.
This would give a wrong picture.
So always use arithmetic average in evaluation of returns.
The variance is a measure of statistical dispersion, averaging the squares of the deviations of its possible
values from its expected value (mean). Whereas the mean is a way to describe the location of a
distribution, the variance is a way to capture its scale or degree of being spread out. The unit of variance
is the square of the unit of the original variable. The positive square root of the variance, called the
standard deviation, has the same units as the original variable and can be easier to interpret for this reason.
If a random variable X has expected value (mean) μ = E(X), then the variance Var (X) of X is given by:
Var (x) = E ( (x-µ)² ) or variance (rm (actual value)= E (rm-r expected)²
Covariance is a measure of how much two variables change together. (Variance is a special case of the
covariance when the two variables are identical.)
33
If two variables tend to vary together (that is, when one of them is above its expected value, then the other
variable tends to be above its expected value too), then the covariance between the two variables will be
positive. On the other hand, if one of them tends to be above its expected value when the other variable is
below its expected value, then the covariance between the two variables will be negative.
The covariance between two real-valued random variables X and Y, with expected values is defined as
Cov x, y = E (X-µ) (Y-µ)
Understanding variance and Standard Deviation
Suppose you invest Rs 100 and use two coins tossing for evaluating returns. For each head you get your
money back plus 20%. For each tail you get your money back less 10% on tossing you have following
outcomes.
Head + Head = 40%
Head + Tail = 10%
Head + Tail=10%
Tail + Tail = -20%
There is a chance of ¼ i.e. .25% to make 40%, 2/4 i.e. .50% to make 10% and ¼ i.e. .25 to lose 20%.
Expected return (.25x40) + (.5 x10) + (.25x-20) =10%
% rate of return
40
+10
-20
Deviation
from Squared Deviation
expected return
+30
900
0
0
probability
-30
.25
Variance =
St dv =
900
.25
.5
Probability
squared deviation
225
0
225
450
√450 =
21
In statistics, correlation (often measured as a correlation coefficient, ρ) indicates the strength and
direction of a linear relationship between two random variables. In general statistical usage, correlation
or co-relation refers to the departure of two random variables from independence. In this broad sense
there are several coefficients, measuring the degree of correlation, adapted to the nature of the data.
Þ x,y = Cov (x,y)/ σ x σ y = E (x- µx) (y-µy)/ σ x σ y
One way to mitigate risk is to go for diversification by forming a portfolio.
Suppose you have invested in your portfolio 60% of NBP securities and 40% of PSO securities NBP
would give a return of 10% and PSO would give 15%. Expected return on portfolio would be (.60x10) +
(.40x15) =12% the σ of NBP is 18.2% and for PSO it is 27.3%.
Now to find expected σ of portfolio we have to go through the process of adding factors of co variance
and correlation co efficient.
For this we have to complete the box as in next slide. This would require variance on NBP by the square
of the proportion of investment and like variance of PSO in the same way. The covariance of these stocks
would be Þ 1 & 2 σ 1 σ 2. This we have assumed as moving positive.
NBP
PSO
NBP
X²1σ²1= (.6)² x (18.2)²
x1 x2 Þ 1&2 σ 1σ 2 = ( .6) x (.4) x
1 x (18.2) x (27.3)
34
PSO
x1 x2 Þ 1&2 σ 1σ 2= ( .6) x (.4) x X²2σ² = (.4)² x (27.3)²
1 x (18.2) x (27.3)
Portfolio variance =X²1σ²1 + X²2σ² + 2(X1 X2 Þ 12 σ 1σ 2) =
((.6)² x (18.2)²) + ((.4)² x (27.3)²) + 2 (( .6) x (.4) x 1 x (18.2) x (27.3)) = 477 or σ = √ 477 = 21.8
In above case we assumed correlation as perfect lockstep .If we assume it as .4 than the result would be =
18.3%
If correlation is assumed as negative (-1) than the St Dev = 0 that never happens.
In Portfolio management we have to determine portfolio and covariance of securities in a portfolio.
Suppose a portfolio is built up of N stocks than portfolio variance would be 1/N x average variance + (11/N) x average covariance.
Suppose N increases than the portfolio variance would steadily approach the average covariance. In case
average covariance is zero than all risks would be eliminated by holding a sufficient number of securities.
That never happens as stocks move together and are tied up to draw positive covariance which set the
limit to the benefits of diversification.
In finance, the beta (β) of a stock or portfolio is a number describing the relation of its returns with that of
the financial market as a whole.
An asset with a beta of 0 means that its price is not at all correlated with the market; that asset is
independent. A positive beta means that the asset generally follows the market. A negative beta shows
that the asset inversely follows the market; the asset generally decreases in value if the market goes up
and vice versa.
Correlations are evident between companies within the same industry, or even within the same asset class
(such as equities). This correlated risk, measured by Beta, creates almost all of the risk in a diversified
portfolio.
The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of
the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of
many risky assets, because it is correlated with the return of the other assets that are in the portfolio. Beta
can be estimated for individual companies using regression analysis against its own sector or a stock
market index.
To calculate a stock's beta you only need two sets of data:
Closing stock prices for the stock you're examining.
Closing prices for the index you're choosing as a proxy for the stock market.
Most of the time beta values are calculated using the month-end stock price for the security you're
examining and the month end closing price of the KSE Index .The formula for the beta can be written as:
Beta = Covariance (stock versus market returns) / Variance of the Stock Market
Alpha is a risk-adjusted measure of the so-called active return on an investment. It is the return in excess
of the compensation for the risk borne, and thus commonly used to assess active managers.
It reflects the movement of a security of an entity in relation to market movement. In an efficient market,
the expected value of the alpha coefficient equals the return of the risk free asset: E(αi) = rf.
35
What Does R-Squared Mean?
A statistical measure that represents the percentage of a fund or security's movements that can be
explained by movements in a benchmark index. For fixed-income securities, the benchmark is the T-bill.
For equities, the benchmark is the S&P 500. In other words R squared measures the proportion of the
total variance in the stocks returns that can be explained by market movements.
For example in case a R squared of an security is .25 than it transpires that one quarter of the risk on this
security is market risk and three quarter is of unique risk.
R-squared values range from 0 to 100. An R-squared of 100 means that all movements of a security are
completely explained by movements in the index. A high R-squared (between 85 and 100) indicates the
fund's performance patterns have been in line with the index. A fund with a low R-squared (70 or less)
doesn't act much like the index.
A higher R-squared value will indicate a more useful beta figure. For example, if a fund has an R-squared
value of close to 100 but has a beta below 1, it is most likely offering higher risk-adjusted returns. A low
R-squared means you should ignore the beta.
R squared is nothing but the square of correlation coefficient.
Asset Pricing Models
Objectives of all these endeavourer evolved around finding value or expected returns on any asset class.
First effort in this regard was made by Bacheller in 1900 . He recognized that past present, future events
can be discounted in security prices not exactly but their likelihood can be mathematically evaluated.
In the first half of 20th century Williams theory ruled by saying that investors should invest in assets that
bear maximum returns without accounting for the associated risks. He assumed that law of large numbers
would insure that actual yield to the portfolio would be the same as the expected yield.
It was 1953 when Markowitz challenged this notion and presented a meaningful measure of portfolio risk
i.e. variance of returns.
Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize
their portfolios, and how a risky asset should be priced. The basic concepts of the theory are Markowitz
diversification, the efficient frontier, capital asset pricing model, the alpha and beta coefficients, the
Capital Market Line and the Securities Market Line.
MPT models an asset's return as a random variable, and models a portfolio as a weighted combination of
assets so that the return of a portfolio is the weighted combination of the assets' returns. Moreover, a
portfolio's return is a random variable, and consequently has an expected value and a variance. Risk, in
this model, is the standard deviation of return.
Risk and return
The model assumes that investors are risk averse, meaning that given two assets that offer the same
expected return, investors will prefer the less risky one. Thus, an investor will take on increased risk only
if compensated by higher expected returns. Conversely, an investor who wants higher returns must accept
more risk. The exact trade-off will differ by investor based on individual risk aversion characteristics. The
implication is that a rational investor will not invest in a portfolio if a second portfolio exists with a more
favorable risk-return profile – i.e., if for that level of risk an alternative portfolio exists which has better
expected returns.
36
In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate
required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio,
given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to nondiversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β)
in the financial industry, as well as the expected return of the market and the expected return of a
theoretical risk-free asset.
The model was introduced by Jack Treynor (1961, 1962)William Sharpe (1964), John Lintner (1965) and
Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and
modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial
Prize in Economics for this contribution to the field of financial economics.
CAPM is a model for pricing an individual security or a portfolio. For individual securities, we made use
of the security market line (SML) and its relation to expected return and systematic risk (beta) to show
how the market must price individual securities in relation to their security risk class.
The CAPM is a model for pricing an individual security or a portfolio. For individual securities, we made
use of the security market line (SML) and its relation to expected return and systematic risk (beta) to
show how the market must price individual securities in relation to their security risk class. The SML
enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market.
Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the rewardto-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:
E (Ri)-Rf/Bi =E (Rm)-Rf or
E (Ri) = Rf + ßi (E (Rm)- Rf)
The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above
equation and solving for E(Ri), we obtain the Capital Asset Pricing Model (CAPM).
Arbitrage pricing theory (APT), in finance, is a general theory of asset pricing, that has become
influential in the pricing of stocks.
APT holds that the expected return of a financial asset can be modeled as a linear function of various
macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is
represented by a factor-specific beta coefficient. The model-derived rate of return will then be used to
price the asset correctly - the asset price should equal the expected end of period price discounted at the
rate implied by model. If the price diverges, arbitrage should bring it back into line.
Return = a + b1 (r factor1) + b2 (r factor2) + b3 (r factor3) +------+ noise. Here it is assumed that each
stocks return depends on specific macro economic factor whereas noise is the unique risk to the particular
company. The macro economic indicators can be identified like yield spread (Return on long government
bond – return on 30 days T-bill), interest rate (Change in T-bill rate), exchange rate (change in $/PKR
parity), Real GDP, (change in Real GDP forecasts)Real GNP (Change in real GNP forecasts),inflation
(Change in forecast of inflation) etc.
The theory was initiated by the economist Stephen Ross in 1976.
Three factor model of Fama shows that stocks of small firms and those with a high book into market
ratio have provided above average return. So it means that these factors are contributing more return as
well risk that have not been accounted for in CAPM. So obviously investor is justified in claiming higher
premium in these securities
R-rf = b market (market factor) + b size (r size factor) + b book to market factor (r book to market factor)
37
Identification of factors:Factors
Market factor
Size factor
Measured by
Return on market index – risk free rate
Return on small firm stocks – return on large firm
stocks
Return on high book to market ratio- Return on
low book to market ratio stocks
Book to Market factor
Jack L. Treynor was the first to provide investors with a composite measure of portfolio performance that
also included risk
He suggested that there were really two components of risk: the risk produced by fluctuations in the
market and the risk arising from the fluctuations of individual securities
Treynor introduced the concept of the security market line, which defines the relationship between
portfolio returns and market rates of returns, whereby the slope of the line measures the relative volatility
between the portfolio and the market.
The Treynor measure, also known as the reward to volatility ratio, can be easily defined as:
(Portfolio Return – Risk-Free Rate) / Beta
The numerator identifies the risk premium and the denominator corresponds with the risk of the
portfolio. The resulting value represents the portfolio's return per unit risk.
Suppose that the 10-year annual return for the KSE (market portfolio) is 10%, while the average
annual return on Treasury bills is 5%. Then assume three distinct portfolio managers with the
following 10-year results:
Managers
Manager A
Manager B
Manager C
Average Annual Return
10%
14%
15%
Beta
0.90
1.03
1.20
(Market) =
(.10-.05)/1 =
.05
(manager A) =
(.10-.05)/0.90 =
.056
(.14-.05)/1.03 =
(.15-.05)/1.20 =
.087
.083
(manager B) =
(manager C)
=
The higher the Treynor measure, the better the portfolio. If you had been evaluating the portfolio manager
(or portfolio) on performance alone, you may have inadvertently identified manager C as having yielded
the best results. However, when considering the risks that each manager took to attain their respective
returns, Manager B demonstrated the better outcome. In this case, all three managers performed better
than the aggregate market.
38
Because this measure only uses systematic risk, it assumes that the investor already has an adequately
diversified portfolio and, therefore, unsystematic risk (also known as diversifiable risk) is not considered.
As a result, this performance measure should really only be used by investors who hold diversified
portfolios
The Sharpe ratio is almost identical to the Treynor measure, except that the risk measure is the standard
deviation of the portfolio instead of considering only the systematic risk, as represented by beta.
Conceived by Bill Sharpe, this measure closely follows his work on the capital asset pricing model
(CAPM) and by extension uses total risk to compare portfolios to the capital market line.
The Sharpe ratio can be easily defined as:
(Portfolio Return – Risk-Free Rate) / Standard Deviation
Using the Treynor example from above, and assuming that the S&P 500 had a standard deviation of 18%
over a 10-year period, let's determine the Sharpe ratios for the following portfolio managers:
Manager
Manager X
Manager Y
Manager Z
(Market)
=
(manager X) =
(manager Y) =
(manager Z) =
Portfolio Return
14%
17%
19%
Standard Deviation
0.11
0.20
0.27
(.10-.05)/.18 =
.278
(.14-.05)/.11 =
(.17-.05)/.20 =
(.19-.05)/.27 =
.818
.600
.519
Like the previous performance measures discussed, the Jensen measure is also based on CAPM. Named
after its creator, Michael C. Jensen, the Jensen measure calculates the excess return that a portfolio
generates over its expected return. This measure is also known as alpha.
The Jensen ratio measures how much of the portfolio's rate of return is attributable to the manager's
ability to deliver above-average returns, adjusted for market risk.
The higher the ratio, the better the risk-adjusted returns. A portfolio with a consistently positive excess
return will have a positive alpha, while a portfolio with a consistently negative excess return will have a
negative alpha
The formula is broken down as follows:
Jensen's Alpha = Portfolio Return – Benchmark Portfolio Return
Where: Benchmark Return (CAPM) = Risk Free Rate of Return + Beta (Return of Market – RiskFree Rate of Return)
So, if we once again assume a risk-free rate of 5% and a market return of 10%, what is the alpha for the
following funds?
Manager
Manager D
Manager E
39
Average Annual Return
11%
15%
Beta
0.90
1.10
Manager F
15%
1.20
First, we calculate the portfolio's expected return:
ER(D) =
ER(E) =
ER(F) =
.05+0.90(.10-.05) =
.05+1.10(.10-.05) =
.05 + 1.20(.10-.05) =
.0950 or 9.5% return
.1050 or 10.50% return
.1100 or 11% return
Then, we calculate the portfolio's alpha by subtracting the expected return of the portfolio from the actual
return:
ER(D) =
ER(E) =
ER(F) =
11% - 9.5% =
15% - 10.5% =
15% - 11% =
2.5%
4.5%
4.0%
Which manager did best? Manager E did best because, although manager F had the same annual return, it
was expected that manager E would yield a lower return because the portfolio's beta was significantly
lower than that of portfolio F.
Sensitivity of Bond prices are measured through duration and convexity analysis. They are calculated on
the basis of relationship of prices and yields on a bond
The duration of a bond is calculated as = ( 1 x PV (C1))/V + (2 x PV (C2))/V + (3 X PV (C3))/V
……… =
Or it can be written down as (1+y/y) – {(1+y) + T (c-y)}/ C{ (1+y) – 1 }} + y
In this C= Coupon rate
T= number of coupon periods (yield to maturity)
Y = Bond yields per payment period
Example 10 % coupon Bond with 20 years paying capacity seminally would have 5 % semiannual coupon
& 40 payments. The result would be incase the yields to maturity is $% = 1.04/.04 – 1.04 + (.05-.04)/
.05{(1.04)is to power40 – 1 } +.04 = 19.74
Formula for yield to maturity is = 102 = ∑is to power 40 x 5/ (I +r) is to power t + 100/ (1+r) is to power t
Modified duration is just an addition to get that how much change in duration can take place against 1
bp change in prices. The higher the yields the lesser would be the duration.
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates.
There is an inverse relationship between convexity and sensitivity - in general, the higher the convexity,
the less sensitive the bond price is to interest rate shifts, the lower the convexity, the more sensitive it is.
Calculation of convexity
Duration is a linear measure or 1st derivative of how the price of a bond changes in response to interest
rate changes. As interest rates change, the price is not likely to change linearly, but instead it would
change over some curved function of interest rates. The more curved the price function of the bond is, the
more inaccurate duration is as a measure of the interest rate sensitivity.
40
Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest
rate, i.e. how the duration of a bond changes as the interest rate changes. Specifically, one assumes that
the interest rate is constant across the life of the bond and that changes in interest rates occur evenly.
Using these assumptions, duration can be formulated as the first derivative of the price function of the
bond with respect to the interest rate in question. Then the convexity would be the second derivative of
the price function with respect to the interest rate.
In actual markets the assumption of constant interest rates and even changes is not correct, and more
complex models are needed to actually price bonds. However, these simplifying assumptions allow one to
quickly and easily calculate factors which describe the sensitivity of the bond prices to interest rate
changes....
The price sensitivity to parallel changes in the term structure of interest rates is highest with a zerocoupon bond and lowest with an amortizing bond (where the payments are front-loaded). Although the
amortizing bond and the zero-coupon bond have different sensitivities at the same maturity, if their final
maturities differ so that they have identical bond durations they will have identical sensitivities. That is,
their prices will be affected equally by small, first-order, (and parallel) yield curve shifts. They will,
however start to change by different amounts with each further incremental parallel rate shift due to their
differing payment dates and amounts. For two bonds with same par value, same coupon and same
maturity convexity may differ depending on at what point on the price yield curve they are located.
Suppose both of them have at present the same price yield combination; also you have to take into
consideration the profile, rating etc of the issuers; suppose they are issued by different entities. Though
both the bonds have same p-y combination bond that may be located on relatively more elastic segment of
the p-y curve compared to bond II. This means if yield increases further, price of bond II may fall
drastically while price of bond I won’t change, i.e. bond II holder are expecting a price rise any moment
and so reluctant to sell it off, while bond I holders are expecting further price-fall and ready to dispose it.
This means bond II has better rating than bond I.
So the higher the rating or credibility of the issuer the less the convexity and the less the gain from riskreturn game or strategies; after all less convexity means less price-volatility or risk, less risk means less
return.
Algebraic definition
If the flat floating interest rate is r and the bond price is B and d is the duration then the convexity C is
defined as
C = 1/B x (d² (B (r))/d r²
41
Chapter 8
Interest Rate Management
To understand interest rate management we have to be clear about dynamics of fiscal and monetary
policies first.
In layman terms fiscal policy means management of government revenues and expenditures and monetary
policy means management of price stability so as to obtain GDP growth. Both are complementary to each
side, but opposed in their operational designs. Since price stability depends on quantum of money supply
that can be altered through government expenditure or taxation so in this respect they complement each
other. But operationally government is more concerned for making its debt financing cost effective that
has little correlation with the central bank operations in managing interest rate structures, so in that
respect they are opposed to each other.
General economics from its beginning has tried to find out the right amount of money for any economy.
Says law under classical economics deals with interest rates, employment, production and quantity theory.
Says famous maxim was that “supply creates its own demand”. It was supported by the interplay of
market forces as referred by Adam Smith as “invisible hand”. As an economic model it assumes that
under given technology, potential output of economy would be determined by the size of its labor force
available to work with the existing stock of capital goods. The production hence defines total supply of
goods and services that can be produced. Say argued that production would be at full employment since
spending would always be great enough to buy all the goods and services that can be produced.
Here than comes the function of investment and savings. Saving as per classical economics is the function
of interest rate, the higher the rate of interest the more would be saved. Investment on the other hand is
the function of rate obtained after employment of capital goods and that should be higher than the interest
rate i.e. borrowing cost. So in this respect low interest rate suits more for investment. This interaction
goes on towards equilibrium but in real world the same can not be realized.
Classical economics also relied upon quantity theory of money that says MV= PY, where M is the supply
of money, v is the velocity or rate of its turnover, P is the price level and Y is the level of real income.
The theory states that the impact of money is limited to the price level. At the heart of quantity theory lies
stable demand for money.
