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MANAGERIAL ECONOMICS
An Analysis of Business Issues
Howard Davies
and Pun-Lee Lam
Published by FT Prentice Hall
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Chapter 17:
Investment Decisions and
the Cost of Capital
Objectives:
After studying the chapter, you should
understand:
1. the concepts of capital budgeting and cost of
capital
2. some simple techniques for the appraisal of
investments
3. some financial models used to estimate the cost
of capital
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Capital and Capital Budgeting
Capital:
is the stock of assets that will generate a
flow of income in the future.
Capital budgeting:
is the planning process for allocating all
expenditures that will have an expected
benefit to the firm for more than one year.
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Investment Appraisal
Firms normally place projects in the following
categories:
1. Replacement and maintenance of old or damaged
equipment.
2. Investments to upgrade or replace existing
equipment
3. Marketing investments to expand product lines or
distribution facilities.
4. Investments for complying with government or
insurance-company safety or environmental
requirements.
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Question for Discussion:
What are the factors you would consider when
making a choice among different investment
projects?
1.
2.
3.
4.
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Simple Technique for Appraisal of
Investment
Payback-period criterion:
Payback period is the amount of time
sufficient to cover the initial cost of an
investment
But it ignores any returns accrue after the
pay-back period; ignores the pattern of
returns; ignores the time value (time cost)
of money.
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Example:
Initial investment:
Cash flow:
$10 million
$2 million per year
Payback-period?
If cash flow :
$4 million per year
Payback-period?
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Discounting
On the other hand, the process of discounting
or capitalization is to turn a future stream of
services or income into its equivalent present
value. When an expected future sum is turned
into its equivalent present value, we say that it
is discounted or capitalized.
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The present value of a single future amount
In general, present value (PV) refers to the value
now of payments to be received in the future (I). The
present value of I after n year at r is:
I
PV= (1+r)n
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Suppose we try to find the present value of a
single future amount of $121, to be received
after two years. Since goods available in the
future are worth less than the same goods
available now, the future amount of $121 is
worth less than $121 at present. Given the
market rate of interest of 10%, its present
value is:
$121
(1+0.1)2
= $100
This means that the future amount of $121 (to
be received after two years) is equivalent to a
value of $100 at present.
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Simple Technique for Appraisal of
Investment
Net-present-value technique:
Net present value (NPV) is the difference
between the present value of a future cash
flow and the initial cost of the investment
project; a firm should adopt a project if the
expected NPV is positive.
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I1
I2
In
NPV = -P + I0 +
+…+
+
2
(1+r) (1+r)
(1+r)n
or
I
NPV = -P +
r
where:
P:
=capital cost, accruing in full at the
beginning of the project
I1,2,…n =net cash flows arising from the project
in years 1 to n
r
=the opportunity cost of capital
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Simple Technique for Appraisal of
Investment
Internal-rate-of-return method:
Internal rate of return (IRR) is the rate of
return that will equate the present value of
a multi-year cash flow with the cost of
investing in a project.
Using the NPV equation: the IRR is the
discount rate that renders the NPV of the
project equal to zero.
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P, n and the expected future cash returns (I) are
known, we try to find IRR.
If the IRR is greater than the market rate of
interest r, it implies that the present value of the
capital good (PV) is greater than its purchase
price (P) and the firm should invest. Conversely,
if IRR is smaller than r, it implies that PV is
smaller than P and the firm should not invest.
What are the differences between NPV
technique and IRR method?
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In most situations, the IRR method will yield
the same results as the NPV method. But:
•there may be more than one value for the IRR that
satisfies the NPV equation; if the sign of cash flows
changes more than once in the life of the project, there
may be multiple solutions
•the NPV rule uses actual opportunity cost of capital
as the discount rate; the IRR rule assumes the
shareholders can invest at the IRR
•IRR is expressed in terms of a percentage rate of
return, it ignores the project’s absolute effect on the
wealth of shareholders
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The Cost of Capital
A firm will invest only if the expected rate
of return exceeds the cost of capital. For a
firm under rate-of-return regulation, if the
permitted rate of return is set above the
cost of capital (or the required rate of
return), the firm will over-invest;
conversely, if the permitted rate is set
below the cost of capital, the firm will
under-invest.
