Download (discount) rate - Robert Uberman

7
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Session Seven Topics
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Introducing interrelation between time and money
Discounting money streams
Key problems with proper discounting
Brealey, Myers: the chapter titled: “Present Value … “
(pp. 11-56)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Time Value of Money
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1 USD today does not equal 1 USD tomorrow!
FV = PV * (1+r)n where:
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r represents a return
n represents number of periods (quite often years)
PV = FV/ (1+r)n
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Theoretical fundaments of relation between
time and value
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Risk of a return different from the planned one (Mind you: also
bigger !!!)
Liquidity: investor converts cash, which is the most universal value
transponder into less liquid assets (Opportunity Cost of Capital),
Purchasing Power: universal (inflation, see Brealey, Myers, pp.
642-645), individual (ultimate goal in investing)
Intrinsic value of money (per se):– J.M. Keynes’ theory.
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Capitalisation
FVt  CF0  (1  rt )
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FVt – Future Value of a given sum
CF0 – present value of a given sum
rt – interest rate in period t (most often annual)
t – capitalisation period
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Brealey, Myers pp. 11-56
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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
t
Capitalisation rate
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The most common way of expressing a capitalisation rate is an
annual one, marked with r letter without index t
However quite often a real capitalisation period is different –
interests are added to a capital after each month, quarter or so.
Then the previously mentioned equitation is converted into:
FVt
r tn
 CF0  (1 
)
n
Capitalisation rate
Present Value
Capitalisation period A
Value after 1 year A
Capitalisation period B
Value after 1 year B
10%
1 000,00
12
months
1 100,00
1
month
1 104,71
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Key equations
PV 
CFn
(1  r ) n
(1)
where:
CFn
R
n
–
–
–
Year n cash flow,
discount rate.
Subsequent year
It is useful to convert a discount rate into a discount factor:
dn 
1
(1  r ) n
(2)
And then calculate Present Value as:
PV  CFn  d n
(3)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Present Value as dependence on a discount
rate
Discount rate
Discounting Period
8%
10%
12%
15%
20%
Present value of 50 000 USD due at the
period’s end
PV,25 yrs
7 301
4 615
2 941
1519
524
PV,75 yrs
156
39
10
1,40
0,06
PV, infinity
0
0
0
0
0
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Present Value as dependence on a discount
rate
Discount rate
Discounting Period
PV,25 yrs
8%
10%
12%
15%
20%
Present value of 50 000 USD annuity for the
given period
533 739
453 852
392 157
323 207
247 379
PV,75 yrs
623 054
499 607
416 582
333 324
250 000
PV, infinity
625 000
500 000
416 667
333 333
250 000
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Various approaches to set an interest
(discount) rate
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There is a huge variety of theories and models covering the issue. The list
below indicates a subjective selection of most commonly used ones:
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Alternative capital cost
Risk-free alternative
Debt cost
WACC
Historical rate of return
Risk Adjusted Discount Rate (RADR)
Hurdle rate
Social rate of return
Discount rate quite often is presented as:
risk-free rate + risk adjustment
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Concept of risk
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Financial and insurance meaning of risk
Individual attitudes towards risk:
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averse,
neutral,
Seeker.
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Homework
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If the PV of 150 USD to be paid in one year is 130 USD,
what is a discount rate? (Brealey, Myers, Chapter 2, Q
2)
You have come to a bank in order to make 1000 PLN
deposit for 5 years, with 7% interest and half-year
capitalisation (period). An financial advisor has stepped
in with an offer of shares which over last 5 years period
brought 40 % return. What would be your decision?
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
8
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Session Eight Topics
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Investment vs Capital Budgeting Decisions
NPV
I(nternal) R(ate of) Return
PI
Payback (discounted)
Brealey, Myers: Chapter titled “Why Net Present Value
Leads to Better Investment Decisions …” (pp. 85-112)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Investment vs. Capital
Budgeting Decisions
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Investment = money committed or property
acquired for future income
Capital budgeting is planning capital outlays for
purchasing new fixed assets to get additional
profit thus it means planning investments
Intra-corporate investment process is usually
much more complicated ro evaluate than
financial investments (share, bonds) since cash
flows are not easily defined
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Examples of Capital Budgeting
Decisions
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Equipment selection decision.
Plant expansion aimed at:
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increase in sales;
backward integration.
Equipment replacement decision caused by
aging machine park.
New equipment purchase aimed at cost
reduction.
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Commonly used measures of
investment efficiency
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Payback (straight)
I(nternal) R(ate of) Return
NPV
PI
Payback (discounted)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Payback (period)
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The payback period estimates the time required
to recover the principal amount of an
investment.
It is often defined as a length of time needed for
an investment's net cash receipts to cover
completely the initial outlay expended in
acquiring the investment
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Payback (example)
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A&B Enterprises is trying to select the best investment from among
three alternatives. Each alternative involves an initial investment of
$100,000. Their cash flows follow:
Year
A
B
C
1
$ 10,000
$ 50,000
$ 25,000
2
$ 20,000
$ 40,000
$ 25,000
3
$ 30,000
$ 30,000
$ 25,000
4
$ 40,000
-
$ 25,000
5
$ 50,000
-
$ 25,000
Which investment will you select using the payback method? Why?
(Brealey, Myers)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Payback – key issues
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What is an investment?
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Capital expenditure
Increase in NWC
Other
How one defines a pay back itself?
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Net profit
Net cash flow
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Payback - limitations
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The payback period method ignores:
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any benefits that occur after the investment is repaid
the time value of money
risk-free cost of money
 risk
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Therefore payback period:
is useless for ranking purposes
 can be used only in relation to near certain flows
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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
NPV
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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
IRR
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IRR vs Yield to Maturity
IRR algorithm
IRR use
Disadvantages of IRR
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
IRR - definitions
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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
IRR vs NPV
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IRR:
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can be calculated only if a cash flow break even only once –
which is typical for many simple investments;
is directly comparable to benchmarks like interests on deposits;
quite often is calculated simultaneously with NPV
can be used as a ranking tool but with attention to various traps
(see Brealey, Myers, pp. 94-101.
NPV
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in practice it is calculated to get IRR;
it can be applied to streams not to be assessed using IRR;
it can not be used as a ranking tool (unless all investments are
equal)
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
PI (Profitability Index)
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Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Discounted Payback (Period)
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The discounted payback period estimates the time
required to recover the principal amount of an
investment but applying discounting.
It is often defined as a length of time needed for an
investment's net cash receipts to cover completely the
initial outlay expended in acquiring the investment with
consideration of time value of money concept.
It is quite often used as an indicator of a risk level
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego
Homework
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An owner of a successful retail business of a traditional handmade
wool clothes in Krynica considers opening a new outlet in Warsaw.
There are two options as far as location is concerned and they can
be characterised as stated below in terms of key economic
parameters. Please select the most efficient one using measures
presented before. Apply 15 % discount/hurdle rate when needed.
Location
(PLN)
Cost/
month
Monthly
turnover
Mark up
Days in
stock
Days
payable
Initial
investm
ent
Premium
10 000
50 000
50 %
30
60
90 000
6 000
35 000
30 %
45
60
30 000
Subarbian
Robert Uberman, Financial Management, KA im Frycza Modrzewskiego