Than comes Keynes, that maintained that the level of production is determined by the aggregate demand
for goods and services. This differed from classical economists that regard production to occur at full
employment whereas Keynes thought that fluctuating prices and interest rate would push the economic
activity toward full employment especially in the short run. The Keynesian model focused on the
determinants of aggregate demand i.e. consumption, investment and government expenditure. Changes in
money supply alter the level of interest rate in the Keynes framework. In fact in this, three transmission
mechanism link monetary policy to GDP i.e. cost of capital channel through investment spending, wealth
channel through consumption and the exchange rate channel through net exports.
Onward comes the ISLM analysis. In fact it is a complex model of GDP determinants that shows how
monetary and fiscal policy interacts, it shows how the money multiplier effects on each and it provides a
partial integration of classical and Keynesians systems in to one conceptual framework. The ISLM model
can be viewed from Fig.1 where I stand for investment, S for savings, L for liquidity preference, M for
Money supply, i for interest rate and Y for income. The slope of ISLM states that if LM curve would be
steeper, than the greater would be the income sensitivity of demand for money and the less would be the
interest sensitivity of demand for money: In case the LM curve would be flatter than the less would be the
income sensitivity of the demand for money, and the greater would be the interest sensitivity. The
42
extremes vertical curve of IS and horizontal curve of LM makes the monetary policy impotent and fiscal
policy supreme. On the other hand vertical curve of LM makes the fiscal policy to loose its potency and
raises the monetary policy to its ultimate power.
Onward going monetarists comes in, who suggest that though fiscal policy has a direct and powerful
impact on spending but they disappear because rising interest rates crowd out private investments.
According to them inflation is the monetary phenomenon because aggregate demand depends primararily
on money supply. The existence of a Philips (a newzeland economist) Curve trade off between inflation
and unemployment depends upon the lags of wages and expectations behind changes in the price level.
Real interest rates initially falls after an increase in the money supply but once inflationary expectations
take hold nominal rates rise.
Fig.1
Now we come to the question of actual operational frameworks of monetary policy. In this regard some
economic variables (monetary aggregates) are required to be understood. They are:M-0 Reserve Money = Currency in circulation+ commercial banks deposits with central bank including
excess reserves and Cash reserve requirements of central Banks+ other deposit account of central bank +
Cash in tills with the commercial Banks. Reserve Money can also be defined as RM= Net Foreign assets
(NFA) + Net Domestic assets (NDA)
M1= Currency in circulation + demand deposits of commercial banks.
M2= Currency in Circulation + Demand deposits + Term Deposits + Foreign Currency Accounts
maintained with the commercial Banks
M3= Currency in Circulation + Demand deposits + Term Deposits + Foreign Currency Accounts +
National Savings Accounts
Money Multiplier = M2/RM
Here it may also be noted that in most of the countries interbank market comprised of commercial banks
are used to implement monetary policy operations i.e. through outright sale/purchase of securities, auction
of government securities or Open market operations through Repo or reverse repos (short term
collateralized transactions through buying or selling of securities). However it is not necessary. In some
countries like Turkey, capital market brokers are also considered part of this arena or in USA only
43
Primary Dealers (mostly banks) appointed by the Federal Reserve can participate in such kinds of
operations.
Monetary policy is implemented by the Central Banks at three levels. At first level, the central banks
carry out their operations by targeting reserve money so as to get targets set for the monetary aggregates
or interest rate or exchange rate or some inflationary number. In the second phase it tries to achieve a
number for M2 or M3, exchange parity or inflationary number set by the government/central Bank. In the
third and as final objective it tries to achieve Real GDP growth in line with Inflationary number set for the
year.(Taking case of Pakistan the operational target is set as interest rates by altering reserve money
(started onward Sept 2009). For second step M2 is targeted and as final target inflationary number and
real GDP growth rate set for the FY are targeted. For instance for FY10, the real GDP growth rate has
been set as 3% and inflation i.e. CPI is expected to be around 12-13% pa. So obviously under this
framework M2 growth should remain around 15-16% pa.) However in all these operational steps the
central bank only alters RM to influence interest rate, exchange rate or number of inflation. Going
forward if objective is to go for monetary aggregate targeting than central bank would remain focused
only on liquidity management. In case of interest rate targeting it would do it through altering RM but
remaining focused for getting desired interest rate. The same goes for exchange rate and inflation
targeting.
To judge interest rate movements one has to take care of inflation numbers (CPI released by the Beuru of
Statistics Government of Pakistan and core inflation released by the SBP in case of Pakistan), rate of real
GDP growth and numbers of M0 and M2. Best indicators can be the changing numbers of yields on T-bill
and KIBOR specifically of less than one year in case of Pakistan and Fed Fund Rate set by the Federal
Reserve Bank in US. In countries like UK, India or EU they also target short term interest rates. In some
other countries like Turkey they target inflation number set for the year as operational target to ultimate
target.
Case study of Pakistan: - Like many central banks, SBP has used monetary aggregates as indicators in
its policy framework. SBP has accorded a high priority to achieving a low rate of inflation. Monetary
policy has also been aimed to support the national objectives of economic growth and ensuring export
competitiveness of the country. However, the distorted terms of trade for most of the years in the last
three decades have contravened the conduct of monetary policy, which has been geared towards the task
of reconciling inflation control with external competitiveness. Moreover, monetary policy remained
subordinated to fiscal needs till the reform process took its roots. Legal framework for market-based
monetary policy was altered; changes in the SBP Act were introduced in 1993 to make SBP responsible
for the formulation and implementation of monetary policy. The Act is now required to be changed to
establish SBP relationship with IFIs in regard to different mode of financing.
Financial Sector Reforms initiated in early 1990s provided the required framework for moving towards
market based monetary policy. In this regard market based Treasury Bills were introduced followed by
Federal Investment Bonds (FIBs) and now Pakistan Investment Bonds (PIBs) in place of FIBs. MTBs are
of 3, 6 and 12 month tenors whereas PIBs are of 3, 5, 7, 10, 15, 20 and 30 years tenors. The MTBs are
available at discount through fortnightly held auctions, whereas PIBs are available at par through
quarterly held auctions with profit payable on biannual basis. This has created a benchmark yield curve
up to 30 years and has developed a correlation of market rates with SBP policy rate i.e. discount rate (the
rate at which SBP provided funds to the banks as lender as last resort) which is used to give monetary
policy signal to the market. However such yield curve is yet to be developed based on Shariah compliant
instruments.
The foremost step towards market based policy was the introduction of Open Market Operations (OMOs)
in January 1995 followed by removal of caps on maximum lending rates in March 1995 and the abolition
of floors on minimum lending rates for project and trade related financing in July 1997. 2005 onward
SBP digressed from its monetary aggregate targeting and has shifted towards interest rate targeting
maintaining implicit target benchmarked to 3 month MTB cut offs.
44
MTB auctions/OMOs/discount window/swap window/ are the main tools used in monetary policy
operations and in all these areas IBs are not able to participate due to non availability of Shariah
Compliant instruments. Only against reserve requirements they have to oblige as per following chart.
Reserve Requirements
Conventional Banks
Islamic Banks
Cash Reserve
Requirements (CRR)
5 % of Total Demand liabilities and
Time Liabilities of less than 1-year
tenor
5% of Total Demand liabilities and
Time Liabilities of less than 1-year
tenor
Statutory Liquidity
19% (excl. CRR) of Total TDL
9% (excl. CRR) of Total TDL*
Requirement (SLR)
* Currently Soverign and some quasi-sovereign Sukuks are eligible for SLR however they have to be kept
within 5% of TDL of IFIs. Going above 5%; IFIs have to provide 3% in cash against their TDL for SLR in
addition to 6% of TDL as CRR. On availability of Sovereign/Quasi Sovereign Sukuks in future, obviously
the SLR for IFIs would be the same as for Conventional Banks.
As regards exchange rate regime, Pakistan moved in a phased manner in liberalization of its foreign
exchange policy for the promotion of exchange rate stability. Pakistan had to abandon fixed exchange rate
and move towards managed and then to free float with a cap on its downward movement till the rupee
was finally set on free float exchange rate from July 21, 2000. The recent refinement of monetary policy
framework to focus on inflation modeling and control would obviously have its implications for the
exchange rate regime. Being a small open economy, Pakistan need to stabilize its exchange rate as it is
generally believed that exchange rate volatility has an adverse impact on trade flows. Exchange rate
volatility leads to uncertainty, which has negative implications on both Exports and Imports. In the recent
past SBP has always remained focused on the critical role of controlling real exchange rate in maintaining
external competitiveness.
45
Chapter 9
Foreign Exchange Markets
In recent global world, the importance of foreign exchange market is quite evident. Objectively they are
supposed to perform following three functions:1. To facilitate easy inflow and outflow of foreign currencies, mainly reserve currency in order to
meet country’s obligations.
2. Function in a manner to avoid abrupt and large size changes in country’s nominal exchange rate.
3. Facilitate market players to hedge their risks.
The foreign exchange market (forex, FX, or currency market) is a worldwide decentralized over-thecounter financial market for the trading of currencies. Financial centers around the world function as
anchors of trading between a wide range of different types of buyers and sellers around the clock, with the
exception of weekends. The foreign exchange market determines the relative values of different
currencies.
The primary purpose of the foreign exchange market is to assist international trade and investment, by
allowing businesses to convert one currency to another currency. For example, it permits a US business to
import European goods and pay Euros, even though the business's income is in US dollars. It also
supports speculation, and facilitates the carry trade, in which investors borrow low-yielding currencies
and lend (invest in) high-yielding currencies, and which (it has been claimed) may lead to loss of
competitiveness in some countries.
In a typical foreign exchange transaction a party purchases a quantity of one currency by paying a
quantity of another currency. The modern foreign exchange market started forming during the 1970s
when countries gradually switched to floating exchange rates from the previous exchange rate regime,
which remained fixed as per the Bretton Woods system.
The foreign exchange market is unique because of its






huge trading volume, leading to high liquidity
geographical dispersion
continuous operation: 24 hours a day except weekends, i.e. trading from 20:15 GMT on Sunday
until 22:00 GMT Friday
the variety of factors that affect exchange rates
the low margins of relative profit compared with other markets of fixed income
the use of leverage to enhance profit margins with respect to account size
As such, it has been referred to as the market closest to the ideal of perfect competition, notwithstanding
market manipulation by central banks. According to the Bank for International Settlements, average daily
turnover in global foreign exchange markets is estimated at $3.98 trillion, as of April 2007. $3.21 Trillion
is accounted for in the world's main financial markets.
The foreign exchange market is the largest and most liquid financial market in the world. Traders include
large banks, central banks, currency speculators, corporations, governments, and other financial
institutions. The average daily volume in the global foreign exchange and related markets is continuously
growing. Daily turnover was reported to be over US$3.2 trillion in April 2007 by the Bank for
46
International Settlements. Since then, the market has continued to grow. According to Euro money’s
annual FX Poll, volumes grew a further 41% between 2007 and 2008.
Of the $3.98 trillion daily global turnover, trading in London accounted for around $1.36 trillion, or
34.1% of the total, making London by far the global center for foreign exchange. In second and third
places respectively, trading in New York City accounted for 16.6%, and Tokyo accounted for 6.0%. In
addition to "traditional" turnover, $2.1 trillion was traded in derivatives.
Exchange-traded FX futures contracts were introduced in 1972 at the Chicago Mercantile Exchange and
are actively traded relative to most other futures contracts.
Because foreign exchange is an OTC market where brokers/dealers negotiate directly with one another,
there is no central exchange or clearing house. The biggest geographic trading centre is the UK, primarily
London, which according to estimates has increased its share of global turnover in traditional transactions
from 31.3% in April 2004 to 34.1% in April 2007. Due to London's dominance in the market, a particular
currency's quoted price is usually the London market price. For instance, when the IMF calculates the
value of its SDRs every day, they use the London market prices at noon that day.
The ten most active traders account for almost 80% of trading volume, according to the 2008 Euro money
FX survey. These large international banks continually provide the market with both bid (buy) and ask
(sell) prices. The bid/ask spread is the difference between the price at which a bank or market maker will
sell ("ask", or "offer") and the price at which a market taker will buy ("bid") from a wholesale or retail
customer. The customer will buy from the market-maker at the higher "ask" price, and will sell at the
lower "bid" price, thus giving up the "spread" as the cost of completing the trade. This spread is minimal
for actively traded pairs of currencies, usually 0–3 pips. For example, the bid/ask quote of EURUSD
might be 1.2200/1.2203 on a retail broker. Minimum trading size for most deals is usually 100,000 units
of base currency, which is a standard "lot".
These spreads might not apply to retail customers at banks, which will routinely mark up the difference to
say 1.2100/1.2300 for transfers, or say 1.2000/1.2400 for banknotes or travelers' checks. Spot prices at
market makers vary, but on EURUSD are usually no more than 3 pips wide (i.e., 0.0003). Competition is
greatly increased with larger transactions, and pip spreads shrink on the major pairs to as little as 1 to 2
pips.
Unlike a stock market, the foreign exchange market is divided into levels of access. At the top is the interbank market, which is made up of the largest commercial banks and securities dealers. Within the interbank market, spreads, which are the difference between the bid and ask prices, are razor sharp and usually
unavailable, and not known to players outside the inner circle. The difference between the bid and ask
prices widens (from 0-1 pip to 1-2 pips for some currencies such as the EUR). This is due to volume. If a
trader can guarantee large numbers of transactions for large amounts, they can demand a smaller
difference between the bid and ask price, which is referred to as a better spread. The levels of access that
make up the foreign exchange market are determined by the size of the "line" (the amount of money with
which they are trading). The top-tier inter-bank market accounts for 53% of all transactions. After that
there are usually smaller banks, followed by large multi-national corporations (which need to hedge risk
and pay employees in different countries), large hedge funds, and even some of the retail FX-metal
market makers. According to Galati and Melvin, “Pension funds, insurance companies, mutual funds, and
other institutional investors have played an increasingly important role in financial markets in general,
and in FX markets in particular, since the early 2000s.” (2004) In addition, he notes, “Hedge funds have
grown markedly over the 2001–2004 period in terms of both number and overall size” Central banks also
participate in the foreign exchange market to align currencies to their economic needs.
The exchange rate parity depends on interest rate differential, exchange rate premium and level of
inflation as compared to other country whose currency is at exchange.
47
Let us now take first case of interest rate differential. In this regard interest rate parity theory says that the
difference in interest rats must equal the difference in between the forward and spot exchange rates. In
case of Pakistan the equation becomes 1+rate on PKR/1+ rate on dollar = forward PKR per $/ spot PKR
per $. This equation gives a parity of Rs 92/$ in future, considering PKR interest rate as 12%, $ interest
rate as 1 % and spot rate as Rs 83/$.
Now let us take the case of exchange rate premium that depend on changes in spot rates of the exchange.
The expectation theory in this regard says that percentage change in between forward rates and today’s
spot rates is equal to the expected change in the spot rate i.e. forward PKR per $/ spot PKR per dollar =
Expected spot PKR per $/ today’s spot PKR per $. In this case, the assumptions are that traders are not
caring about either risk which is not factually correct.
In case of inflation, the theory of purchasing power parity says that difference in the rates of inflation will
be offset by a change in the exchange rate i.e. Expected (1+ inflation rate in Pak)/ Expected (1+ inflation
rate in US) = Expected spot rate of PKR per $/ today’s spot rate of PKR per $. In this case S/PKR parity
comes out as Rs 88 considering inflation rate in Pakistan as 10, in US as 3% and current spot rate as Rs
83 per US$.
However apart from above academic exercises, the life is not as simple. Further studies have established
that spot rates calculated as such are most of the times exaggerated. No doubt, the forward rates seem to
contain risk premium but the sign of this premium swings backward and forward most of the time.
However most probably the nominal exchange rate can stay, if Current Account deficit remains within
control and committed inflows from multilateral agencies, friendly countries and other means are ensured.
It can move to a mid i.e. at Rs 88/US$ in case of some adverse movements and can peak at Rs 92 per US
$ in FY10 & FY11.
Case example of Pakistan. Pakistan is a part of emerging economies and has just reached to the GDP size
of $ 126-130 billion. Therefore obviously, the size of its foreign exchange market is yet small as
compared to other emerging markets. In FY06, its daily volume was around $ 200 million that increased
to $250 million in 2007 and $ 350 million in 2008. In 2009 and 2010, it has grown to the size of $ 400600 million. This increase is significant but there are other important issues that make its activities more
volatile as compared to other nations.
The figures provided above, pertain to interbank market which is the official channel, whereas non
official channel known as KERB is also very active and some time overshadows activities of formal
market creating problems for its apex regulator i.e. SBP. Efforts are under way to streamline this anomaly
through formation of exchange companies, but still SBP has not succeeded in getting control of this
segment to its satisfaction.
Exchange rate policy by definition and practically is part of monetary policy. It underwent several
changes since 1949. The exchange rate of Pakistan remained fixed in terms of pound sterling up to
September 1971 and subsequently in terms of US$. Since January 1982, the exchange rate regime of PKR
was a system of managed float, based on a basket of currencies. In 1991 with initiation of financial sector
reforms, the direction was set to turn it in to free float that was finally achieved in 2000-2001. Pakistan
uses US$ as its reserve currency. As regards changes in its nominal value, it also went through various
changes. In Sept, 49, the decision was taken not to devalue PKR while 48 currencies in the sterling area
went in to devaluation in spite of the fact that current account (CA) deficit in 1948-49 was around 2.5% of
its GDP. Luckily, Korean War helped Pakistan to come out of this crisis and in 1950-51, Pakistan
witnessed surplus in its CA. However on ending of Korean boom, Pakistan again went in to CA deficit.
On 31st July, 1955, first time PKR was devalued. In 1956-57, the position worsened to such an extent that
Governor SBP in its policy statement singled out balance of payments and inflation as the two main
culprits for the economy. Since that time, the same legacy is hovering over Pakistan’s economy. Nominal
exchange rate remained fixed at Rs 4.76 per US$ since 1955, but since export bonus scheme was in vogue
48
at that time, so effectively it was a multiple exchange rate. In 1971 it depreciated to RS 7.76 for exports,
however in 1972 it was unified as Rs 11 per US $.
Another issue that confronted Pakistan at that time was significant overvaluation of Real Effective
Exchange Rate (REER) that appreciated by 56% in 1972 and 25% in 1973. To adjust this and in order to
make the exports competitive, the PKR was devalued 56.73% at that time. The main feature of adjustment
in feeding CA deficits has been the aid from donor agencies mainly from the US. The same features still
hold our economy and we have not been able to come out of this mess.
The foreign exchange market in Pakistan gets its inflows through export proceeds, remittances and FDI.
The amount received from IMF is for meeting current account deficit and does not add up in to FX
market activities. Further SBP intervenes some time to smooth out the market that can come under
pressure on account of lumpy payments or can plunge on receipt of some major amount. Under financial
sector reforms started in 1991, current account has been made totally convertible in 1993, meaning that
any foreign account holder (FE-25) can send its money outward without any restriction. Likewise this
account can receive amount in cash or from outside without any restriction. In capital market investments,
the amount can be sent in or send out through SCRA, an account maintained with the banks on behalf of
investors. Capital account convertibility is not yet allowed in Pakistan.
The year FY08 remained volatile for the FX market, witnessing huge contraction in the NFA i.e. around
Rs 375 billion. This figure coincided with depletion in the bank deposits remaining to the same quantum.
The outflow mainly went to the Gulf States for better investment opportunities, however the trend is now
on reverse, on account of recessionary mood in these countries. At that time the rupee depreciated by
more than 18%. However on access of IMF aid, the things have stated moving towards some
improvements, but theses are short term arrangements. Opportunities exist to encash them on the back of
declining inflation and world coming out of recession. Forward points, an indicator of future trend of FX
market going as high as Rs 3.72 per US $ in June 08 are now softening out. FX reserves have also
improved which is required mainly to support import obligations and to support FX market in case of its
dire need to avoid undue fluctuations in nominal exchange rate. In wake of these changes, SBP has
succeeded in shifting oil payments to the interbank market. Further KERB market is also showing some
discipline resulting in little spread in between interbank and KERB market.
Another disciplinary arrangement for FX market i.e. Foreign Exchange exposure limit (FEEL)
implemented by the SBP after replacing NOSTRO limits had made the market more flexible and
disciplined to move within some range of banks paid up capital. Previously they were 10% of paid up
capital, however recently they have been relaxed to 20%. This has made the FX market to arrange their
funds by using somewhat wider space.