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Weighted Average Cost of Capital (WACC):
Cost of debt (rd): interest rate paid to creditors net of
taxes
Cost of equity (re): rate of return to shareholders in
order to induce them to invest in the firm
WACC : rd 
D
(D + E)
+ re 
E
(D + E)
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The Modigliani-Miller (M-M)
Proposition
Assumptions:
•there are no taxes
•the capital market is efficient and competitive
•there are no transaction costs
•there are no costs associated with bankruptcy
•shareholders can borrow on the same terms as
corporations
•the cost of debt is constant, whatever the level of
gearing
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The Modigliani-Miller (M-M)
Proposition
• If the assumptions hold, the total market value of two
firms that are identical except for their levels of
gearing must be the same, and their WACCs must be
the same
•If they were not the same, investors could improve
their position by “arbitrage”, selling the shares of one
and buying shares in the other, which would alter the
relative prices of shars until the WACCs become equal
•The level of gearing is therefore irrelevant to the
WACC and the value of the firm
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The Cost of Equity Capital
1. Dividend valuation approach DVA
(or dividend growth/discounted cash flow
model):
Rate of return = Dividend/Price + Expected
Dgrowth
rate
1
re =
+g
P0
The DVA relies on the equivalence of the market
price of a stock, P0, with the present value of the
dividends ( or cash flows) expected from the
stock. The discount rate in finding the present
value is considered to be the cost of equity capital.
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Assumptions
There are few assumptions behind the method:
(a) future dividends are expected to grow at a
constant rate perpetually;
(b) future dividends can be discounted at a
constant cost of equity capital;
(c) future dividends remain a constant
proportion of earnings over time;
(d) the firm is an all-equity-financed firm, or it
has a constant level of leverage (or a constant
debt-equity ratio).
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DVA:
expected dividend
D1
D2
D3
PV= (1 + r) + (1 + r)2 + (1 + r)3
+ ...
discounted rate, cost of equity capital
Dt
]
PV=  [
t
(1 + r)
Assume D1 grows at constant rate of g:
D1
D1(1+g)
D1(1+g)2
+
+ ...
PV= (1 + r) +
(1 + r)2
(1 + r)3
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D1
Let A = (1 + r)
(1 + g)
Let B = (1 + r)
PV = A(1 + B + B2 + …)
(1)
 B on both sides:
PV  B = A(B + B2 + B3 + …)
(2) - (1):
PV(1 - B) = A
PV = A
(1 - B)
D1
(1 + r)
PV = (1 + r) 
(r - g)
Given PV = P0
D1
r= P +g
0
(2)
1-B
= 1 - (1 + g)
(1 + r)
(1+r) -(1 + g)
=
(1 + r)
(r - g)
=
(1 + r)
D1 = D0 (1 + g)
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The Cost of Equity Capital
2. Capital asset pricing model (CAPM):
Cost of equity capital = risk-free rate +
beta (market rate - riskfree rate)
Re = Rf +  (Rm - Rf)
Therefore, if we use the CAPM to estimate a
firm’s cost of equity capital (Re, or the required
rate of return), we have to estimate a firm’s beta,
the risk-free rate of return, and the market risk
premium (the difference between Rm and Rf).
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In the CAPM, the measure of market risk is
known as beta ().
For example, the returns from an asset with
a beta of 0.5 will fluctuate by 5% for each 10%
fluctuation in the market’s returns.
It has been shown that the required risk premium
for an asset is directly proportional to its beta.
Therefore, the holder of an asset with a beta of 0.5
will require a risk premium only half as large as
that offered by the market as a whole.
If the market is efficient, the cost of equity capital
will be equal to the expected rate of return.
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