SOC 202 Lecture Notes - Project Y, Weighted Arithmetic Mean, Capital Budgeting
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COST OF CAPITAL
LO1 How to determine a firm’s cost of equity capital.
LO2 How to determine a firm’s cost of debt.
LO3 How to determine a firm’s overall cost of capital.
LO4 How to correctly include flotation costs in capital budgeting projects.
LO5 Some of the pitfalls associated with a firm’s overall cost of capital and what to do about them.
Answers to Concepts Review and Critical Thinking Questions
1. (LO3) It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than
this, value is created.
2. (LO3) Book values for debt are likely to be much closer to market values than are equity book values.
3. (LO5) No. The cost of capital depends on the risk of the project, not the source of the money.
4. (LO3) Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs.
5. (LO1) The primary advantage of the DCF model is its simplicity. The method is disadvantaged in that (1) the
model is applicable only to firms that actually pay dividends; many do not; (2) even if a firm does pay
dividends, the DCF model requires a constant dividend growth rate forever; (3) the estimated cost of equity
from this method is very sensitive to changes in g, which is a very uncertain parameter; and (4) the model does
not explicitly consider risk, although risk is implicitly considered to the extent that the market has impounded
the relevant risk of the stock into its market price. While the share price and most recent dividend can be
observed in the market, the dividend growth rate must be estimated. Two common methods of estimating g are
to use analysts’ earnings and payout forecasts or to determine some appropriate average historical g from the
firm’s available data.
6. (LO1) Two primary advantages of the SML approach are that the model explicitly incorporates the relevant
risk of the stock and the method is more widely applicable than is the dividend discount model model, since
the SML doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML
method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must be
estimated, and (2) the method essentially uses historical information to estimate these parameters. The risk-free
rate is usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the market risk
premium is usually estimated from historical risk premiums and, hence, is not observable. The stock beta,
which is unobservable, is usually estimated either by determining some average historical beta from the firm
and the market’s return data, or by using beta estimates provided by analysts and investment firms.
7. (LO2) The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it were to
issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the company has
an accurate estimate of its cost of debt. If the debt is privately-placed, the firm could still estimate its cost of
debt by (1) looking at the cost of debt for similar firms in similar risk classes, (2) looking at the average debt
cost for firms with the same credit rating (assuming the firm’s private debt is rated), or (3) consulting analysts
and investment bankers. Even if the debt is publicly traded, an additional complication is when the firm has
more than one issue outstanding; these issues rarely have the same yield because no two issues are ever
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a. This only considers the dividend yield component of the required return on equity.
b. This is the current yield only, not the promised yield to maturity. In addition, it is based on the book
value of the liability, and it ignores taxes.
c. Equity is inherently more risky than debt (except, perhaps, in the unusual case where a firm’s assets have
a negative beta). For this reason, the cost of equity exceeds the cost of debt. If taxes are considered in this
case, it can be seen that at reasonable tax rates, the cost of equity does exceed the cost of debt.
9. (LO5) RSup = .12 + .75(.08) = .1800 or 18.00%
Both should proceed. The appropriate discount rate does not depend on which company is investing; it depends
on the risk of the project. Since Superior is in the business, it is closer to a pure play. Therefore, its cost of
capital should be used. With an 18% cost of capital, the project has an NPV of $1 million regardless of who
10. (LO5) If the different operating divisions were in much different risk classes, then separate cost of capital
figures should be used for the different divisions; the use of a single, overall cost of capital would be
inappropriate. If the single hurdle rate were used, riskier divisions would tend to receive more funds for
investment projects, since their return would exceed the hurdle rate despite the fact that they may actually plot
below the SML and, hence, be unprofitable projects on a risk-adjusted basis. The typical problem encountered
in estimating the cost of capital for a division is that it rarely has its own securities traded on the market, so it is
difficult to observe the market’s valuation of the risk of the division. Two typical ways around this are to use a
pure play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based on the
perceived risk of the division.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to
space and readability constraints, when these intermediate steps are included in this solutions manual, rounding
may appear to have occurred. However, the final answer for each problem is found without rounding during any
step in the problem.
1. (LO1) With the information given, we can find the cost of equity using the dividend growth model. Using this
model, the cost of equity is:
RE = [$2.40(1.055)/$52] + .055 = .1037 or 10.37%
2. (LO1) Here we have information to calculate the cost of equity using the CAPM. The cost of equity is:
RE = .053 + 1.05(.12 – .053) = .1234 or 12.34%
3. (LO1) We have the information available to calculate the cost of equity using the CAPM and the dividend
growth model. Using the CAPM, we find:
RE = .05 + 0.85(.08) = .1180 or 11.80%
And using the dividend growth model, the cost of equity is
RE = [$1.60(1.06)/$37] + .06 = .1058 or 10.58%
Both estimates of the cost of equity seem reasonable. If we remember the historical return on large
capitalization stocks, the estimate from the CAPM model is about two percent higher than average, and the
estimate from the dividend growth model is about one percent higher than the historical average, so we cannot
definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so:
RE = (.1180 + .1058)/2 = .1119 or 11.19%
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4. (LO1) To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in
dividends each year was:
g1 = ($1.12 – 1.05)/$1.05 = .0667 or 6.67%
g2 = ($1.19 – 1.12)/$1.12 = .0625 or 6.25%
g3 = ($1.30 – 1.19)/$1.19 = .0924 or 9.24%
g4 = ($1.43 – 1.30)/$1.30 = .1000 or 10.00%
So, the average arithmetic growth rate in dividends was:
g = (.0667 + .0625 + .0924 + .1000)/4 = .0804 or 8.04%
Using this growth rate in the dividend growth model, we find the cost of equity is:
RE = [$1.43(1.0804)/$45.00] + .0804 = .1147 or 11.47%
Calculating the geometric growth rate in dividends, we find:
$1.43 = $1.05(1 + g)4
g = .0803 or 8.03%
The cost of equity using the geometric dividend growth rate is:
RE = [$1.43(1.0803)/$45.00] + .0803 = .1146 or 11.46%
5. (LO1) The cost of preferred stock is the dividend payment divided by the price, so:
RP = $6/$96 = .0625 or 6.25%
6. (LO2) The pretax cost of debt is the YTM of the company’s bonds, so:
P0 = $1,070 = $35(PVIFAR%,30) + $1,000(PVIFR%,30)
R = 3.137%
YTM = 2 × 3.137% = 6.27%
And the aftertax cost of debt is:
RD = .0627(1 – .35) = .0408 or 4.08%
a. The pretax cost of debt is the YTM of the company’s bonds, so:
P0 = $950 = $40(PVIFAR%,46) + $1,000(PVIFR%,46)
R = 4.249%
YTM = 2 × 4.249% = 8.50%
b. The aftertax cost of debt is:
RD = .0850(1 – .35) = .0552 or 5.52%
c. The after-tax rate is more relevant because that is the actual cost to the company.
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