Now going forward, let us see what can be the fate of Exchange rate in Pakistan. One of the questions that
dictates the exchange rate parity are the difference in interest rate on other currencies specifically $ in
respect to PKR, the difference of forward exchange rate from its spot rate and how expected spot rates for
$ and PKR are going to be determined for the next year and what relationship one can foresee in between
inflation in Pakistan with respect to other countries. Apart from these factors, the paramount factor is the
demand and supply position of S with respect to PKR that some time alters on the basis of government
and central bank policies. In this regard, KERB market has its role as well in shift of market flows and in
making market sentiments
The most important issue in developing FX market right now is to bring hedging products in the market.
SBP has initiated Derivatives market in 2004 with introduction of FX options and other interest rate
derivatives. Forwards and currency swaps already existed in the market. Sensing huge differential
between LIBOR and KIBOR, market opted for cross currency swaps in FY07 and FY08, but with
significant depreciation in PKR, most of the corporate burnt their figures. However since most of them
were naturally hedged against their export proceeds, so in nut shell they landed just on square. Moreover,
this experience and others by using forwards have revealed that most of the corporate players are not
49
aware about the risks of use of cross currency swap and other derivatives. As for forwards, they are
mostly demand driven and operate in an environment where no price discovery mechanism exists, so
ultimately they also end up without providing future prices prudently.
These are the hassles of the FX market in Pakistan that can be streamlined with the initiatives of SBP in
collaboration with market players. However market side lacks capable staff at the moment. This puts an
extra responsibility on banks or other financial institutions or even corporatism to work seriously on
capacity building of their staff working in their treasuries.
50
Chapter 10
Derivatives
Robert Frost an American poet once wrote “Some say the world will end in fire, some say in ice”. This
exactly applies on derivatives to explain what its dynamics are.
The quantum of global derivatives market has surpassed an amount of 1.14 quadrillion dollars (one and
12 zeros) i.e. 548 trillion $ in listed credit derivatives and 596 trillion dollars in notional/Over the counter
(OTC) derivatives. In contrast the world GDP is estimated around 60 trillion dollars. So one can question
that how the size of derivatives market can grow to 1,140 trillion dollars in comparison to 60 trillion
dollars of world GDP. The answer is, it can, through betting. Any one can bet any amount one may like
and that is where the huge risk comes in.
Regulations are either non existent or weak on this area and that was the reason of its being an instrument
in bringing global meltdown of 2008-09. G-20 in its recent meeting has vowed to make stringent
regulations for this part of financial market.
Derivatives are those financial instruments whose price is dependent on or derived from the value of some
other underlying assets. The most common underlying assets include Stocks, Bonds, Commodities,
currencies, interest rates, Other than these any other random event/uncertain event, like temperature,
weather can also be used for derivative contract. Broadly speaking, two distinct groups of derivatives
contracts exist viz: Exchange traded and OTC. Over the Counter derivatives are contracts that are traded
(and privately negotiated) directly between two parties, without going through an exchange or other
intermediary. Products such as swaps, forward rate agreements and exotic options are almost traded in
this way. Reporting of OTC amounts are difficult because trade can occur in private without activity
being visible on any exchange. According to Bank of International settlement (BIS) as of June 2008,
notional outstanding amount in OTC stands as $ 648 trillion of which 67 % are interest rate contracts, 8 %
are credit default swaps, 9 % are foreign exchange contracts, 2 % are commodity contracts, 1 % are
equity contracts and 12 % are others. In absence of counterparty, these contracts are subject to
counterparty risk. Exchange traded derivatives are products that are traded via specialized derivatives
exchanges or other exchanges. They can be futures, options and swaps. Some of the notable exchanges
include Korea Exchange (lists KOSPI index futures and options), Eurex (lists interest rate and index
products) Chicago Mercantile and Chicago board of Trade, New York Mercantile Exchange. According
to BIS, the combined turnover of exchange traded derivatives has ranged in between $ 300-500 trillion on
quarterly basis in 2005-08.
Derivatives contracts can be made as much complex as one likes, however in strict definition those
contracts where exchange of notional does take place, like in forwards or currency swaps, are not treated
as derivatives.
Derivative contracts are based on zero sum game i.e. somebody gains is somebody’s loss, so they can not
be conceived without considering hedgers, speculators and arbitrageurs active in the market. One
recently introduced concept is the positive sum game that is more close to Islamic finance that permits
hedging but no speculation.
Derivatives are mainly used to mitigate future risks, however they do not add value since hedging is a
zero sum game and secondly investors mostly use them on do it yourself alternatives basis.
Derivatives markets can be traced back to middle ages. They were developed to meet the needs of farmers
and merchants. First future exchange was established in Japan in 16th century. The Chicago Board of
51
Trade was established in 1848.The international monetary market was established in 1972 for future
trading in foreign currencies
Insurance is a kind of mitigating risk but it has its limitations. To avoid zero NPV it tries to cover
administrative costs, adverse selection, and moral hazard risks in its premium. Apart from this simple
format, the derivatives on the other hand have lot of varieties, i.e. from simple to highly exotics, creating
a world of their own. Size of its activities is manifold as compared to total world GDP
Derivatives can be categorized as Exchange Traded Contracts or products traded over The Counter
Market
Here one has to understand that in the financial markets three kinds of players always exist. They are (1)
Hedger-Hedgers face risk associated with the price of an asset. They use futures or options markets to
reduce or eliminate this risk (2) Speculators- Speculators wish to bet on future movements in the price
of an asset. Derivatives can give them an extra leverage to enhance their returns (3) ArbitrageursArbitragers work at making profits by taking advantage of discrepancy between prices of the same
product across different markets.
Derivatives can be plain vanilla or exotic. The simple forms can be

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


Forward
Futures
Options
Forward Rate Agreement (FRAs)
Swaps
Forward contract is a binding contract which fixes now the buying/selling rate of the underlying asset to
be bought/sold at some time in future. There can be long Forward i.e Binding to buy the asset in future at
the predetermined rate or Short Forward i.e Binding to sell the asset in future at the predetermined rate.
Pay offs can be:Pay Off = ST – K (for the long forward)
Pay Off = K – ST (for the short forward)
Here T = Time to expiry of the contract
ST = Spot Price of the underlying asset at time T
K = Strike Price or the price at which the asset will be bought/sold
52
A futures contract is a standardized contract, traded on a futures exchange, to buy or sell a
certain underlying instrument at a certain date in the future, at a specified price
Specification of a standard contract say Gold can be




Commodity Name
Exchange Name
Size of Contract : 100 troy ounce
Delivery month: Feb/April/June/Aug/Oct/Dec
Since in future exchange is the counterparty so both buyers and sellers have to provide some
margin specified by the exchange that alters on daily basis. The margins can be:Initial Margin-An Initial margin is the deposit required to maintain either a short or long position
in a futures contract.
Maintenance Margin-Maintenance margin is the amount of initial margin that must be
maintained for that position before a margin call is generated.
Margin Call-If the amount actually falls below the maintenance margin, a margin call is given to
the investor to replenish the account to the initial margin level, otherwise the account is closed.
Variation Margin-The additional funds deposited to make up to the initial margin.
In the delivery month the Futures’ Price is almost equal to the prevailing Spot Price.
Or we can say that with the passage of time the Futures’ Price gradually approaches the
prevailing Spot Price. Why Because of No Arbitrage Principle.
Assume Notations
T = Delivery/Expiry time of the futures’ contract
F0 = Futures Price now to be delivered at time T
ST = Spot Price of the underlying at delivery time T
If F0 > ST there is an arbitrage opportunity
Short the futures contract, buy the asset and make the delivery
Pay Off = F0 - ST > 0
If F0 < ST
Parties, who want to buy the asset, would immediately go long the futures’ contract and wait for
the delivery.
Because of increased demand for the futures, the futures’ price would go up to the actual
market spot price of the asset to remove the anomaly.
Suppose
Commitment to sell 1000 barrels after 3 months at the then prevailing spot price say ST
Futures Price for delivery after 3 months = 18.75
Strategy
Go short a 6 months future contract to lock in a price now
At maturity go long a futures to close the position
53
Scenario
Cash flow from sale at
spot rate
Gain/Loss on futures
If ST = 19.5
19.5
18.75-19.5
If ST = 17.5
17.5
18.75-17.5
If ST = 18.75
18.75
0
Long Hedge
When a company knows it will have to purchase a certain asset in the future and wants to lock
in a price now.
By going long an appropriate futures contract the hedger can lock in a price he will be paying
after time T to buy the asset.
Suppose
Commitment to buy 1000 barrels after some time T at the then prevailing spot price say ST
Futures Price = 18.75
Strategy
Go long a 6 months future contract to lock in a price now
At maturity go short a futures contract to close the position
Scenario
Price paid after 6 months at
spot rate
Gain/Loss on futures
If ST = 19.5
- 19.5
19.5-18.75
If ST = 17.5
If S = 18.75
T
54
-17.5
-18.75
17.5-18.75
0
Case studies (Futures)
A British bank with a history of 233 years collapsed because of imprudent use of derivatives.
One of the traders Nick Leeson, who was basically responsible to make arbitrage profits on
Stock Index Futures on Nikkei 225 on the Singapore and Osaka exchanges.
Instead of looking for arbitrage opportunities, the trader started making bets on the index and
went long the futures.
Unfortunately the market fell by more than 15% in the 1995 leading to margin calls on his
positions.
Because of his influence on the back office, he was able to hide the actual position and sold
options to make for the margin calls.
But his view on the market proved to be wrong and losses mounted to an unmanageable
amount.
Another case
METALLGESELLSCHAFT, A US Subsidiary of a German Company used hedging strategies,
which went against them, resulting in heavy cash outflows.
Being an Oil Refinery and Marketing Company, they sold forward contracts on oil maturing up to
10 years.
To hedge their position, they went long the available futures contracts with maturities up to 1
year.
They planned to use “Stack & Roll” strategy to cover their short forwards contracts. But due to
decreasing oil prices they had margin calls on their futures contracts. They were unable to meet
those heavy cash outflows.
Ultimately the US team of the company was kicked out and a new team from Germany came to
USA and liquidated the contracts making heavy losses.
Another Case
On January 24, 2008, the bank (Societe General a French bank) announced that a single
futures trader at the bank had fraudulently caused a loss of 4.9 billion Euros to the bank, the
largest such loss in history.
Jerome Kerviel went far beyond his role -- taking "massive fraudulent directional positions" in
various futures contracts.
.He got caught when markets dropped, exposing him in contracts where he had bet on a rise.
Due to the loss, credit rating agencies reduced the bank's long term debt ratings: from AA to
AA- by Fitch; and from Aa1/B to Aa2/B- by Moody's.
The alleged fraud was much larger than the transactions by Nick Leeson that brought down
Barings Bank.
Options
An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an
underlying asset at a specific price on or before a certain date
55
Unlike a forward/future, this contract gives the right but not the obligation. So its not a binding
contract.
The holder will exercise the option only if it is profitable on the basis of payoff structures
Call option
A call gives the holder the right to buy an asset at a certain price within a specific period of time.
Put option
A put gives the holder the right to sell an asset at a certain price within a specific period of time.
The type of option and the relationship between the spot price of the underlying asset and the
strike price of the option determine whether an option is in-the-money, at-the-money or out-ofthe-money.
Exercising an in-the-money call or in-the-money put will result in a payoff. Neither a call nor put
that is at-the-money will produce a payoff.
Call Option
Put Option
In-the-Money
Spot > Strike
Spot < Strike
At-the-Money
Spot = Strike
Spot = Strike
Out-of-the-Money
Spot < Strike
Spot > Strike
Kinds of options
On the basis of exercise the options can be:American options
56
Can be exercised at any time between the date of purchase and the expiration date.
Mostly American options are exercised at the time of maturity. But when the underlying makes
cash payments during the life of option, early exercise can be worthwhile.
European options
Can only be exercised at the end of their lives
On the basis of versatility the options can be:Vanilla Option
A normal option with no special or unusual features
Exotic Option
A type of option that differs from common American or European options in terms of the
underlying asset or the calculation of how or when the investor receives a certain payoff.
Bermuda Option-A type of option that can only be exercised on predetermined dates, usually
every month
Compound Option-An option for which the underlying is another option. Therefore,
there are two strike prices and two exercise dates. These are the four types of compound
options:
-
Call
Put
Call
Put
on
on
on
on
a
a
a
a
call
put
put
call
Asian Option-An option whose payoff depends on the average price of the underlying asset
over a certain period of time as opposed to at maturity. Also known as an average option.
Digital Option- An option whose payout is fixed after the underlying stock exceeds the
predetermined threshold or strike price. Also referred to as "binary" or "all-or-nothing option."
Shout Option- An exotic option that allows the holder to lock in a defined profit while
maintaining the right to continue participating in gains without a loss of locked-in monies.
Barrier Option- A type of option whose payoff depends on whether or not the underlying asset
has reached or exceeded a predetermined price.
Chooser Option-An option where the investor has the opportunity to choose whether the option
is a put or call at a certain point in time during the life of the option
Quantity-Adjusting Option (Quanto Option)-A cash-settled, cross-currency derivative in
which the underlying asset is denominated in a currency other than the currency in which the
option is settled. Quantos are settled at a fixed rate of exchange, providing investors with shelter
from exchange-rate risk.
57
Forward Rate Agreement (FRA)
An over-the-counter contract between parties that determines the rate of interest, to be paid or
received on an obligation beginning at a future start date. On this type of agreement, it is only
the differential that is paid on the notional amount of the contract.
Also known as a "future rate agreement”
Example
Client has a six month borrowing requirement in three months and wants to hedge its floating
interest rate exposure
Client can enter into a 3*9 FRA Agreement with bank whereby:
Bank will pay 6m KIBOR rate to the customer.
Customer will pay a fixed rate to bank.
Since the exchange will take place at the start of the borrowing period, only the net discounted
amount will be exchanged
FRA Rate Calculation:
Current KIBOR rates:
3 month
9 month
9.30% = i3
9.80% = i9
FRA (3*9) rate
= {[1+ (i9*9/12)]/[1+(i3*3/12)]}*[12/6]
=9.82%
A client needs to borrow Rs.100m for 6 months in 6 months time. The clients borrowing rate is
KIBOR+1.Suppose, today 6 month KIBOR is quoted @10.00%.
After Month
Do Nothing
Buy 6*12 [email protected]%
KIBOR rises to
11%
Borrow@12%
Borrow@12%,
Kibor fall to 9%
Borrow @ 10%
get 0.5% from seller. your cost
11.5%
Borrow@9%,
Pay 1.5% to seller. your cost
11.5%
58
Swap
A swap is a derivative in which two counterparties agree to exchange one stream of cash flows
against another stream. These streams are called the legs of the swap
There are two basic types of swaps:
•
•
Interest Rate Swap
Currency Swaps
An agreement between two parties where one stream of future interest payments is exchanged
for another based on a specified principal amount. Interest rate swaps often exchange a fixed
payment for a floating payment that is linked to an interest rate.
EXAMPLE
Counterparties: A and B Maturity: 5 years A pays to B: 6% fixed p.a.. B pays to A : 6-month
KIBOR. Payment terms: semi-annual. Notional Principal amount: PKR 10 million.
Payments at the
end
Half
year
period
1
2
3
4
5
6
7
8
9
10
Fixed
payments
rate
Floating
Payments
KIBOR
300000
300000
300000
300000
300000
300000
300000
300000
300000
300000
rate
6m
337500
337500
337500
325000
325000
325000
312500
312500
312500
325000
Typical Characteristics of the Interest Rate Swaps:
The principal amount is only notional.
Opposing payments through the swap are normally netted.
The frequency of payment reflects the tenor of the floating rate index.
59
Net Cash From A to
B
-37500
-37500
-37500
-25000
-25000
-25000
-12500
-12500
-12500
-25000
-250000
Currency Swap
A swap that involves the exchange of principal and interest in one currency for the same in
another currency. It is considered to be a foreign exchange transaction and is required by law to
be shown on the balance sheet.
To further elaborate the modus operandi and underlying fundamentals of a swap transaction we
shall discuss a simple ready against six month forward swap. As the first leg of the transaction
is in ready therefore it would be executed today at the today prevailing exchange rate. For sake
of simplicity we shall make the following assumptions
READY USD/PKR Rate
PKR 6-month interest rate
USD 6-month interest rate
60.00
11.00%
6.00%
In order to ensure that no opportunities of arbitrage arise the Therefore, interest rate differential
being (11-6) 5% the theoretical depreciation in rupee would be
60.00 * 5% * ½ (as interest rates are quoted on annual basis the six months impact would be
roughly ½) = 1.5
This will result in a six month forward rate of 60 + 1.5=61.5
Cross-currency swaps offer companies opportunities to reduce borrowing costs in both
domestic and foreign markets
A currency swap involves the exchange of payments denominated in one currency for payments
denominated in another. Payments are based on a notional principal amount the value of which
is fixed in exchange rate terms at the swap's inception
Consider a Pakistani Exporter having exports’ proceeds in USD. He/She has a PKR(KIBOR)
loan liability on its balance sheet and he/she wants to convert this PKR liability to USD(LIBOR)
liability to exploit the low interest rates as compared to that of PKR.
In doing so he/she is taking on exchange risk but with his exports’ proceeds in FX he/she has a
natural hedge.
Pricing-basic features
Market price, i.e. the price at which traders are willing to buy or sell the contract
For exchange-traded derivatives, market price is usually transparent.
Complications can arise with OTC or floor-traded contracts though, as trading are handled
manually, making it difficult to automatically broadcast prices.
Arbitrage-free price, meaning that no risk-free profits can be made by trading in these
contracts
60
Forward Mechanism
US D
Interest Rate
PKR Mark
up Rate
USD/PKR
Spot
US D
Amount
Tenor
Bid
4.00%
Offer
4.25%
8.00%
8.50%
60.00
60.05
100
181 days
SELL USD IN FORWARD (EXPORT)
USD
Borrowing
100 4.25%
Sell USD
Invest
PKR
100
60
6000
8%
After 181
days
PKR Cash
in flow
Export
process
shall be
used to
pay
USD Cash
outflow
Forward
Rate
Swap
points
USD is at
BUY USD IN FORWARD (IMPORT)
PKR
6005
8.50%
2.14 Borrowing
253.11
6000 Buy USD
Invest
238.03 USD
100
60.05
6005
100
4%
2.0
After 181
days
6238.03
102.14
61.08
Paisa 1.08
PREMIUM
61.08
PKR Cash
out flow
USD shall
be used to
Pay import
6258.11
USD cash
inflow
102.01
Forward
Rate
Swap
points
USD is at
61.35
Paisa 1.3
PREMIUM
61.35
Future Mechanism-Currency
Spot$/Euro
3 month future rate
Standard size of 3
months contract in
Euro
61
Bid
1.3505
1.353
offer
1.351
1.3535
As of today 125,000
In a month time rate
1.354
moves to (Spot
$/Euro)
3 months Future Rate 1.3565
Actual trade amount
750,000 Euros
Sell Euro
Futures
(Export)
Which
Contract
Type of
contract
No of contract
Tick size
Actions
required
today i.e.
transaction
date
Sell contract of
Euro Futures
Actions
required after
30 days i.e.
Receipt/
Payment date
Futures Market
Buy contracts
of Euro
Futures
Spot Market
Sell Euros
Outcome of
Hedge
Opportunity
Gain/Loss in
Spot
Actual Sell
Could have
sell @ 1.3505
Futures
Market
Sell futures
62
Next following
the actual
receipt date of
contract
Sell Euro
Futures
Amount/Std
contract size
Minimum price
movement *
contract size
1.3545
1.357
Due in 30 days
Buy Euro
Futures
Import
Which Contract
Round off 6
0001*125000=
$12.50
Type of
contract
No of contract
Tick size
Next
following the
actual
payment date
Buy Euro
Futures
Amount/Std
contract size
Minimum
price
movement *
contract size
6 * 1.353=
1.014,750
Buy contract of
Euro Futures
6 * 1.3535=
1.015,125
6 * 1.357 =
1,017,750
Futures Market
Sell contracts
of Euro Futures
6 * 1.3565 =
1,017,375
Spot Market
Buy Euros
750,000 * 1.354
= 1,015,500
1,015,500
1,012,875
1,014,750
2,625 (gain)
Opportunity
Gain/Loss in
Spot
Actual Buy
Could have
bought @
1.351
Futures
Market
Buy futures
Round off 6
0001*125000=
$12.50
750,000 *
1.3545 =
1,015,875
1,015,875
1,013,250
1,015,125
-2,625 (loss)
contract@
Buy Futures
Contract@
Loss
1,017,750
-3000
contract@
Sell Futures
Contract@
Gain
1,017,375
2,250
Valuing Option
The value, or premium, of an option is determined by the future price of its underlying asset.
Of course, no one can really know for certain what an asset’s future price will be.
To help estimate this price, techniques have been developed using probabilities and statistics.
Current Price of Asset
Strike Price
Time to Expiration
Volatility
Risk-Free rate
The Black-Scholes model and the Cox, Ross and Rubinstein binomial model are the primary
models used for pricing options.
The binomial option pricing model uses an iterative procedure, allowing for the specification of
nodes, or points in time, during the time span between the valuation date and the option's
expiration date.
The Black Scholes Model is regarded as one of the best ways of determining fair prices of
options The model assumes that the price of heavily traded assets follow a geometric Brownian
motion with constant drift and volatility. When applied to a stock option, the model incorporates
the constant price variation of the stock, the time value of money, the option's strike price and
the time to the option's expiry.
DCF model does not work in case of option since in that our standard procedures for valuing an
asset is to (1) figure out expected cash flow and (2) discount them at the opportunity cost. This
is not practical for option; however by combining stock investment and borrowing, the option
equivalent can be calculated. In this case, suppose we have a stock with an exercise price of Rs
60, than assuming the day when the option is at the money and by taking the short term risk
free rate as 1.5% for 8 months and 1.0 % for a year, we assume that the price of the stock may
fall by a quarter to 45 or rise by one third to 80. In the case if price falls to 45 than the option is
worthless but in case of moving to 80 the pay off is 80-60 = 20. Now suppose you buy 4/7
shares and borrow 25.46 from the bank than it would turn in to given scenario. 4/7 shares of
valuing 45 would value 25.71 and valuing 80 would value 45.71. The repayment of loan with
interest would come out as 25.71.
In this method we borrowed money and exactly replicate it with the pay off from a call option.
The number of shares needed to replicate one call is called hedge ratio or option delta which
is = spread of possible option prices/ spread of possible share prices = 20-0/80-45= 20/35= 4/7
Now to value call option we would use given formula =value of 4/7 shares -25.46 bank loan = 60
x (4/7) – 25.46 = 8.83 (value of call).
To calculate value of put we would go reverse, that in the case stock at 80 would give a payoff
of 0 and at 45 would give a pay off of 15. This would give option delta of 0-15/80-45 = -3/7. The
63
delta of put option would always be negative. Now with this case, the option payoffs can be
replicated by selling 3/7 shares and lending 33.95 making it 34.29 after one year. Now at sale of
3/7 shares of 45 you get -19.29 and against shares of 80 you get -34.29 (that you would lend).
This give 0 payoffs for stock valuing 80 and 15 against stock valuing 45. From this, value of put
would be -3/7 shares + 33.95 as lending = -3/7 x 60 +33.95 = 8.23
In the above case the call option should sell at 8.83. If the option price is higher than 8.83 you
can have payoff by buying 4/7 shares, selling a call option and borrowing 25.46. Similarly if the
prices are less than 8.33 you can make equally payoff by selling 4/7 shares, buying a call and
lending the balance. In either case there would be an arbitrage opportunity. This provides us
another way to value the option. In this we pretend, that investors are indifferent about risk, work
out the expected future value of the option and discount it back at the risk free rate to get the
current value. If investors are indifferent about risk than Expected return on stock = 1.0% per 8
months. In this case we have presumed that stock can either rise by 33.33 % to 80 or fall by 25
% to 45. The probability of price rise is = Expected return = (probability of rise x 33.3) + ( (1probability of rise) x (-25) ) =1.00%. Probability of rise can be ascertained as ρ =interest rate –
downside change/ upside change – downside change =.01 – (- .25)/.333 – (-.25) = . 446. The
expected value of the call option would be (probability of rise x 20 + ( (1-probability of rise) x 0)
= (.446 x 20) + (.554 x 0) =8.92. PV of call would be = 8.92/1.01 = 8.83
valuing the put option through risk neutral valuation method we would proceed as
(probability of rise X 0 ) + ((1 – probability of rise ) X 15 ) = (.446 X 0) + ( .554 X 15) = 8.31 PV
of put option would be 8.31/1.01 = 8.23
Relationship of call and put
In European option there is a simple relationship between call and the put i.e. value of put =
value of call –share price + PV of exercise price = 8.83 -60 + 60/1.01 = 8.23
One of the most widely used options pricing techniques is the Binomial Pricing Theory. It
involves the construction of a binomial tree, and this tree is used to represent all of the possible
paths that the price of an underlying asset may take during the life of the option.
An example of a two-step option valuation of a European Call will be used here to demonstrate
the general functioning of this pricing method. For this model a few assumptions have to be
made:
1. The direction and degree of the underlying asset’s fluctuation is given. Assume for each
stage of the tree that the underlying asset’s price may either go up or down by 10%.
2. The risk free interest rate is known with certainty. For this example assume 12%.
3. The current price of the stock is used to project forward possible movements through the
binomial tree. For the purpose of this example a price of $10.00 is used, with the option having
a strike price of $10.50. Thus, the option is out of the money
4. No arbitrage.
The following notation will be used in this example:
So = Current price of the stock, Let So = $10.00
X = Strike or Exercise price of option
r = Risk-free rate interest, Let r = 12%
T = Time between periods in years. This example has two 3-month periods, making T =
3months/12months or .25. T = .25
U = Degree or percentage change in upward movement, Let U = 1.1
D = Degree or percentage change in downward movement, Let D = 0.9
Pu = Probability of an upward movement
64
Pd = Probability of a downward movement
A two-step binomial tree model would, in theory, look like this
Figure 1
U = 1 upward movement in the price of the asset.
UU = 2 consecutive upward movements in the price of the asset.
D = 1 downward movement in the price of the asset
DD = 2 consecutive downward movements in the price of the asset.
UD = An upward or downward movement in the price of the asset followed by an upward or
downward movement in the price of the underlying asset.
The tree with all of the possible asset prices would look like this:
65
It is assumed that the strike price of the option is $10.50, and the following possible option
prices are then calculated as follows:
Cuu =
12.10 – 10.50
Cud =
9.90 – 10.50
Cdd =
8.10 10.50
= 1.60
= -.60, nil
= - 2.40,nil
These prices are two periods forward, and the valuation occurs at the present period. Thus, the
prices of the options may be calculated through working a path back through the tree, eventually
ending up at the first node. For example, the option price at node U is calculated as the
expected value of the two nodes that follow it discounted by the risk-free rate of interest.
However, to calculate the expected value one needs to calculate the probability of an upward
and downward movement. This probability of an upward movement may be calculated through
using the following formula:
Subbing in the values assumed at the beginning of this
Pd is 0.3477.
example, Pu is found to be 0.6523 and
= $1.04
This expected value has to be discounted back one period to node U. This is the present value
equation:
= $1.01
The tree would now look like this:
66
Where the value of the call at time zero is found through this equation:
Therefore, the price of this call is $0.97
The big advantage of binomial model over the Black-Scholes model is that it can be used to accurately
price American options. This is because with the binomial model it's possible to check at every point in an
option's life
The main limitation of the binomial model is its relatively slow speed
The Black-Scholes Model was first discovered in 1973 by Fischer Black and Myron Scholes, and then
further developed by Robert Merton. It was for the development of the Black-Scholes Model that Scholes
and Merton received the Nobel Prize of Economics in 1997 (Black had passed away two years earlier).
The idea of the Black-Scholes Model was first published in "The Pricing of Options and Corporate
Liabilities" of the Journal of Political Economy by Fischer Black and Myron Scholes and then elaborated
in "Theory of Rational Option Pricing" by Robert Merton in 1973
The Black and Scholes Call Models
C = Theoretical Call Premium
r = Risk-Free Interest Rate
sigma = Standard Deviation of Stock Returns
T = Time until expiration (years)
N = Cumulative Standard Normal Distribution
67
X = Option Strike Price
S = Current Stock Price
e = Exponential Function
1)
2)
3)
4)
5)
6)
Assumptions
The stock pays no dividends during the option's life
European exercise terms are used
Markets are efficient
No commissions are charged
Interest rates remain constant and known
Returns are log normally distributed
Others models
For rapid calculation of a large number of prices, analytic models, like Black-Scholes, are the
only practical option. However, the pricing of American options (other than calls on non-dividend
paying assets) using analytic models is more difficult than for European options
To handle American option pricing in an efficient manner other models have been developed.
Three of the most widely used models are:
Roll, Geske and Whaley analytic solution: The RGW formula can be used for pricing an
American call on a stock paying discrete dividends.
Black's approximation for American calls: Black's approximation basically involves using the
Black-Scholes model after making adjustments to the stock price and expiration date to take
account of early exercise.
Barone-Adesi and Whaley quadratic approximation: An analytic solution for American puts
and calls paying a continuous dividend.
Advantage: The main advantage of the Black-Scholes model is speed -- it lets you calculate a
very large number of option prices in a very short time
Limitation: The Black-Scholes model has one major limitation: it cannot be used to accurately
price options with an American-style exercise as it only calculates the option price at one point
in time -- at expiration
Volatility
Volatility is a measure of the rate and magnitude of the change of prices (up or down) of the
underlying
If volatility is high, the premium on the option will be relatively high, and vice versa
Once you have a measure of statistical volatility (SV) for any underlying, you can plug the value
into a standard options pricing model and calculate the fair market value of an option
Implied Volatility is the estimated volatility of a security's price
In short, the more a stock is expected to make a big move due to some important news release
or earnings release in the near future, the higher will be the implied volatility of that stock
68
In fact, implied volatility rises as the date of that important release approaches
Under such circumstances, market makers also hike implied volatility in order to charge a higher
price for the higher demand
Volatility measures are



Standard Deviation
Beta
R-Squared
Alpha
They are further supported by Hedging Greeks that are





Delta
Gamma
Vega
Theta
Rho
Delta
Options Delta measures the sensitivity of an option's price to a change in the price of the
underlying stock
In layman terms, delta is that options Greek which tells you how much money a stock options
will rise or drop in value with a $1 rise or drop in the underlying stock
This means that the higher the delta value a stock option has, the more it will rise with every $1
rise in the underlying stock
Gamma
Options Gamma is the rate of change of options delta with a small rise in the price of the underlying stock
Just as options delta measures how much the value of an option changes with a change in the
price of the underlying stock, Options Gamma describes how much the options delta changes
as the price of the underlying stock changes
Vega
Options Vega measures the sensitivity of a stock option's price to a change in implied volatility
When implied volatility rises, the price of stock options rises along with it. Options Vega
measures how much rise in option value with every 1 percentage rise in implied volatility
Model's fair market value, however, is often out of line with the actual market value for that
same option. This is known as option mispricing. The answer can be found in the amount of
expected volatility (implied volatility) the market is pricing into the option
Theta
Options Theta measures the daily rate of depreciation of a stock option's price with the
underlying stock remaining stagnant. In layman terms, Theta is that options Greek which tells
you how much an option's price will diminish over time, which is the rate of time decay of stock
options.
Time decay is a well known phenomena in options trading where the value of options reduces
over time even though the underlying stock remains stagnant
Rho
Options Rho measures the sensitivity of a stock option's price to a change in interest rates
Options Rho is definitely the least important of the Options Greeks and have the least impact on
stock options pricing. In fact, this is the options Greek that is most often ignored by options
69
traders because interest rates rarely change dramatically and the impact of such changes affect
options price quite insignificantly measure used to describe how a basis point change in yield
affects the price of a security
Price Value at Basis Point (PVBP):- It gives a picture of increase or decrease in price on
increase or decrease in one basis point in yield. This simple relationship is widely used in the
market to anticipate loss or gain.
Value at Risk (VAR)
The Question Being Asked in VAR is
“What loss level is such that we are X% confident it will not be exceeded in N business days?”
Advantages
It captures an important aspect of risk in a single number
It is easy to understand
It asks the simple question: “How bad can things get?”
There are three methods of calculating VAR:
The Historical Method
The Variance-Covariance Method
The Monte Carlo Simulation
The historical method simply re-organizes actual historical returns, putting them in order from
worst to best
It then assumes that history will repeat itself, from a risk perspective
70
With 95% confidence, we expect that our worst daily loss will not exceed 4%
If we invest $100, we are 95% confident that our worst daily loss will not exceed $4 ($100 x 4%)
This method assumes that stock returns are normally distributed
The Variance-Covariance Method
It requires that we estimate only two factors:
Expected (or average) return
Standard deviation
It allows us to plot a normal distribution curve.
The advantage of the normal curve is that we automatically know where the worst 5% and 1%
lie on the curve. They are a function of our desired confidence and the standard deviation
71
A Monte Carlo simulation refers to any method that randomly generates trials, but by itself
does not tell us anything about the underlying methodology
A Monte Carlo simulation amounts to a "black box" generator of random outcomes
Because of the time variable, users of VAR need to know how to convert one time period to
another
They can do so by relying on a classic idea in finance: “The standard deviation of stock returns
tends to increase with the square root of time”
72
Derivatives Market in Pakistan
In Pakistan derivatives came first in form of Stock futures in 2001 that were not cash settled, however in
2003, the cash settlement was allowed. So now deliverable futures are available on 30 days settlement
basis (discontinued by SECP on April 8, 2009), whereas cash settled futures are available on 30, 60, 90
days basis. Stock index futures are also available now in a number of contracts. Each contract is to buy or
sell a fixed value of the index. Stock index future contract occurs 90 days after the contract is purchased.
In addition Options are also on cards. However future market has not picked up significantly due to the
reason that customers mostly prefer in ready trading (T+2) or CFS (having less than one month
settlement/now discontinued by SECP without providing any instrument for leveraging) in absence of
price discovery and due to convergence mechanism. Hence volume in derivatives on stock is mostly
reflected in 30 days futures.
Another platform for derivatives in Pakistan is National Commodity Exchange Ltd (NCEL) with 3 month
futures in gold. It now undertakes NCEL 10 tola futures, NCEL mini gold futures, NCEL Irri rice-6
futures and NCEL Palm oil futures. Trading volume on this exchange has remained thin in the past due to
significant rise in the commodity prices last year. Now with downward trend and later with less volatility
in prices, the exchange is expected to revive its business in the time to come.
SBP issued first of its instructions on derivatives through its Financial Derivatives Business Regulation
(FDBR) in 2004. The purpose was to develop formal OTC market in Pakistan. The regulations permitted
FX options, Forward Rate Agreements (FRAs) and Interest rate swaps (IRS). Other products including
Cross Currency Swaps (CCS) were allowed to be approved on case to case basis by the SBP. Under these
regulations on date, five banks i.e. Chartered Bank, Citi bank, Deutsce bank, Royal bank of Scotland and
UBL are the authorized dealers.
Table.1 Derivatives Market in Pakistan (FY07 and FY08)
PKR in billion
IRS*
H1FY07
78.4
H2 FY07
80.0
H1FY08
84.0
H2FY08
106.9
CCS
30.1
89.6
156.3
194.9
FX options
10.9
42.5
47.3
88.7
FRAs
.2
.3
.0
2.6
Total
119.6
212.4
287.6
393.1
*Includes IRS in PKR and FX
73
The data in Table 1 reflects growth of derivatives market of Pakistan (OTC) by 229% just in two years.
The largest segment in this remained cross currency swaps with almost 50% share in overall transactions.
The main factors behind these contracts were almost stable exchange rates (up till H1 FY08) and increase
in discount rate i.e. widening of gap between KIBOR and LIBOR. Though SBP allowed these
transactions to those corporate who were naturally hedged against exchange risk (on the basis of their
export proceeds) but when PKR declined significantly, the corporate felt the pinch. Telecom, Textile,
Cement, Fertilizer, Sugar, Refineries were the main sectors who were engaged in the CCS. Now it seems
that most of them are on their way to wind up their contracts with final position to emerge on finalization
of data for H1 FY09.
Contrary to CCS, FX options became lucrative in H2 FY08 for Corporate to hedge their exchange risk
when exchange rate came under pressure particularly in this period. Fertilizer, Telecom, Cement, textile
and automobiles were the main contributors of this contract. The activity could have and can increase
further in case SBP allows $/PKR option not available as yet. Currently transactions on FX options are
allowed against G7 currencies only.
IRS has also shown substantial growth on the basis of rising interest rate scenario. Telecom, Textile and
cement were the main contributors for the contract. Since IRS includes FCY IRS as well, hence its
volume can probably go down in H2 FY09, since one of its contributor i.e. GOP has concluded its
contract against Eurobond in Feb, 09. The contract had a share of 42% in total volume of FCYIRS.
FRAs and IRS are one and the same product in terms of structure i.e. continuation of FRA means IRS.
Both can be floating against fixed or floating against floating rate of interests. However in both cases
prime requirement is to have price discovery which is non existent since no interbank market exists in
Pakistan in this regard as yet. Only 3 authorized dealers or one or two banks have been found active in the
IRS/FRAs market. Till some activities are generated on interbank level, one may not expect growth of
swap market in Pakistan.
The case of $/PKR currency swaps are somewhat different as activities generated in them are demand
driven to meet SBP requirements against banks short/long position in their FC exposures.
Liquidity meltdown and volatility in rates are going to effect derivatives volume in H1 FY09 in Pakistan;
however importance of derivatives as hedging tool can not be denied. For this regulations are required to
be made further stiff with proper capacity building in institutions for dealing in derivatives business.
The revival of derivatives market in H2 FY09 depends on market performance taking its clues from
macro indicators on track towards recovery. However caution would prevail in the market till recession is
countered not looking possible prior FY10.
The same holds good for the world market as well. Along with fight against recession, countries are also
serious enough in containing demon of derivatives within safe limits to get benefit out of its activities
without getting their fingers burnt.
Commodity futures contracts have recently been introduced from the platform of National
Commodity Exchange Limited Karachi. Currently they only trade in Gold futures and plan to
expand the contracts on agricultural commodities and interest rates.
SBP took initiative in 2004 by granting Authorized Derivative Dealers (ADD) license to five
commercial banks
Pakistan has got volatile financial markets due to:
1.
Political Uncertainty
74
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Monetary Policy
Fiscal Policy
Foreign Investment/Disinvestment
War On Terror
Who need them
Equities/Interest Rate/Currency Portfolios
Mutual Funds
Pension Funds
Banks
Majority Stockholders/Owners
Foreign Investors
Corporate
Farmers
SBP approved Derivatives
FX Options
Dealing in FX option is permitted in G-7 currencies only with 1 year tenor and the restriction to
cover them on back to back basis by the ADDs/NMIs
Interest Rate Swaps
Dealing in IRS is permitted in PKR Rupees only up to 5 years tenor
Forward Rate Agreement
Dealing in FRAs is permitted in PKR only up to 24 months tenor
Derivatives at Bourses
Karachi Stock Exchange is the biggest stock exchange of Pakistan
As on December 31, 2007, 654 companies were listed with the market capitalization of Rs.
4,329,909.79 billion (US $ 70.177) having listed capital of Rs. 671.269 billion (US $ 10.880
billion)
KSE has been well into the 6th year of being one of the Best Performing Markets of the world as
declared by the international magazine “Business Week”
Products
Settlement Basis
Since
Ready Market
T+1
2001
Deliverable Futures
30 Days
2003
Cash Settled Futures
30, 60 & 90 Days
2007
COT (Stopped in 2006)
T+22
1994
CFS (Stopped in 2009)
T+22
2005
Product
Settlement Basis
Month 2008
SIFC Trading
90 Days
March
Sector Index Trading
90 Days
April
On coming products
75
Options
90 Days
August
Within 5 years, the volume of trades in Derivatives is expected to reach 50%of the total trading
volume at the KSE
Some analysts suggest that the March 2005 crisis was due to delivery pressures on account of
Deliverable Future Contracts, concluding in the fourth week of March 2005
To prevent another crisis, the Securities & Exchange Commission had advised the KSE to
introduced Cash Settled Futures
Non-Deliverable Future Contracts have been introduced in 2007
Non-Deliverable Futures have not gained momentum due to:
1.
2.
Absence of price discovery & convergence mechanics
Presence of scrip level circuit breakers, as opposed to Market halts
National Commodity Exchange Ltd (NCEL) is the first technology driven, de-mutualized,online commodity futures exchange in Pakistan
NCEL’s shareholders are Karachi Stock Exchange, Lahore Stock Exchange, Islamabad Stock
Exchange, Pak Kuwait Investment Company (Pvt.) Limited, and Zarai Taraqiati Bank Ltd
NCEL is regulated by Securities and Exchange Commission of Pakistan.
Pakistan's National Commodity Exchange Limited (NCEL) has formally started rice trading
based on three-month futures contracts becoming the country's first electronic commodity
trading platform.
NECL had first started operations on May 11, 2007 with three-month futures trading in gold and
the first delivery was successfully executed in mid-August
NCEL is planning to launched futures related to following commodities in the near future:
 Cotton Seed
 Oil Cake
 Palm Oil
 Rice Irri-6
76
Chapter 11
Credit Derivatives and their role in Global Financial Crisis
Typical Credit Derivatives are (1) Credit Default Swap (CDS) (2) Collateralized Debt Obligations
(CDOs).
Credit risk is the risk of financial loss due to a reduction in the credit quality of a debtor. Types of credit
risk includes Default Risk and Credit Deterioration Risk.
Default Risk is the risk that an obligor does not repay part or his entire financial obligation whereas Credit
deterioration risk is the risk that the credit quality of the debtor decreases.
Financial instruments designed to transfer credit risk from one counterpart to another are CDs and CDOs.
In this legal ownership of the reference obligation is usually not transferred. However Credit Derivatives
allow an investor to reduce or eliminate credit risk or to assume credit risk.
From a more technical point of view, credit derivatives are financial instruments, whose value is derived
from the credit quality of an underlying obligation.
The main reasons for the rise of credit derivatives are:
The general desire to reduce credit risk in the financial markets, expressed by increased regulatory
requirements as the Basel II Accord (addition of market and operational risk in addition to credit risk in
arriving at banks risk weight age assets), an increase in personal bankruptcies and recent corporate and
sovereign bankruptcies and an increase in the ability to value and manage credit risk. These risks have
visibly seen in the Latin American Debt Crisis, the saving and Loan Crisis, the Asian Financial Crisis, the
Russian Debt Crisis, Argentinean Crisis and the Enron Bankruptcy Filing
Like any swap, the CDS is an exchange of two payments: on the one hand a fee payment and on the other
a payment that only occurs if a credit event occurs.
A default swap is similar to knock-in put option. Default Swap buyer has a short position in the credit
quality of the reference obligation and vice versa.
Why Credit Default Swaps are required? Because for, hedging, Yield Enhancement, Convenience &
Cost Reduction, Arbitrage or for Regulatory Capital Relief
Buying a default swap means buying protection whereas selling a default swap means selling protection
or assuming risk.
The default swap premium, also called fee, price or fixed rate, is often referred to as the default swap
spread.
77
What Constitutes Default? They can be Bankruptcy, Failure to pay, Obligation Acceleration,
Obligation Default, Repudiation/Moratorium or Restructuring.
Settlement of CDS can take place through
Cash Settlement = N * [Reference Price – (Final Price +Accrued interest on reference obligation)]
Physical Settlement N * Reference Price
Cash flow statement of a CDS can be like this:Time
Recovery
Value
Fee
protection
seller
6 months
NA
$ 5
$ 0
- $ 5
12 months
NA
$ 5
$ 0
- $ 5
18 months
NA
$ 5
$ 0
- $ 5
24 months
NA
$ 5
$ 0
- $ 5
30 MONTHS
NA
$ 5
$ 0
- $ 5
36 months
$ 400
$ 5
- $ 600
$ 595
Total
to
Contingent
payment
protection
buyer
to
Net Cash Flow
to
Protection
Buyer
$ 570
Global Scenario
A CDO gathers reference assets such as loans, bonds, or other debt instruments and sell of pieces of
interests from the pool or tranches to investors.
78
Depending on which type of debt instrument the CDO holds, it can also be referred to as a Collateralized
loan obligation (CLO), a Collateralized bond obligation (CBO), or a Collateralized mortgage obligation
(CMO).
The process is comprised of

Ramp-up period

Cash-flow period

Unwind period
Special purpose vehicles (SPV) with securitization payments do it in form of tranches. A collateralized
debt obligation squared (CDO-squared) is backed by a pool of collateralized debt obligation (CDO)
tranches.
This is identical to a CDO except for the assets securing the obligation. Unlike the CDO, which is backed
by a pool of bonds, loans and other credit instruments; CDO-squared arrangements are backed by CDO
tranches.
79
The reasons for current US recession
The economy was at risk of a deep recession after the dotcom bubble burst in early 2000 and September
11 terrorist attacks. Central banks around the world tried to stimulate the economy by creating Liquidity.
However lenders approved subprime mortgage loans to borrowers with poor credit.
Consumer demand drove the housing bubble to all-time highs in the summer of 2005, which ultimately
collapsed in August of 2006. This Increased foreclosure activity. Declaration of Bankruptcy by large
lenders and hedge funds went immensely high. Fears gripped the market regarding further decreases in
economic growth and consumer spending.
Above all biggest Culprit of current sub prime crisis can be attributed to the behavior of Lending funds to
the people with poor credit and a high risk of default. The result was obvious.
Credit rating agencies and bond insurers played major roles in the disconnect between the true credit
quality and promised performance of the securities. If the ratings had been more accurate, fewer investors
would have bought into these securities, and the losses may not have been as bad. Rating agencies were
enticed to give better ratings in order to continue receiving service fees, or they run the risk of the
underwriter going to a different rating agency. Investors were the ones willing to purchase CDOs at
80
ridiculously low premiums over Treasury bonds. Investors are also responsible for the whole mess
because it is up to individuals to perform due diligence on their investments and make appropriate
expectations. Another party that added to the mess was the hedge fund industry. It aggravated the problem
not only by pushing rates lower, but also by fueling the market volatility that caused investor losses.
81
Chapter 12
Capital Budgeting and Risks
Cost of capital is defined as the expected return on a portfolio of all the companies existing securities. It is
the opportunity cost for investment in the firm’s assets and therefore the appropriate discount rate for the
firms average risk projects.
If the firm has no significant amount of debt outstanding then the companies cost of capital is just the
expected rate of return on the firms stock.
In case if a firm is constituted of two different assets than each should have different discount rate as per
its opportunity cost?
For example in case of speculative ventures, new products, expansion of existing business or for
improvement in technology the discount rate can be set as 30%, 20%,15% and 10%
Cost of capital is defined as the expected return on a portfolio of all the companies existing securities. It is
the opportunity cost for investment in the firms assets and therefore the appropriate discount rate for the
firms average risk projects.
If the firm has no significant amount of debt outstanding then the companies cost of capital is just the
expected rate of return on the firms stock.
In case if a firm is constituted of two different assets than each should have different discount rate as per
its opportunity cost.
For example in case of speculative ventures, new products, expansion of existing business or for
improvement in technology the discount rate can be set as 30%, 20%,15% and 10%
Normally the firms have debt in their portfolio. So in that case companies cost of capital would be = r
assets = r portfolio = debt/debt + equity (r debt) + equity/debt + equity (r equity). In case an investor
expect a return of 7.5% on the debt with a proportion of 30% in the portfolio and 15% on equity with a
proportion of 70% in the portfolio then the expected return on the asset would be = ( 30/100 x 7.5) +
(70/100 x 15) = 12.75%
The blend of debt and equity in a portfolio constitutes weighted average cost of capital (WACC)
In case you are aware of cost of your debt that you normally do than to arrive at cost of equity CAPM
should be used that says
Expected Stock return = rf + ß(rm-rf)
Setting discount rates
Some time long term government securities and short term bills have wide spreads than in that case
difference of that spread can be used as risk free rate. For example 10 years PIBs have a rate of 6% and 6
Month T Bill has a rate of 1.5, than for rf rate of 6.0-1.5= 4.5% can be used.
82
Some time you don’t have convenient price record to calculate beta than in determining discount rate
avoid fudge factors.
For example a project has one cash flow of one million after one year that suits for 10% discounting but
you are not sure about completion of the project. In this case there can be two scenarios
Possible cash flows probability
Probability
weighted CF
1.2
.25
.3
1.0
.50
.5
.8
.25
.2
Forecast
1 million
However an other option can also be added that there is a chance of 0 cash flow at year 1 This would give
a forecast of .9 million. PV=.90/1.1=.818
Possible
flows
cash probability
Probability
weighted CF
1.2
.225
.27
1.0
.45
.45
.8
.225
.18
0
.10
.0
Forecast
.90
Some Determinants of asset Betas
In cyclical firms betas are some time measured through accounting beta or cash flow beta. These are just
like real betas except that changes in book earnings or cash flow are used in place of rate of return on
securities.
Firms having higher fixed costs relative to variable costs carry higher beta i.e. higher risk.
The beta of PV revenue is a weighted average of the betas = ß fixed cost x PV fixed cost/PV revenue + ß
variable cost x PV variable cost/PV revenue + ß PV asset x PV asset/PV revenue. In this equation the
betas of revenues and variable cost should the same as they respond equally to underlying variable
remembering that ß of fixed costs is 0.
83
Certainty Equivalents
Use of constant discount rate does not hold ground in real world. So to solve this involves converting the
expected cash flow to certainty equivalents
Suppose you have a property to be completed after one year for Rs 420000. Since prices are uncertain you
apply 12% discount rate instead of 5% as rf rate. This gives a PV of Rs 375000. Now to know about
certain cash flow you use = PV = certain cash flow X 1.05 = 375000 = 393750. In other words the certain
value of Rs 393,750 has the same value as the uncertain Rs 420000 has. So in this case we arrive at two
different amounts. One is 420000-375000 = 45000 and 420000-393750 = 26250. The difference of
45000-26250= 18750 is the haircut for the risk equivalent. So CEQ or certainty equivalent is the value
equivalent of safe cash flow.
It can also be calculated through CAPM by using C1-лcov (C1-rm) x Cov (C1,rm) , where Lambda or л is
the measure of the market price of risk. It is defined as (rm-rf) σm². For example rm-rf= .08 and the σm=
.20 then lambda is .08/.20²=2
Use of Single Risk adjusted rate for long lived projects
Suppose you have two projects A (risky) and B (less risky) Obviously you would get less cash flows in B
and use higher rate of discount in A, say 12% and rf rate of 6% in case of B. In these cases you would get
following results
year Cash flow (A)
PV at 12% (A) Cash flow (B)
PV at 6% (B)
1
100
89.3
94.6
89.3
2
3
100
100
79.7
71.2
240.2
89.6
71.2
79.7
71.2
240.2
Use of Single Risk adjusted rate for long lived projects
year
Implied result would be
Forecasted cash flow for A
Certainty equivalent cash flow Deduction of risk
1
100
94.6
5.4
2
100
89.6
10.4
3
100
84.8
15.2
Not using a single risk adjusted discount rate
Suppose you have a project that would take preliminary arrangement during one year with a cost of Rs
125000. After one year the management ventures to go further with a cost of one million and with a
chance of 50% success. On success the project would generate annual cash flow of Rs 250000 in
perpetuity per year.
In this case:• C0 = -125000
• C1 = 50% chance of – 1000000 and 50% chance of 0 =.5 (-1000000) + .5 (0) = -500000
84
•
C t = 50% chance of 250000 and 50 chance of 0 = .5(250000) + .5 (0) =125000
Using 25% discount rate instead of normal 10%
•
NPV = -125000 - 500000/1.25 +Σ∞ţ=2 ( 125000/(1.25) ) = Negative 195000
In case the project is in success than using normal risk one can get positive NPV at normal discount rate
of 10% by investing one million = -1,000,000 + 250000/.1 = 1,500,000. In such case the expected pay off
would be .5 (1500000) + .5 (0) = 750000. This is better option against investment of 125000. Of course
the Certainty equivalent would be less than that. Suppose in that case if the certainty equivalent is half of
the cash flows than still the NPV would be =C0 +CEQ/1+r =-125 + .5 (750) / 1.07 =225.25 (in this case
7% discount rate has been used instead of 10%).
85
Chapter 13
A project is not a black box
Like computer which is a black box we do know that what it is supposed to do but mostly we don’t know
how it works and if something breaks how to fix it. This holds same for the projects that if its risks are
diversiable then still there is a need to understand that why the venture can go wrong,
In DCF the assumption are that companies hold assets passively. This ignores the opportunities to expand
the business if it is successful and to bail out if it is not.
This requires use of sensitivity analysis, breakeven analyses and Monte carlo simulation or use of real
options.
Sensitivity analysis
Suppose you are in manufacturing business with the market size of one million scooters. Size of your
contribution is 100000 scooters i.e. 1% of the market size. With an investment of Rs 15 billion you are
supposed to get NPV 0f Rs 3.43 billion in a period of 10 years with preliminary cash flow forecasts as
follows
(Rs in billion)
Y0
Investment
15
Y 1-10
Revenue
37.5 (assumed price per article
375000)
Variable cost
30
Fixed cost
3
Depreciation
1.5
Pre tax profit
3
Tax
1.5
Net profit
1.5
Operating cash flows
3
Net cash flow
-15
3
Now with this position you go for sensitivity analysis with respect to items that can vary. This would be
like this:-
86
Range
NPV (Rs in
billion
Market size
Pessimist
.9 mill
Expect
1 mill
Optimist
1.1 mill
Pessimist
+1.1
Expect
+3.4
Optimist
+5.7
Market share
.04
.1
.16
-10.4
+3.4
+17.3
Unit price
350000
375000
380000
-4.2
+3.4
+5.0
Variable cost
360000
300000
275000
-15.0
+3.4
+11.0
Fixed cost
4 bill
3 bill
2 bill
+4.0
+3.4
+6.5
From the previous figure it appears that the most dangerous variables appear to be market share and unit
variable cost. In pessimistic and optimistic scenarios they are affected a lot.
Limits to sensitivity analysis
Value of information is important in getting optimistic or pessimist. In some case like unit variable cost
you can arrive at near to exact information but in other cases it is very difficult and any error can put you
in difficulty, however broadly financial managers rely on scenario analysis as well. Like change in oil
prices or some other commodity prices can have impact on your products. So managers account for these
factors in their projections.
Breakeven analysis
From this managers try to asses that how bad sales can get before the project begins to lose money. This
is called Break even analysis. For breakeven analysis please see the given chart
inflow
outflow
Unit
sales Rev Y 1-10
(thousands)
Y0
Inv Variable
cost
Y1-10
Fix Cost
PV inflows
PV
outflows
NPV
Taxes
0
0
15
0
3
-2.25
0
19.6
-19.6
100
37.5
15
30
3
1.5
230.4
227.0
3.4
200
75.0
15
60
3
5.25
460.5
434.4
26.5
From this chart one can see that PV of inflows and outflows has been calculated on different assumptions.
So by plotting these PVs one can get that two lines would cross at 85000 articles that transpires that at
this point the NPV = 0. Break even charts help managers to appreciate operating leverage that is project
exposure to fixed costs. High operating leverage means high risk. In the instant case the fixed cost is not
substantial, so the managers can venture to go for reducing variable cost to improve profitability
Monte Carlo Simulation
Sensitivity analysis allows you to consider the effect of changing one variable at a time. You can consider
the effect of a limited number of plausible combinations of variables. Monte carlo simulation allows you
to consider all possible combinations. It involves three steps
•
87
Step 1.Model the project
•
Strep 2. Specify probabilities for forecasts error.
•
Step 3 Select numbers for forecast errors and calculate cash flow
Now for Step 1 Sensitivity analysis would be based on the following implicit model of cash flows
•
•
•
Cash flow :- (revenue – costs – depreciation) x (1-tax rate ) + depreciation
Revenues :- Market size x market share x unit price
Costs =
(market size x market share x variable unit cost) + fixed cost.
Now taking case of market size, either it would stay or go up or down. So it can be written down as
Market size for Y 1 in case of rise by .1 = 1 x (1 + .1) =1.1 million. For second Y it can be = Market size
Y 2 = market size Y 1 x (1 + forecast error Y 2). Like wise price adjustments can be made.
Step 2:- In specifying probabilities you have to set some range of errors as plunge is going by 15% or rise
by 5-10 % by taking advice from your marketing department.
Step 3:- The computer now works on samples from the distribution of forecasts errors resulting in
calculating cash flows for each period. In simulating cash flows the role of probability distribution is very
important as garbage in is always garbage out
Step 4:-Calculate PV based on these cash flows
Mote Carlo Simulation is bit complicated but allows you to sort out uncertainty and interdependencies in
the project.
Real Options:
Real options are the options to modify the projects to avail opportunities or even to abandon it in case if it
is not proving worthwhile. In this different scenarios are built like a tree i.e. one moving towards buoyant
demand and the other moving towards sluggish demand. They move in different steps and each step
managers have to decide about availing option on either side.
Let us take example of an aero plane company. It has two options either to buy a turboprop costing $ 550
thousand and a piston engine costing $ 250 thousand. Than the decision is taken to buy piston plane and if
demand increases at first y than to buy another plane that would be available at $ 150 thousand after one
year. However the option of availing turboprop also remains on agenda to compare profitability of both
options
Now suppose you have a forecast for getting pay off of $ 800,000 in high demand and $ 100000 in case of
low demand in case you buy new piston plane next year. in case of no expansion the pay off is estimated
around $ 410000 at high demand and $180000 at low demand. The discount rate is set as 10%. The pay
offs next year would be = probability high demand x pay off with high demand) + (probability at low
demand x pay off with low demand) i.e.
•
•
In case of expansion = (.8* x 800) + (.2* x100) = 660000 = NPV = -150000 + 660000/1.10 = $
450000
In case of no expansion = (.8* X410) +(.2* x180) = $ 364000 = NPV = -0 + 364000/1.10 = $
331000.
So obviously expansion pays
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.8 and .2 has been assumed as option No 2 at the end of year. As first option in the tree the assumption is
.6 for high demand and .4 for low demand.
Now we come back to comparing option of using Turbo and piston planes
•
•
•
•
•
For piston plane we get $ 550000 ( $ 100000 cash flow + S 450000 as NPV i.e. -150 +(.8 x 800 +
.2x 100)/1.10) at high demand and $ 185000 at low demand ( $ 50000 + NPV (.4 x220 + .6 x
100)/1.10 = $ 135000) .
The NPV = -250000 + (.6 (550) + .4 (185)/1.10 = $ 117000
In case of Turbo prop
NPV = -550000 + .6 (150) + .4 (30)/1.10 + .6 (.8 (960) + .2 (220) ) + .4 ( .4 (930) + .6 (140)
)/(1.10)² =96000
This provides a picture that piston plane option is a good option but this is not the end of the
story. For the second year we have opted to expand the piston plane that would make our NPV as
= -250000 + .6 (100) + .4 (50)/1.10 + .6 ( .8 (410) + .2 (180) ) + .4 ( .4 (220) + .6 (100) )/ (1.10)²
= $ 52000
So the value of the option to expand is 117000 – 520000 = 650000
In these cases the managers have to make tradeoffs depending on market conditions and forecasts.
Strategy and Investment decisions
To make good investment decisions you require understanding your firm’s competitive advantage. This is
where corporate strategy and finance comes together.
First lesson in this regard is to rely on market values in order to prevent forecast errors.
Example:Suppose you own a properly with a departmental store costing 100 million. It provides cash flow of 8
million a year for 10 years .The real estate prices appreciates by 3% per year Than at 10% discount rate it
gives NPV of 1 million i.e. 100 x (1.03)¹⁰ = 134 million or NPV= -100 + 8/1.10 + 8/ (1.10)²----134
+8/(1.10)¹⁰ = 1 million
In this case the ending value of real estate is very important as if it goes 120 million than the NPV would
go negative by -5 million
Such a business always requires to be divided in to a real estate subsidiary and a retailing subsidiary
which rents it and operates it.
First option in this case would have been to acquire the estate and rent it out for 10 million. It is a better
option. However suppose that property may get a rent of 7 million from its retailing subsidiary than still
the departmental store would get a pay off of 1 million i.e. 8million – 7 million =1 million. Suppose that
rental prices and the real estate prices increase by 3% than after 3 years the real estate subsidiary would
charge $ 7.43 million in Y 3. In Y 5 the pay off would become zero. So the economic life of departmental
store comes out as 5 years. After that real estate would become more valuable for some other use
Economic Rents and Competitive advantage
Economic rents are profits that more than cover the cost of capital.
With increase in global competition firms can not rely on industry structure to provide high returns
For this managers have to ensure that the firm is positioned within its industry to secure competitive
advantage, by providing cost leadership, product differentiation and focus on a particular market niche.
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Example:One industry plans to introduce new technology in respect of gargle blasters going forward for at least
three generation. For moving forward the assumptions would be (1) cost of capital say 20% (2)the
production facilities should have indefinite life (3)The demand curve and the cost of capital would remain
static (4) The tax structure is going to remain unchanged if it is in favor of the business.
Suppose for two generation i.e. for 2014 and 2022 the position is estimated as under
Technology
Capacity
Industry
Company
Capital cost/unit
Manuf cost/unit
Salvage value /
unit
First generation
120
0
17.50
5.50
2.50
24
17.50
3.50
2.50
Second generation 120
First step in this respect would be to forecast the prices: For example on entry of your company sharing
10% of the market, the current capacity may go to 382 million. In that case the price would come down to
5.75:- Demand 90x (10- 5.75) = 382 This would bring NPV of companies to = –investment + PV (price –
manufacturing cost) = -2.50 + (5.75-5.50)/.20 = -1.25 (Here discount rate of 20% has been used). At this
point it would be profitable for the companies to dispose of their business at 2.50 rather than taking loss
of -1.25.
This would bring the supply down. An equilibrium would be at 6.0 where NPV would become zero i.e. =
- 2.50 + (6.0 -5.50)/.20 =0
To reach 6 the numbers required would be 90x (10-6) = 360 so in this case the market has to withdraw
382-360 = 22 million units
However in the second generation with reduced manufacturing cost on account of your new technology
you can add number of units in the market with the same price
Introduction of new technology and its announcement in the market also adds up value of your stock
Agency problems, management compensation and the management of performance
In public entities, shareholders are the ultimate principals and top managers are the stock holder’s agents
whereas the middle management and employees are the agents of the top management.
In running a business following ingredients are required:Processes: - How companies develop plans and budgets for capital investments. How they authorize
specific projects, and how they check whether projects perform as promised.
Information: - Getting accurate information and good forecasts to decision makers.
Incentives: - Making sure managers and employees are rewarded appropriately when they add value to
the firm
Performance measurement: - You can’t reward value added unless you can measure it
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Capital investment processes
The investment processes starts with preparation of an annual budget. Further strategic planning is also
done with top-down view of the company. In fact firms capital investment choices should reflect both the
bottom up and top down processes- capital budgeting and strategic planning respectively.
After capital budget is approved companies go for appropriate proposals that require detailed forecasts,
discounted cash flow analysis and back up information.
Specific attentions are given to the departments as ;1.
2.
3.
4.
Research and development.
Marketing
Training and personnel development
Pre and post audits
Good information
Running a business requires good information that can be arranged through :1.
2.
3.
4.
Establishing consistent forecasts.
Reducing forecasts bias.
Providing information needed by the senior management.
Eliminating conflict of interest.
Incentives
Managers would act in the interest of shareholders if they have the right incentives. Suppose they are not
rightly compensated or just depends on fixed salary with no bonus, no option facility than what happens ;1.
2.
3.
4.
Work with less efforts
Undue means can be adopted
Prefer jobs in large firms
Would not make efforts in expansion of the business or indulge in some risky venture.
In nut shell agency cost can be reduced in two ways either by monitoring the managers’ efforts very
stringently or giving them the right incentives to maximize value. Both treatments differ on the basis of
the structure of the firm or country to country.
Residual Income or Economic Value Added (EVA)
Top managers are normally compensated on the basis of firms’ stock price performance but lower
manager compensation depends more on accounting measures. In judging performance, however the
focus should be on value added that is the returns over and above the cost of capital. To quantify them
one way is to know about the net return on investment which is the ratio of the after tax operating income
to the net (depreciated) book value of assets. Suppose against investment of Rs 1000 million the company
is generating earnings of 130 million than the ROI is 13% which should be grater than cost of capital say
10%.
The other way is to know about the net income after deducting the PKR return required by the investors.
This is called residual income, economic value added or EVA. The formula is EVA = residual income =
income earned – income required = income earned – (cost of capital X investment). In above case it
would be EVA = 130 - (.10 x1000) = + 30 million. In case of use of discount rate of 20% it would
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become negative i.e. -70. This can also be arrived at by using formula for knowing economic profit i.e.
EP = (ROI –r) x capital invested = (.13 -.10) x 1000 = +30 million
In case, if you propose to tie mangers remuneration to business profitability than it is better to use EVA.
Different agencies normally publish EVA of different firms.
Economic profitability
To know about the profitability of the company following formula is used :-Economic Income (EI) =
cash flow + change in present value = C1 + (P1-P0)/P0
Since any reduction in PV represents economic depreciation and any increase in PV represents negative
economic depreciation, so EI =- cash flow – economic depreciation where economic depreciation =
reduction in PV.
Rarely companies go for calculating PV; instead they use book value (BV) which is the original cost less
depreciation computed according to schedule. Book income = cash flow – book depreciation = C1 +
(BV1-BV0) or Book ROI = C1 + (BV1 –BV0)/BV0
However to be accurate, one should try to match book depreciation schedule with typical patterns of
economic depreciation
Corporate financing and Market efficiency
In some ways the investment decisions are simpler than financing decisions. NPV has always got the
pivotal role in making these decisions. However in case of financing it always confronts with given
questions:1.
2.
3.
4.
5.
Whether the firm may reinvest most of its earnings or distribute it to the stock holders.
Whether form should raise funds through equity or through debt.
Should borrow short term or on long term basis.
Should borrow through normal long term bond or through convertible bond
How to move in the market full of different options like swaps, caps and strips.
Market efficiency
It has now been established through research that prices of stocks and commodities seemed to follow a
random walk. What we mean by random walk. For instance you have Rs 100 to play with. At the end of
each week a coin is tossed and if it comes up head you win 3%, if it is tail you lose 2.5%. This process if
repeated each week gives a positive drift of .25% per week. It is a random walk because each week
successive changes in value are independent i.e. the odds each week are the same. It is obvious that there
is a very little pattern in these price movements. However it can be tested more precisely by calculating
the coefficient of co relation between each days price change and the next. In case of persistent price
movement it would be positive otherwise not
Forms of market efficiency
Economists define three forms of market efficiency which are distinguished by the degree of information
reflected in security prices
In the first level prices reflect the information contained in the record of past prices. This is called the
weak form of efficiency.
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The second level of efficiency requires that prices reflect not just prices but all other published
information such as you might get from reading the financial press. This is known as the semi strong form
of market efficiency.
Finally we might envisage a strong form of efficiency in which prices reflect all the information that can
be acquired by painstaking analysis of the company and the economy
Market anomalies and behavioral finance
To study market anomalies behavioral psychology is important since people are not 100% rational 100%
of the time.
Two points are important in this regard:1. Attitude of investors towards risk :- Prospects theory in this regard states that (a) value investors
place on particular outcome as determined by the gains or losses that they have made since the
asset was acquired or the holding last reviewed (b) investors are particularly averse to the
possibility of even a very small loss and need a correspondingly higher return to compensate for
it.
2. Belief about probabilities: - Most investors do not have a PhD in probability theory and may
make systematic errors in assessing the probability of future out come.
Six lessons of market efficiency
The efficient market hypothesis emphasizes that arbitrage will rapidly eliminate nay profit opportunities
and drive market prices back to fair value. In this regard six lessons are:1. Markets have no memory i.e. sequence of past price changes contain no information about
future changes.
2. Trust market prices since they impound all available information about the value of each
security.
3. Read the entrails i.e. if we can learn to read the entrails, security prices can tell us a lot about
the future.
4. There are no financial illusions i.e. investors are unromantically concerned with the firms
cash flows and the portion of those cash flows to which they are entitled.
5. The do it yourself alternative i.e. in an efficient market investors will not pay others for what
they can do equally well themselves.
6. Seen one stock seen them all i.e. investors don’t buy a stock for its unique qualities; they buy
it because it offers the prospects of a fair return for its risk. This means that stocks should be
like every brand or of substitute. Therefore the demand for a company's stock should be
highly elastic.
Patterns of corporate financing
Common stock is the simplest form of finance. The common stock holders own the corporation. They are
therefore entitled to whatever earnings are left over after the firms debts are paid. Stockholders have also
the ultimate control over how the firms assets are used.
The second source of finance is preferred stock. Preferred is like debt in that, it promises a fixed dividend,
but preferred dividends are within the discretion of the board of Directors. Normally legal and tax experts
treat preferred stock as part of the company’s equity.
The third important source of finance is debt. Debt holders are entitled to payment of interest or principal.
If the company is not able to pay the debt than the case moves to bankruptcy.
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Debt ratios in the recent years have increased, however variety of debt instruments are endless. The
instruments differ in maturity, inertest rate (fixed or floating), currency, seniority, security and whether
the security can be converted in to equity.
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Chapter 14
Pay out policy
The precise question in this respect is asked that what would be the effect of the change in pay out policy
considering firms capital budgeting and borrowing decisions.
Companies can pay out cash to their shareholders in two ways either through dividend or through
buyback of some of their outstanding shares.
Mostly, if taken together they result in high proportion of earnings
Repurchase of shares started worldwide in 1983 and still they are rare in our country.
Through research it has been established that worldwide only about a fifth of the companies pay
dividends. The remaining are either going through cash constraints or they are mostly growth oriented
companies.
Dividends are paid to those stock holders who are registered on a particular date. Stocks are normally sold
with dividend or cum dividend until a few weeks before the record date and then they are traded ex
dividend. The companies are not supposed to declare dividends what ever they like. For example
companies are not allowed to pay a dividend out of legal capital which is the par value of their
outstanding shares.
Most companies pay regular cash dividends but they can go for special dividend as well. They can also
issue shares at discount to the share holders as well as part of dividend. They are often in form of stock
split which is different from stock dividend where it is a transfer from retained earnings whereas in case
of stock split it is shown as reduction in the par value of the stocks.
As to second alternate, Companies can use their cash to repurchase stocks that are kept in the companies’
treasury and resold if the company needs money. There can be four ways for buy back. First one is to get
it like an ordinary investor, second one is to call them through a tender that are normally at discount, the
third option is to get them through a Dutch auction i.e. by providing different prices and the company has
the option to get them at the lowest price. The final option Is to get them through mutual negotiation.
Normally in asymmetric world investors regard those companies well who pay regular dividends or carry
out repurchase operations as it indicates that companies carrying out such operations are well placed in
cash.
On dividend pay outs, economists are divided in three groups. First one says that the dividend payments
increase firms value. The second group i.e. Miller and Modigliani (MM) says that dividend policy is
irrelevant in a world without taxes, transaction costs or other market imperfections. The third group
stresses for paying low dividends.
To show the irrelevance of dividend policy, say, one firm pays out third of its worth as dividend and
raises the money by selling new shares. The transfer of the value to the new stock holders is equal to the
dividend payment. Thus total value of the firm remains unaffected. In this process, the old stock holders
are effected. In case payment of dividend is made through sale of new shares then claim of old stock
holders would decline on account of increase in number of shares. In case of no dividend the share
holders would sell their shares to get money. This would reduce their holdings in the company
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An Illustration:Suppose dividend of Rs 10,000 is paid which is raised by new issues. The value of the company is Rs100,
000. The value of original stock holders = value of the company – value of new shares = (100,000 +
NPV) -10,000 = 90,000 + NPV. this implies that original stock holders have received cash by Rs 10,000
by incurring capital loss of 10,000 . This is just recycling of cash implying that dividend policy is
irrelevant for original stock holders.
Now on share pricing side, say the company has 1000 shares of Rs 100 with NPV of 20,000. This would
make the total stock worth as 100,000 + 20,000=120,000 /1000 = 120 per share. After payment of
dividend the position would come out as 90,000 + 20,000 = 110,000. That works out share as Rs 110
The process can be reversed through repurchase i.e. reduction in dividend is offset by reduction in number
of outstanding shares. However this also have no effect on shareholders wealth.
Repurchase policy
Switching from cash dividend to repurchase has also no effect on shareholders wealth. They forgo cash
dividend but end up holding 9000 shares with a value of Rs 100. On the same pretext suppose company
has a wealth of 1000,000 with 1000 shares. Company repurchase 10% of these shares that dose not
change the value of companies wealth, however the investors demand 10% higher prices. So with this,
company buys 10000/110 = 90.9 shares leaving outstanding shares as 909.1. In case company allows 10%
as dividend than each share would receive 1000/90.91 = Rs 11 per share. This implies that investors have
less number of shares by 10% but they have earnings stream as 10%. The value of each share is therefore
11/ (.1 x 1.1) = 100
Hence from this one can conclude that firm value can not be increased by changing the amount of the
form of distribution.
On the other hand the supporters of large payouts points out that there is a natural clientele for high pay
out stocks. Especially Trusts, endowment funds prefer high dividend stocks as they are regarded as spendable income.
Pay out policy
The leftist always favored lesser dividend in case they are heavily taxed and asked to use retained cash to
repurchase the shares. This would help stock holders to take advantage of capital gain side in case they
get tax advantage on this side. They imply that in case if dividend is taxed heavily than the investors
would prefer stocks with low dividends
Debt Policy
The firms mix of debt and equity financing is called its capital structure. Of course capital structure is not
just debt versus equity. There are many flavors of debt and many kinds of equity i.e. common and
preferred plus hybrids such as convertibles.
Like pay out policy MM also holds in case of debt policy that financing decisions does not matter in a
perfect market.
MM proposition 1 says that there should be complete separation of investment and financing decisions. It
implies that any firm can use the capital budgeting procedures without worrying about where the money
for the capital expenditures comes from. So if the firm uses a mix of debt and equity financing, its overall
cost of capital will be exactly the same as its cost of equity with all equity financing
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Financial managers try to find the combination of securities that has the greatest overall appeal to the
investors, the combination that maximizes the market value of the firm.
Suppose a firm has an equity of Rs 50000 against 1000 shares and has a debt of Rs 25000 than Value (V)
of the firm is Rs 75000. This kind of stock is known as levered equity and the investors have to bear costs
of financial leverage or gearing. Suppose special dividend is paid of Rs 10,000 by raising debt than in that
case if the worth of firm remains at 75000 than equity must be Rs 40000. In case firm value is raised to
Rs 80000 than the equity would be Rs 45000. The conclusion is that a policy which maximizes the market
value of the firm is best for the firms stock holders.
The example provides two assumptions that pay out policy can be ignored. Secondly Increase of debt can
be a risk as it may carry higher cost.
Now we move towards MM hypotheses. Suppose there are two firms one is un levered (Vu) and the other
is levered (Vl)
MM postulate says that market value of any firm is independent of its capital structure. This comes from
the view that as long investors can borrow or lend on their own account as the firm, they can undo the
effect of any change in the firms capital structure. This would keep the value of unlevered firm equal to
the value of the levered firm.
However in making debt decisions, operating income has important role to play. Suppose you decide to
structure your capital 50% of debt and 50% of equity with debt borrowed at 10% then only your policy
would pay off if you get operating income above 1000. This is illustrated in the next slide
No of shares
500
Price per share
Rs10
Market value
5000
Debt (MV)
5000
interest
10%
outcome
Operating Inc
500
1000
1500
2000
interest
500
500
500
500
Equity earnings
0
500
1000
1500
EPS
0
1
2
3
Return on Shares %
0
10
20
30
Leverage increases the expected stream of EPS but not the share price. The reason is that change in
expected earnings steam is exactly offset by a change in the rate at which the earnings are discounted.
Expected return on assets = rA = Expected operating income/ market value of all securities or
= (D/(D + E) x (rd) + ( E/(D + E) x ( r E)
Expected return on equity = rA + (rA-rD) x D/E
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MM second postulate is that rate of return on the stock of a levered firm increases in proportion to the
debt equity ratio (D/E) expressed in its market value.
rah = expected operating income/ market value of all securities. Say it is 1500/10000 = .15 or 15 %.
Suppose the firm now goes ahead with its borrowing plan with debt borrowed at 10%. The expected rate
of return on assets is still 15% then
rE = rA + (rA – rD) x D/E = .15 + (.15 -.10) x 5000/5000 =.20 or 20%
MM first postulate says that financial leverage has no effect on shareholders wealth. Postulate 2 says that
rate of return increases as debt-equity ratio increases. The answer to this is that any increase in expected
return is offset by an increase in risk.
As regards change of betas in regard to capital structure, one has to remember that debt holders bear much
less risk than equity holders. Normally large blue-chip firms have the debt beta in the range of .1 to .3
ßA = ß portfolio = ßD x (D/V )+ ßE x (E/V) . Suppose in this case if debt before refinancing has a beta of
.1 and the equity has the beta of 1.1 then ßA = (.1 x .5) + (1.1 x .5) = .6. However this kind of mix
increases risk. Suppose debt beta increases to .3 than .6 = (.3 x .5 ) + (ßE x .5) = ßE = 3
Weighted Average cost of capital
Sometime the financing decisions are stated not as maximizing overall market value but as minimizing
the weighted average cost of capital. As per MM postulate if proposition I holds that these two objectives
are equivalent but if it does not hold, then capital structure that maximizes the value of the firm would
also tend to minimizes the WACC, provided the operating income is independent of capital structure.
However this has two pitfalls. One is that shareholders always want to see the increase in firms value and
secondly in case we reduce the WAAC than reciprocally the investor would also expect more return thus
offsetting the overall impact.
Traditionalists insist for reducing WACC as the prime objective. They argue that moderate leveraging
increases the expected return but they do not move in line with postulate 2. Therefore WACC declines at
first but then rises. It reaches to some minimum at some intermediate debt ratio. Secondly in real world
the markets are not perfect.
There is a simple message that when firms changes their mix of debt and equity, the risk and expected
returns of these securities change, but the overall cost of capital does not change. This could remain as if
other complications do not enter like tax matters that makes After tax WACC = rD (1-T) x D/V + rE x (E/
V). In this rD (1-t) is after tax cost of debt
Taxes
Taxes play important role in making debt financing decisions. In US, other countries and in Pakistan
different tax rates are available for corporate or personal taxes. Tax shields are calculated according to
these rates According to MM the value of firm = value if all – equity financed + Tc D. In fact tax shield
provides extra advantage to the entity financed by the debt. According to MM it does not matter much
that how much the firm is sliced but there is another slice and that is government. Obviously if firm can
reduce the slice of the government pie than it is better-off for the stock holders.
Depending on capital structure, either the rupee of operating income will accrue to the investors as debt
interest or equity income. So the firm objective should be to borrow if (1-Tp) is more than (1-TpE) x (1Tc) otherwise it is worse
98
The trade off theory
The trade off theory emphasis upon taxes and financial distress The value of a firm can be = value if all –
equity financed +PV (tax shield) – PV ( Cost of financial distress). According to theory the firm should
increase debt until the value from PV (tax shield) is just offset at the margin by increase in PV (cost of
financial distress).
The costs of financial distress are :1.
Bankruptcy cost (a) court fees (b) indirect cost reflecting the difficulty of managing a company
undergoing liquidation or reorganization
2.
Cost of financial distress short of bankruptcy (a) doubt about a firms creditworthiness can disrupt
its operations (b) conflict of interest between bond holders and stock holders may lead to poor
operating and investment decisions ( C ) to avoid these new debt contracts can be arrived at but
they do have a cost as well.
The trade off theory balances the tax advantage of borrowing against the financial distress. Under this
theory high profitability mean high debt capacity and a strong tax incentive to use that capacity.
Pecking order theory
According to this theory the firms should use internal financing when available and choose debt over
equity when external financing is required. Pecking theory is a consequence of asymmetric information as
managers know more about firms than investors do. Debt is better than equity because as and when new
issues are announced the stock prices fall. Optimists managers would always prefer debt to undervalued
stocks. The pecking order theory says that equity will be issued only when debt capacity is running out
and financial distress threatens.
Financing and Valuation
There are two ways to take financing in to accounts.
1. First is to calculate NPV by discounting at an adjusted discount rate. Usually the after tax weighted
average cost of WACC = rD ( 1-Tc) x (D/V )+ rE x (E/V)
2. The second approach called APV or adjusted present value emphasizes to discount at the opportunity
cost of capital and then adds or subtracts the PV of financing side effects (includes interest tax
shields, issue costs, special financing packages offered by suppliers or government). APV = base –
case NPV + sum of financing effects (a) base- case value is the all equity financed venture (b)
discount rate for the base-case value is just the opportunity cost.
Firms’ value depends on free cash flows that is the amount which can be paid to all investors, debt as well
equity, after deducting cash needed for new investments or increase in working capital. FCF dose not
include interest tax shield. The WACC accounts for tax shield by using the after tax debt. APV adds PV
of tax shield to base- case value.
Calculating WACC
Step .1 Opportunity cost of capital = r = rD X (D/V )+ rE x (E/V)
Step 2 Calculate cost of debt at the given debt ratio and then calculate cost of equity = rE = r + (r – rD )
x (D/E)
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Step 3. Suppose current debt ratio is .20 that you want to double it i.e. .40 than step 3 would require
recalculation of WACC. Suppose cost of debt is 6% and equity is 12.4% than going back to step 1 it
would be
r = .06 x (1-.35) (.4) + .124 x (.6) = .0900 = 9.00%
Now coming back to debt equity ratio of .2/.8 =.25 we assume that debt cost remains the same but equity
cost comes down to 10.8 than =
WACC = .06 ( 1-.35) (.2) + .108 (.8) = .0942 or 9.42%
Businesses are usually valued in two steps. First FCF are forecasted to a valuation horizon and discounted
back to PV. The horizon value is usually estimated by using the perpetual growth DCF formula or by
multiplying forecasted EBIT or EBITDA by multiples observed for the similar firms .After valuing the
business subtract its debt to get the value of the firms equity
Debt financing
Government securities provide benchmark rates in the market as they are risk free in a sense of default
The valuation of zero coupon and coupon bearing bonds has already been explained in the earlier chapter.
However in addition, it is apprised that normally these securities are issued at nominal rate but in some
countries to accommodate inflationary impacts, inflation linked bonds i.e. TIPS are issued.
Spot rate is the rate fixed today for a one period loan i.e. PV = 1/1+r1. The term structure is the series of
these spot rates. Yield to maturity is the single rate of discount for cash flows arriving on at a bond.
In bonds, prices are always inverse to yields. Term structure represents the yields at different time zones.
Sensitivity of Bond prices-duration
Sensitivity of Bond prices are measured through duration and convexity analysis. They are calculated on
the basis of relationship of prices and yields on a bond
The duration of a bond is calculated as = ( 1 x PV (C1))/V + (2 x PV (C2))/V + (3 X PV (C3))/V ………
=
Or it can be written down as (1+y/y) – {(1+y) + T (c-y)}/ C {(1+y) – 1 }} + y
In this C= Coupon rate
T= number of coupon periods (yield to maturity)
Y = Bond yields per payment period
Example 10 % coupon Bond with 20 years paying capacity seminally would have 5 % semiannual coupon
& 40 payments. The result would be incase the yields to maturity is $% = 1.04/.04 – 1.04 + (.05-.04)/
.05{(1.04)is to power40 – 1 } +.04 = 19.74
Formula for yield to maturity is = 102 = ∑is to power 40 x 5/ (I +r) is to power t + 100/ (1+r) is to power t
Modified duration is just an addition to get that how much change in duration can take place against 1 bp
change in prices.
The higher the yields the lesser would be the duration.
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Sensitivity of Bond Prices-Convexity
In finance, convexity is a measure of the sensitivity of the duration of a bond to changes in interest rates.
There is an inverse relationship between convexity and sensitivity - in general, the higher the convexity,
the less sensitive the bond price is to interest rate shifts, the lower the convexity, the more sensitive it is.
Calculation of convexity
Duration is a linear measure or 1st derivative of how the price of a bond changes in response to interest
rate changes. As interest rates change, the price is not likely to change linearly, but instead it would
change over some curved function of interest rates. The more curved the price function of the bond is, the
more inaccurate duration is as a measure of the interest rate sensitivity.
Convexity is a measure of the curvature or 2nd derivative of how the price of a bond varies with interest
rate, i.e. how the duration of a bond changes as the interest rate changes. Specifically, one assumes that
the interest rate is constant across the life of the bond and that changes in interest rates occur evenly.
Using these assumptions, duration can be formulated as the first derivative of the price function of the
bond with respect to the interest rate in question. Then the convexity would be the second derivative of
the price function with respect to the interest rate.
In actual markets the assumption of constant interest rates and even changes is not correct, and more
complex models are needed to actually price bonds. However, these simplifying assumptions allow one to
quickly and easily calculate factors which describe the sensitivity of the bond prices to interest rate
changes
.
Why bond convexities differ
The price sensitivity to parallel changes in the term structure of interest rates is highest with a zerocoupon bond and lowest with an amortizing bond (where the payments are front-loaded). Although the
amortizing bond and the zero-coupon bond have different sensitivities at the same maturity, if their final
maturities differ so that they have identical bond durations they will have identical sensitivities. That is,
their prices will be affected equally by small, first-order, (and parallel) yield curve shifts. They will,
however start to change by different amounts with each further incremental parallel rate shift due to their
differing payment dates and amounts. For two bonds with same par value, same coupon and same
maturity convexity may differ depending on at what point on the price yield curve they are located.
Suppose both of them have at present the same price yield combination; also you have to take into
consideration the profile, rating etc of the issuers; suppose they are issued by different entities. Though
both the bonds have same p-y combination bond that may be located on relatively more elastic segment of
the p-y curve compared to bond II. This means if yield increases further, price of bond II may fall
drastically while price of bond I won’t change, i.e. bond II holder are expecting a price rise any moment
and so reluctant to sell it off, while bond I holders are expecting further price-fall and ready to dispose it.
This means bond II has better rating than bond I.
So the higher the rating or credibility of the issuer the less the convexity and the less the gain from riskreturn game or strategies; after all less convexity means less price-volatility or risk, less risk means less
return.
Algebraic definition
If the flat floating interest rate is r and the bond price is B and d is the duration then the convexity C is
defined as
C = 1/B x (d² (B (r) )/d r²
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Term structure
The expectation theory and liquidity preference theories explain about term structure
Expectation theory says that investors would earn the same expected return in a two year loan as from
investing in two successive two years loans i.e. (1 +r2²) = (1 +r1) x ( 1+ f2) or if done in two years
successive loans than for period 1 = (1 +r1) x (1 + 1r2). suppose the one year spot rate is 1.2% and two
years spot rate is 1.8% than f2 would be (1+ r2)²/ ( 1 +r1) -1 or = (1.018)²/(1.012) -1 = .024 or 2.4%.
One should remember that long term bond prices are more volatile than short term bonds. This creates
grounds for liquidity preference theory which is based upon assumption that investors holding long term
bonds are right in demanding higher risk premium usually called liquidity premium
Kinds of Debt
Debt can be either procured from the banking sector or through accessing capital market. We are going to
look for the category derived from the market. They are in form of bonds. In Pakistan they are termed as
Term Finance Certificate to incorporate Islamic features. The bonds can be issued in the domestic as well
in the international market. The bonds first issued comprise primary market and than on later trading
comprise secondary market.
The corporate debt is riskier than government debt as it carries default risk more than the government
securities. Its risk premium is set on credit ratings given by approved rating agencies. It also embodies
options of call, put, collars and can be a convertible security in to equity. Investment grade bonds are up
to BBB and lower than this i.e. Ba or BB the bonds are categorized as junk bonds.
In case of their valuation the steps are i.e. Bond value = Bond value assuming no chance of default-value
of put option on assets. Hence overall Bond value can be = value of call + PV of promised payment to the
bond holders = value of put + asset value.
In case of valuing government loan guarantees the value of guarantee = loan value with the guarantee –
loan value without the guarantee.
Index of creditworthiness (Z) is used to find the credit scoring assigned to some company. In this Z
=return on assets + 5 interest cover. This is also called Multiple Discriminant analysis (MDA). In this
different weighted is assigned to five covers = Z = (w) X (net working capital)/ (total assets) + (w) X
(retained earnings)/ (total assets) + (w) X (EBIT)/ total assets + (w) X (shareholders equity)/ (total
liabilities) + (w) X (sales)/ (total assets). The companies with less than 1.20 are predicted to go bankrupt
and score in between 1.20 and 2.90 is termed as hovering in the grey area.
There are other market based models as well including VAR that has been discussed in the derivatives
chapter.
Ratio
AAA
AA
A
BBB
BB
B
CCC
EBIT interest cover
21.4
10.1
6.1
3.7
2.1
0.8
0.1
102
Return on capital %
34.9
21.7
19.4
13.6
11.6
6.6
1.0
Gross profit margin %
27.0
22.1
18.6
15.4
15.9
11.9
11.9
Total Debt/Capital %
22.9
37.7
42.5
48.2
62.6
74.8
87.7
The bonds can be categorized as domestic bonds, foreign bond (issued by a foreign company) or a
Eurobond (issued by a local company in the international market)
The bond issuance requires following formalities:1.
2.
3.
4.
Approval from SECP in case of listing.
Rating by a rating agency
Trust deed signed between bond holder and a trust company.
Terms of bonds indicating maturity period, mode of payment, whether issued on fixed or floating
rate of return, whether incorporates call, put ,collars or convertible options, seniority in payment,
unsecured or secured. The majority of secured bonds consists of mortgage bonds. Short term
unsecured securities are mostly termed as notes. Equipment trust certificates are normally issued
to finance new rolling projects. Asset backed securities are the sale of cash flows from the assets
formed in bundles of lended money to some one. Repayment provisions: - to ensure timely
payments companies normally form sinking funds in which mandatory some amount is to be
satisfied. For call and put options the company has to set aside some amount before time
Convertible Bonds are issued to raise money at cheaper price as it gives the right to the investors to
convert it in to the equity. The following three factors play an important role in valuing convertible bond.
(1) Dividends, as their payments deprive bond holders to get them, however if they are quite high than
investor would prefer to get them before maturity (2) option value of convertible can result in dilution of
shares since their numbers can increase, but if investors prefer to buy them from an exchange than this
may not happen (3) Changing bond value can impact on convertible value since most of the time bond
prices remain on changing and particularly in case of default the bond holder can not be even sure of the
value of its bond.
Private placements and project finance are different from funds sought through listed securities, since in
private placements you procure funds from one or two financial institutions just by signing an IOU. This
arrangement is very simple but on flip side the security so issued is difficult to trade in the secondary
market. The publicly issued bonds on the other hand are highly standardized products and can be
frequently traded.
Project finance is on the other hand is a loan extended for a specific project. Normally they are of longer
term and mostly practiced by large international banks. In this regard we would carry out a case study of
HUBCO.
Corporate financing
Corporate financing can be arranged by issuing different securities. Normally it starts with venture capital
which is an equity investment in young private companies till they reach to the point where they can raise
their funds through public offerings. Such venture capital is normally provided by the investment
103
institutions or by wealthy individuals. However going forward financial managers have to take care of
following points in deciding how to issue capital.





Larger is cheaper.
Watch out for under pricing.
The winners curse may be a serious problem for IPOs.
New stock issues may depress the price.
Shelf registration often makes sense for debt issues by black chip firms
Leasing
A rental agreement that extends for a year or more and involves a series of fixed payments is called a
lease. The lease contract specifies the monthly or semiannually payments, with the first payment usually
due as soon as the contract is signed. The payments are usually level, but their time period can be tailored
to the users need.
The questions can be asked that why to get an equipment rather to buy it. The reasons can be (a) in short
term they are convenient (b) maintenance is normally provided © standardization can lead to low cost (d)
tax shield can be used. On the other hand leasing (a) avoids capital expenditure controls (b) leasing
preserves capital © leasing may be off balance sheet financing or (d) may affect book income
Operating leases have to be calculated on the basis of equivalent costs. For example in a case of machine
the annual rental payments have to be sufficient to cover the PV of all the costs of owning it and operating
it. The decision rule in this regard is that buy the machine if the equivalent cost of ownership and
operation is less than the best lease rate you can get from an outsider
For operating leases the decision centers on lease v/s buy, however for financial leases the decion
amounts to lease v/s borrow. Financial leases extend over most of the economic life of the leased
equipment. They are not cancellable and their payments are fixed obligations equivalent to debt service.
A financial lease is superior to buying and borrowing if the financing provided by the lease exceeds the
financing generated by the equivalent loan. The principle implies this formula = Net value of lease =
initial financing provided – ΣΝ X lease cash flow/ {1+rD (1-Tc)}t.
From lessor point of view following cash flows can give the value. Suppose in a case where Tc = 0 and
the cash flows are to be discounted than value of lease would be as per given chart = +100 –Σ7 x
16.9/1.10⁷ = +100 -99.18 = .82 or 820. so in this case the net gain is 720
Y0
Cost
+100
payments
-16.9
104
1
2
3
4
5
6
7
-16.9
-16.9
-16.9
-16.9
-16.9
-16.9
-16.9
Chapter 15
Financial analysis and planning
Financial planning rests on financial analysis considering key financial ratios summarizing companies
financial strengths and weaknesses.
Executive papers rest on balance sheet, income statement, cash flow statements and statements reflecting
plowback and payout positions.
For financial planning the basics questions can be
1.
2.
3.
4.
5.
External capital required.
Operating cash flow.
Investment in net working capital.
Investment in fixed assets.
Dividends
Four steps are required in order to arrive at final conclusions.
1. Projection of next years operating cash flow.
2. Projection of next years additional investment in working capital and fixed assets.
3. To calculate difference between step 1 and 2 above to arrive at deficit for deciding that in
which way it is going to be met like through issuing new securities or through some other
means.
4. Finally preparing a Performa balance sheet to incorporate the additional assets and the
increase in debt and equity.
Finally internal growth rate and sustainable growth rates are arrived at by looking in to:Internal growth rate = (retained earnings/net assets) X (net income/equity) X (equity/ net asset)s =
(Plowback ratio x return on Equity X equity/net assets)
Sustainable growth rate = plowback ratio X return on Equity
Working capital management
Working capital management is management of short term assets and liabilities.
It starts with looking in to accounts receivables , than comes the management of inventory. Next and
final task is to look for the cash management.
Accounts receivables are made up of unpaid bills or trade credit. The remainder is made up of consumer
credit. In this regards, following questions are important i.e. how much time they would take in final
payment, whether they are supported with some IOUs, whether credit extension has been done on the
basis of credit worthiness and finally how the settlement is going to take place.
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To secure bills, receivables commercial draft as sight draft or time draft can be arranged. Further bankers
acceptances can be used or in selling goods, overseas irrevocable letter of credit can be arranged. Firms
are not allowed to discriminate between customers by charging them different prices.
In credit decision making either you can refuse credit. In case you offer credit than considering
probability of recovery as Þ, the expected profit would be = Þ PV (Rev-Cost) – ( (1- Þ) PV (Cost)
In extending credit one has to focus on maximizing profit, keep an eye on dangerous accounts, and look
beyond the immediate orders.
In collection of bills, large firms rely on full fledged credit operation, however small firms that mostly
rely on arrangement known as factoring. In this, job is farmed out to a factor. The factor and the client
than agree on credit limits for each customer and on the average collection period. The client than notifies
each customer that the factor has purchased the debt. Thereafter for any sale the client sends a copy of the
invoice to the factor, the customer makes payment directly to the factor and the factor pays the client on
the basis of the agreed average collection period regardless of whether the customer has paid or not.
Inventory management is the second most important function of the working capital management.
Inventories mostly consist of raw material, work in process or finished goods awaiting sale and shipment.
Holding inventories carry cost like storage and insurance and further they earn no interests but contrarily
carry risk of spillage. In US the companies have brought down the levels of inventories to the firm assets
from 12% to 6%. Toyota of Japan follow ‘just in time approach’ meaning that auto parts are kept at
minimum and ordered on as and when required basis
Cash management is an important part of working capital management. In order to keep the firm ready to
meet its cash requirements they do keep a balance in between cash and investments made in short term
securities.
However there are several ways to use cash efficiently like in US they can be kept in money market
deposit accounts (MMDA) that does not come under reserve requirements and pays interest. Payments
can also be arranged through debit or credit cards or through checks. Electronic fund transfers have made
it easy for transfer of cash in bulk.
For short term investment, different options are available like investing in T-bill, Bank time deposits and
certificate of deposits, Commercial papers, term Finance Certificates, Bankers acceptances, Repo,
common and preferred stocks, mutual funds etc etc.
Short term financial planning
Short term financial decisions differ in two ways from long term decisions such as capital investment and
the choice of capital structure. Firstly they generate short lived assets and liabilities and second they are
usually easily reversed.
All businesses require capital that is mostly invested in plant, machinery, inventories, accounts
receivables and in all the other assets that are required to run the business efficiently. Typically these
assets are not purchased all at once but obtained gradually and the total costs of these assets are called the
firms cumulative capital requirement. These cumulative requirements grow irregularly depending on
seasonal factors.
Most financial managers attempt to match maturities of assets and liabilities i.e. they finance long lived
assets like plant and machinery with long term borrowings and equity. Secondly most firms make a
permanent investment in net working capital i.e. current assets – current liabilities. This investment is
financed from long term sources. Some firms choose to hold more liquidity than others since there are
106
some advantages to holding a large reservoir of cash particularly for smaller firms that face relatively high
cost to raise funds on short notice
To grasp changes in working capital, the financial analysts first try to collapse single figure for the
working capital i.e. like for Y 2003 -2004 the working capital comes out as 30 against 55 as current assets
- 25 as current liabilities . After this they try to match it with their sources and uses as
•
•
•
•
Sources (value in PKR)
Issued long term debt
Reduced inventories
Increased accounts payable
7
1
7
•
•
•
•
Cash from operations :
Net income
Depreciation
Total sources
12
4
31
•
•
•
•
•
•
•
•
Uses
Repaid short term bank loan
Invested in fixed assets
Purchased marketable securities 5
Increased accounts receivable
Dividend
Total uses
Increase in cash balance
5
14
5
1
30
1
Cash flows and profits are constantly monitored by capturing different characteristics of working capital
that can be cash, raw material, finished goods or receivables.
Another problem for financial manager is to forecast future sources and uses of cash. These forecasts
serve two purposes. First they provide a standard or budget against which subsequent performance can be
judged. Second they alert the manager to future cash flow needs. Cash in fact has a habit of disappearing
fast. Preparing the cash budget, its inflows and out flows are accounted for by establishing a minimum
operating cash balance to absorb unexpected cash inflows and outflows.
Short term financing plan is also prepared. This is done by arranging loans from banks or stretching
payables. Further funds can be arranged through issuing securities, commercial papers or through
syndicated loans. This all require careful calculation of inertest rate and term to maturity.
Mergers
Scale and pace of merger activity have grown remarkably in the current world. However merger adds
value only if the two companies are worth more together than apart.
The financial economists now view mergers as part of a broader market for corporate control since
activities in the market goes far beyond ordinary mergers. It includes leveraged buyouts, spin offs,
divestitures and privatization.
Mergers can be of three kinds i.e. (1) horizontal meaning combination of two firms in the same line of
business, (2) vertical meaning combination of two companies at different stages of production and (3)
conglomerate meaning combination of companies in unrelated lines of business.
107
Reasons for mergers are mostly to benefit from economies of scale or economies of integration, acquire
complementary resources or surplus funds, eliminate inefficiencies and finally to go for industry
consolidation. Some other reasons can be to go for diversification, to increase EPS and to lower
financing costs.
Mergers gains can be estimated in case of merger of firm A and B as Gain = PV AB – (PVA + PVB) = Δ
PV AB
In case of takeover of firm B the cost can be estimated as Cost = cash paid – PVB. For estimating NPV
the equation would be NPV = gain – cost = Δ PV AB – (cash – PVB)
Some companies begin their merger analysis with a forecast of the firms future cash flows. Any revenue
increases or cost reduction attributable to the merger are included in the forecast which are discounted
back to the present and compared with the purchase price i.e. Estimated net gain = DCF valuation of
target, including merger benefits – cash required for acquisition.
In case the stock prices anticipate the merger than the market value of B would be different and most
probably higher than its intrinsic value. This always makes the task difficult for financial managers to
evaluate the actual worth of B.
Sometime the merger is financed by the stock than in that case its cost would be = N (number of shares
each worth P AB) X P AB – PV B.
In case of merger financed through stocks the information available to acquiring firm A can play some
role as they are supposed to have more information than outsiders. This is called asymmetric information.
Mechanics of merger can be as follows (1) See what the law says (2) form of acquisition to be decided
that whether the full fledge merger is to take place by assuming all the assets and liabilities or the
acquisition is to be financed through stocks or by taking sellers assets partially or completely. In third
form the payment would be made to the selling firm rather than directly to its stockholders.
Merger accounting is than the next step. In this if the premium is allowed above book value of the selling
firm than obviously it may be due to true value of tangible assets or due to intangible assets like goodwill
or due to some tax advantages attached with the selling firm.
Mergers come in waves. Historically they occurred in 1920, 1967-69, 1980, 1990-2000. Mostly they
have been followed with surge in stock prices. However the exact reasons can be found in some other
factors as well like advancement in technology or to increase productivity or to match with some
regulatory requirement. But results suggest that there are good as well bad mergers taken place in the
history.
Corporate restructuring
Apart from mergers the company structure can be altered with some other ways like Leveraged Buyouts
(LBO), spinoffs and carve-outs, privatization, workouts and bankruptcy.
LBO differs from ordinary acquisitions in two ways. First a fraction of the purchase price is financed by
debt. If not all, of this debt is junk i.e. below investment grade. Second the company goes private and its
share no longer trade on the open market. The LBOs shares is held by a partnership of investors and is
often referred to as private equity. When the group is led by the companies management the transaction is
called the management buyouts (MBOs). The three main characteristics of LBOs are high debt (designed
to be paid down), incentives via stock options or direct ownership of shares and finally private ownership.
108
Spin off or split up is a new independent company created by detaching part of a parent company’s asserts
and operations. Shares in the new company are distributed to the parent companies stockholders.
Carve outs are similar to spin offs except the shares in the new company are not given to the existing
shareholders but are sold in a public offering.
Privatization is a sale of government owned company to private investors
In bankruptcy some firms are forced to reorganize by the onset of the financial distress. At this point they
need to a reorganization plan with their creditors or file for bankruptcy.
Governance and Corporate control
The world financial system is dominated by bank based or market based financial systems. US and UK
are dominated by market based systems whereas Japan and EU are dominated by bank based systems.
Other than these, their exists family conglomerates (groups) as well. Each have their strengths and
weaknesses. Banking system suits for well established corporate. Market based system demands
transparency and allows free access to market transactions. Finally conglomerates come in where
businesses are at start or they are short of funds.
With increase of financial market activities corporate governance needs to come in. In fact governance is
the effort to improve life in entirety, quality of output, efficiency in delivery of products of an
organization and ensuring the best value for the money. In theory and practice there are multiplicities of
factors shaping governance of a business organization. Therefore business needs to be governed by a set
of rules which reflects interest of all stakeholders. Corporate governance sets up a system of entrusting
the Directors and Managers with responsibilities in relation to running corporate affairs. On the other
hand it is also concerned with the accountability of those Directors and Managers. The whole affair of the
Corporate Governance lies in concepts like transparency, accountability, merit, ethics, fairness and
responsibility. To be simple corporate Governance is a set of relationship between a company
management, its Board of Directors, its share holders.
The Cadbury Committee document, the OECD code combined, Combined code of London Stock
Exchange, the Blue Ribbon Committee in the US, Code of Corporate governance issued by the SEC of
Pakistan and Prudential Regulations issued by the State bank of Pakistan are some of its examples
109
Chapter 16
About Finance
One does know
NPV: - If one buys cash flow at cheaper price as compared to the capital market, than obviously it is
going to pay. This is the simple idea behind NPV which is calculated by discounting future cash flows.
The CAPM:- In investment there are two kinds of risks. One that you can diversify and one that you can
not diversify. The non diversifiable risks are measureable. The same is affected by a change in the
aggregate value of all assets in the economy. This is called the beta of the investment. Through CAPM
one can determine it rate of return and this is the element which the people really cares about.
Efficient Capital Market ideas rests on three flavors i.e. The weak form based on random walk theory,
semi strong form saying that prices reflect all public information and strong form saying that prices reflect
all acquirable information. The efficient capital market ideas started working since 1970.
Value additivity and the law of conversation of value sates that the value of the whole is equal to the sum
of the values of the parts. Like PV (project) = PV C1 + PV C2 +------PV Ct. Further in case of projects A
and B the same would be equal to PV of a composite project AB.
Capital structure theory says that in perfect markets, changes in the capital structure do not affect value. It
emphasize that as long as the total cash flow generated by the firms assets is unchanged by the capital
structure, the value of the firm is independent of its capital structure.
Option theory refers to opportunity to trade in the futures on terms that are fixed today. Different models
like Binomial or Black Schole are now providing ways to value an option which is helping financial
managers to arrive at their decisions.
Agency theory sorts out the conflict of interests within a company to make it a profitable entity.
One does not know?
Project Risks and Returns;- we know that positive NPV is the key to success but some time the
companies in the same group do not perform in line. This bring forward questions that whether the rents
are windfall gains or they have taken place due to some planning. Still research is going on to find out its
valid answers.
Risk and return are yet to be determined with precision. For instance CAPM provides a way to find out
effect of risk on value of an asset but still there is no certain way to get exact values keeping in view some
statistical or theoretical facts. APT or Three factor model of Fama and APT provide some answers but
this do not end up with the precise answer.
Efficient market theory is perfect but it does not cover the reasons for abnormal market behavior.
110
Closed end funds are portfolio of common stocks, so it can be presumed that from values of these stocks
one can get the value of closed end funds, but this is not the case as normally stocks of the closed end
funds sell less than the value of funds portfolio. For this no exact explanation is available.
About new securities and new markets search is going on and one can not end up with this search any
time.
About pay out policy one can not be sure and lay down a common policy as it depends on certain facts
and ground realities.
Very little is known about that what risks should a firm take and secondly how to quantify the value of
liquidity required by it for smooth sailing.
About mergers and difference in financial architecture there exists no single hypothesis to explain about
their worth making or failures.
The above is the list about known or unknown facts about finance. This provides you a base to start
working on your own list and work on it.
111
Chapter 16
Exercises
1. Investment is made of Rs 100.000 with assurance to resell it at Rs 115000 at the end of
year.
(a) What would be its rate of return
(b) If the rate of interest is 10% what would be its PV
(c) What would be its NPV?
(d) Whether the investment is in profit or other wise.
2. A zero coupon bond having inflow of Rs 100,000 at end of one or two year has a yield of
10% pa
(a) What is its PV in case of term to maturity of one year and what would be its PV in
case of term to maturity of two years.
(b) Investment of Rs 100,000 today in case of two years coupon bearing bond bears a
yield of 10% pa, what would be its PV.
3. If the rate of interest is 10% and the aim is to provide Rs 100000/- each year in perpetuity.
What would be the amount that must be set aside today and in case one decides to give an
increase of 4% per year than what would be the amount to be set aside today.
4. A building can be sold today at Rs 420000/ with an offer to rent it at Rs 8000 per annum
for two years. The rate of appreciation for the building is 3% per annum. The discount rate is
5%. Find minimum rent through annuity calculation. The annuity factor for two years at 5%
is 1.859.
5. Find PV of equity when an investor is expecting its resale value at the end of year as Rs
110 with dividend as Rs 5 and rate of return as 15%. In case of second year dividend with an
increase of 10% the equity has a resell value of Rs 115. Find its PV as well.
6. Elaborate term structure of interest rate in Pakistan in terms of Government securities,
Repo, KIBOR. Draw yield curve of risk free rate in Pakistan when 3, 6, 12 months T Bill
rates are 12.43%,12.58% and 12.46% and 3, 5, 10, 20 and 30 years PIB yields are 12.29%,
12.38%, 12.54%,13.20% and 13.45%. Whether this yield curve is steep, humped or inverted
and what it signifies.
7. What are the formulas for the variance, standard deviation, covariance coefficients and
correlation Coefficients and R Squared? If R squared number is .25 than what this implies.
8. Explain Modern portfolio, CAPM, Arbitrage Pricing and three factor pricing theory just by
definition.
112
9. Write-down ratios of the followings.
(a) Price earning multiple (PER)
(b) Book value per share (BVPS)
(c) Cash flow per share
(d) Quick or acid test ratio
(e) Return on assets (ROA)
(f) Return on Equity (ROE)
(g) Time interest earned (TIE)
10. In determining projects, what is meant by sensitivity analysis, break even analysis, montcarlo simulation and real options? Explain with examples.
11. What are the main sources of funds for the corporate? On what grounds they are designed by
considering pay out or repurchase of shares decisions. How far Miller and Modigliani postulates
holds true in designing these policies. Since MM postulates are in the middle, what are other two
views?
12. What are the six lessons of the market efficiency? Whether you agree with them. Please
explain by giving examples.
13. What are derivatives and how far they are relevant in mitigating financial risks? Name five
kinds of derivatives with their definition. What are the advantages and disadvantages of
exchange traded and OTC traded derivatives.
14. What are the main ingredients of working capital management? How they are arranged.
Please explain. Further elaborate on techniques that how short term finance is arranged and what
are the instruments used for the purpose.
15. The known ideas in Finance are (a) NPV (b) Capital asset pricing model (c) efficient markets
(d) value additivity and the law of conservation of value (e) capital structure theory (f) option
theory (g) agency theory. Please explain all of them briefly.
MCQ’s
1. Finance is (
). It is categorized under ( ) ( ) ( ).Financial managements is nothing
but (
). Companies buy (
) assets. They include tangible assets as (
) and intangible
assets as (
). In order to pay for these assets they sell (
) assets as (
). The
decision about which asset to buy is termed as (
) or (
). The decision about how to
raise the money is termed as (
) decision. The appropriate words to be put in are (1)
financing, (2) real (3) bonds (4) investment (5) airplane (6) fund management (7) financial (8)
capital budgeting (9) brand names (10) science of controlling revenue and expenditure (11)
Corporate (12) personal (13) Public.
2. (a) True or false
1. Distant cash flows are riskier than near term cash flows. Therefore long term projects
require higher risk adjusted discount rates.
2. Financial mangers should always use the same risk adjusted discount rate for short and
long lived projects.
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(b) Which of the company is likely to have the higher cost of capital?
1. A’s sale force is paid a fixed annual rate. B’s is paid on commission basis,
2. C produces machine tools. D produces break fast cereal.
(c) Which discount rate is IRR?
CO
1.
2.
3.
-4000
-4000
-4000
C1
C2
2000
2000
2000
4000
4000
4000
Discount rate
0%
50%
28%
NPV
+2000
-889
0
3. True or false
(a) Sensitivity analysis is unnecessary for the projects with asset betas that are equal to
zero.
(b) Sensitivity analysis can be used to identify the variables most critical to a projects
success.
(c) If only one variable is uncertain sensitivity analysis gives optimistic and pessimistic
values for project cash flow and NPV.
(d) The breakeven sales level of a project is higher when breakeven is defined in terms of
NPV rather than accounting income.
(e) Monte Carlo simulation can be used to help forecasts cash flows.
(f) Monte Carlo simulation eliminates the need to estimate a projects opportunity cost of
capital.
(g) Decision trees can help identify and describe real options.
(h) The options to expand increases NPV.
(i) High abandonment value decreases NPV
(j) If a project has positive NPV the firm should always invest immediately.
4. True or False
(a) A firm that earns the opportunity cost of capital is earning economic rents.
(b) A firm that invests in positive NPV ventures expects to earn economic rents.
(c) Financial Managers should try to identify areas where their firms can earn economic
rents, because it is there that positive NPV projects are likely to be found.
(d) Economic rent is the equivalent annual cost of operating capital equipment.
(e) In Pakistan most shares are owned by the individual investors.
(f) An insurance company is a financial intermediary
(g) Investment in partnership can not be publicly traded.
5. Fill in the blanks using following terms, floating rate, private equity, Short sale, common
stock, convertible, subordinated, preferred stock, senior, warrant
a. If a lender ranks behind the firm’s general creditors in the event of default, his or her
loan is said to be___________.
b. Interest on many bank loans is based on a ____________ of interest.
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c. A(n) ___________ bond can be exchanged for shares of the issuing corporation.
d. A(n)____________gives its owner the right to buy shares in the issuing company at a
predetermined price.
e. Dividends on____________can not be paid unless the firm has also paid any
dividends on its___________.
f. Equity that is not publicly traded and is used to finance the business start up,
leveraged buyouts etc are known as ______________.
g. ______________ is the sale of security that investor does not own.
6. True or false. Use of the WACC formula assumes
a. A project supports a fixed amount of debt over the projects economic life.
b. The ratio of the debt supported by a project to project value is constant over the
projects economic life.
c. The firms rebalance debt each period, keeping the debt to value constant.
7. True or false. The APV method
a. Starts with a base-case value for the project.
b. Calculate the base-case value by discounting project cash flows, forecasted assuming
all equity financing at the WACC for the project.
c. Is especially useful when debt is to be paid down on a fixed schedule.
8. True or false
a.
b.
c.
d.
e.
Longer maturity bonds necessarily have longer durations.
The longer bonds duration, the lower its volatility.
Other things equal, the lower the bond coupon, the higher its volatility.
If interest rates rise bond duration rise
Convexity is the relationship between yield and prices, the higher the convexity the
weaker
the relationship is.
f. Corporate Bonds carry lesser return than government securities.
g. Yield curve is the relationship between price and yield.
h. Term structure is the relationship between time horizon and yields of the bonds.
9. Match (1) Direct (2) Full service (3) operating (4) Financial (5) Rental (6) Net (7) Leveraged
(8) Sale and lease back (9) Full Payout with the following statements.
a.
b.
c.
d.
e.
f.
g.
The initial lease period is shorter than the economic life of the asset.
The initial lease period is long enough for the lessor to recover the cost of the asset.
The lessor provides maintenance and insurance.
The lessee provides maintenance and insurance.
The lessor buys the equipment from the manufacturer.
The lessor buys the equipment from the prospective lessee.
The lessor finances the lease contract by issuing debt and equity claims against it.
10. True or false
115
a. Hedging transactions in an active future market have zero or slightly negative NPVs.
b. When you buy a future contract, you pay now for delivery at a future date
c. The holder of a financial future contract misses out on any dividend or interest payments
made on the underlying security.
d. The holder of a commodity futures contract does not have to pay for storage costs, but
foregoes convenience yield.
e. Hedging but not speculation is permissible in Islamic Finance.
11.True or false. Efficient Market hypothesis assumes that
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
There are no taxes.
There is perfect foresight.
Successive price changes are independent.
Investors are irrational.
There are no transaction costs.
Forecasts are unbiased.
Financial decisions are less easily reversed than investments decisions.
There is almost perfect negative correlation between successive price changes.
Prices reflect all publicly available information.
Expected return on each stock is the same.
12. Fill in the blanks with words provided as (1) spot price (2) Forward v/s Future contract (3)
Long v/s short position (4) Basis risk (5) Mark to Market (6) Net convenience yield
a. The advantage from owning the commodity rather than the promise of future
delivery less the cost of storing the commodity is termed as____________.
b. Profits and losses on a position are settled on a position on a regular basis is
termed as ______.
c. Investors in agreement to buy an asset and investors in agreement to sell an asset
is termed as ____________.
d. The risk that arises because the price of the asset used to hedge is not perfectly
correlated with that of the asset that is being hedged is termed as __________.
e. Price paid for immediate delivery is termed as _______________.
f. The contracts to buy or sell at a future date at a specified price either bilaterally or
through an exchange are termed as ____________.
13. True or false
a. A firm that earns the opportunity cost of capital is earning economic rents.
b. A firm that invests in positive NPV ventures expects to earn economic rent.
c. Financial managers should try to identify areas where their firms can earn economic
rents, because it is there that positive NPV projects are likely to be found.
d. Economic rent is the equivalent annual cost of operating capital equipment.
e. The approval of a capital budget allows managers to go ahead with any project included
in the budget.
f. Capital budgets and project authorizations are mostly developed bottom up. Strategic
planning is a top down process.
g. Project sponsors are likely to be overoptimistic.
h. Investments in marketing (for new products) and R & D are not capital outlays.
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i. Many capital investments are not included in the companies’ capital budget.
j. Post audits are typically undertaken about five years after project completion.
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Bibliography
1. Economics by Samuelson-Norhaus
2. Financial Management by Eugene F Brigham and Erhardt
3. The analysis and use of Financial Statements by Gerald I White-Ashwinpaul & Sondhi
Dov Fried
4. Fundamentals of Financial management by Brigham and Houston
5. Principles of Corporate Finance Richard A Brealey-Stewart-Myers Fraklin Allen
Pitabas Mohenty.
6. Principles of Money Banking and Financial Markets by Lawrence S Ritter, William L
Silber and Gregory F. Udell
7. Various websites specifically of Wikedia.
8. Data source for tables and graphic presentations- SBP and various websites
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Index
(Page no’s would be allotted on final composition)
Annuity
Alpha coefficient
Arbitrage pricing theory (APT),
American options
Average rate of return rule
Asset management ratios
Asset Betas
Balance Sheet
Basic Earning power (BEP) ratio
Banker’s acceptance
Beta (β)
Binomial Pricing Theory
Black-Scholes Model
Breakeven analysis
Corporate Finance
Coupon Bearing Bond
Cash flow
Call option
Certainty Equivalents
Capital asset pricing model (CAPM).
Call transactions
Clean transactions
Capital market
Currency Market
Common stock
Current ratio
Call Risk
Country Risk
Credit Risk.
Currency Risk
Correlation
Convexity
Currency Swap
Credit Derivatives
Capital Budgeting
Dividend yield
Dividend pay out
Debt Market
Derivatives market
Delta
Duration of a bond
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Debt Policy
Earning per share
Earning growth rate
Economic Value added EVA:
EBITDA
Equity
European options
Economic Rents
Economic profitability
Finance
Free Cash flow
Financial Statement
Financial Ratios
Fixed turnover ratio
Foreign Exchange Market
Financial Market
Forward
Futures
Forward Rate Agreement (FRAs)
Gamma
Governance and Corporate control
Internal rate of return rule
Income statement
Insurance Market
Income Risk
Industry Risk or Unique Risk
Inflation Risk.
Interest Rate Risk
Jensen ratio
KIBOR
Long
Liquidity Ratios
Long Hedge
Leasing
Managerial Finance
Market Capitalization rate
Market value added (MVA)
Market value ratios
Market Book ratio
Money Market
Manager Risk
Market Risk
Modern portfolio theory (MPT)
Modified duration
M1
120
M2
M3
Money multiplier
Maintenance Margin-
Margin Call
Monte Carlo Simulation
Market efficiency
Mergers
Net present value
NOPAT (Net operating profit after tax)
Net operating working capital
National Commodity Exchange Ltd (NCEL)
Operating current assets
Operating current liabilities
Operating long term assets
Operating cash flow
Options
Personal Finance
Public Finance
Project valuation
Present value
Perpetuity
Plowback ratio
Price Earning ratio
Pay out ratio
Profitability index rule
PKRV
Preferred Stock
Profitability ratios
Profit margin on sales ratio
Price earning ratio (P/E) multiple
Price/ cash flow ratio
Principal Risk
Put option
Pay out policy
Pecking order theory
Quick or acid test ratios
Quantity theory of money
Return on common equity (ROE)
Repo
Reserve Money
R-Squared
Rho
Real Options:
Residual Income or Economic Value Added (EVA)
Repurchase policy
Statement of retained earnings
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Statement of cash flows
Standard Deviation
Sharpe ratio
Swaps
Short Hedge
Sensitivity analysis
Total operating assets or capital:
Total asset turnover ratio
Total Debt to total assets ratio
Times interest earned (TIE) ratio
Three factor model of Fama
Trey-nor measure
Theta
Taxes
Trade off theory
Term structure
Variance
Volatility
Variation Margin
Vega
Value at Risk (VAR)
Weighted Average cost of capital
Working capital
Zero coupon Bonds
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Profile about writer
Muhammad Arif has served SBP for more than 30 years. Basically he remained involved in
catering money market activities, interest rate management and market product development.
After leaving SBP in 2007 as Head of Financial markets and Strategy Department, he served as
Head of Research of Arif Habib Investments. Now he is Research Consultant to ‘The Financial
Daily’ a notable English newspaper and member of the visiting faculty on the subjects of
Financial Management/Investment Banking/Islamic Economics at Sheikh Zayed Sultan Institute
University of Karachi and BIZTEK. During his tenure of service he also served on deputation to
the UN Poverty alleviation group in Bangkok on development of Fixed Income Market in
Pakistan. He also remained member of Task Force of IFSB, a Malaysian based group of Islamic
countries on development of Islamic Finance. He also remained member of Investment
Committee of Access to Justice Fund of Supreme Court of Pakistan. He also represented
Pakistan in 28 member group formed in Bangkok under Chiang Mai declaration on development
of fixed income Market in member countries. Further to these he has also represented Pakistan in
different forums in other countries on issues pertaining to development of financial markets in
various jurisdictions.
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