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10-1
Chapter 10
Answers to Review Problems
Finance For Executives – 4th Edition
1. Historical returns.
a.
If one accepts that stocks are riskier than corporate bonds, which are riskier than government
bonds, which are riskier than Treasury bills, then the annual data does not appear to support a
naïve understanding of theory. In 2000, 2001, 2002, and in 2005, the returns on stocks were less
b.
These apparent anomalies can be explained mainly by changes in long-term interest rates, the
slope of the yield curve, or changes in the risk perception by the market for corporate bonds.
c.
The market risk premium for each of the periods observed can be found in the table below.
Time Period
Market Risk Premium
versus Government Bonds
Market Risk Premium
versus Treasury Bills
1994
9.09%
–2.58%
1995
5.91
31.98
1996
23.89
17.75
1997
17.51
28.10
10-2
2003
27.23
27.66
2004
2.37
9.68
2005
-2.90
1.93
2006
14.60
10.99
2007
-4.39
0.83
2. Risk and return.
a.
The statement is dangerous although it could be true since the future is unknown. Future returns
b.
Investors will hold bonds or stocks depending on their tolerance to risk, their need to be assured
c.
This is false as can be seen from the table of returns in question 1. The value of a bond will fall
3. The cost of equity and the cost of debt.
Both statements are false.
10-3
a.
The statement ignores growth prospects for the company stock. According to the dividend
discount model with constant growth expectations (i.e., equation 10.5), the return expected by the
company shareholders, kE, is:
b.
The interest expenses represent the cost of financial liabilities such as debt to banks or bonds.
Liabilities of any company include these debts but also other liabilities such as accounts payable
4. The cost of debt.
The current market price of the bond is $1,100 (110 percent of $1,000 par value). Using a
spreadsheet as it is shown in the text to solve equation 10.1, we get kD = 6.76 percent.
A
B
C
D
E
F
G
1
Number of periods
12
2
3
Coupon payment
$80
4
5. The cost of equity.
According to the dividend discount model with constant growth expectations (i.e., equation 10.5)
the return expected by the company shareholders, kE, is:
10-4
kE
percent2.9092.005.00420.005.0
50$
10.2$ ==+=+=
According to the capital asset pricing model (i.e., equation 10.11):
kE = RF + (RM – RF) × βOnogo
6. Practical application of the capital asset pricing model.
This question is about some of the practical problems encountered in applying the capital asset
pricing model (CAPM). Of the variables in the model, RF (the risk-free rate) is directly
observable and (the firm’s equity beta) can be fairly easily measured by regressing the returns
of a particular security, or securities belonging to the same industrial sector, on the returns of a
market index. It is the expected average return on the market, RM, which creates the measurement
Why have some investment banks been using very low market risk premiums? Since the lower
the market risk premium, the lower the cost of capital that is used to discount expected future
cash flows, company valuations will be higher. A cynic might suspect the banks have a strong
incentive to obtain high valuations since their fees will be larger. Sellers of a company in a
10-5
7. Calculating the weighted average cost of capital (WACC).
a.
According to equation 10.12 extended to a third source of capital—preferred stock—Tale’s cost
of capital, or weighted average cost of capital (WACC) is:
b.
The director confuses the cost of debt before tax with its cost after tax. The relevant cost of debt
in calculating the WACC is obviously the cost after tax, which is 3.90 percent [6% × (1 – 0.35)].
The relevant cost of debt is thus cheaper than the cost of preferred equity financing (4.5 percent).
8. Estimating the cost of capital of a firm.
The relevant cost of capital for CAT is its weighted average cost of capital, or WACC, as given in
equation 10.12 extended to a third source of capital—short-term debt:
10-6
To compute the cost of the long-term debt, we use a spreadsheet as it is shown in the text to solve
equation 10.1. We get kD = 7.82 percent.
A
B
C
D
E
F
G
1
Number of periods
10
2
3
Coupon payment
$90
(9 percent of $1,000)
4
5
Market price
$1,080
(108 percent of $1,000)
6
According to the capital asset pricing model, (see equation 10.11):
kE = RF + (RM – RF) × βCAT
where RF = 5.2 percent is the risk-free rate, RM – RF = 4 percent is the market risk premium, and
βCAT = 1.03 is CAT’s equity beta coefficient. Thus,:
9. Estimation of the cost of capital of a division.
To estimate the equipment division’s weighted average cost of capital, you need to estimate its
after-tax cost of debt and its relevant financing ratios as well as its appropriate cost of equity
according to the capital asset pricing model using the data on proxy firms. Apply the following
procedure:
Step 2: Estimate the division’s cost of equity based on data from proxy firms.
According to the capital asset pricing model (see equation 10.11), we have:
kE = RF + (RM – RF) × βdivision
−+
=
Equity
Debt
)rateTax1(1
equity
asset
For proxy A:
44.0
00.1)40.01(1
70.0 =
−+
=
asset
10-8
Step 2.2: Estimate the equipment division’s asset beta as the average of the proxies’ asset
betas
61.0
3
72.068.044.0 =
++
=
asset
Step 2.3: Estimate the equipment division’s equity beta by relevering the division’s
kE = 5.2% + 4% × 0.914 = 8.86%
Step 3: Calculate the division’s weighted average cost of capital using the division’s target debt-
to-equity ratio of 0.83, which is equivalent to a debt-to-total financing ratio of 0.45.
10. Estimation of cost of capital for a spinoff.
a.
The CEO wants to have an estimate of the value of a division that is to be sold before beginning
discussions with the company’s investment bankers. The issue is the appropriate discount rate to
use in the valuation of the division’s expected cash flows—the company WACC or a WACC that
will reflect the business and financial risk of the division to be sold?
10-9
−+
=
Equity
Debt
)rateTax1(1
β
βequity
asset
where the tax rate is 30% and D/E is the debt-to-equity ratio for each airline at market valuations.
This formula would give A = 0.64, B = 0.41, C = 0.69, D = 0.66, and E = 0.46. If we can
assume that the average of these asset betas would offer a reasonable proxy for the asset beta of
the division, this will give us Division = 0.57. Next, one needs to estimate what the equity beta
would be for the division, taking into account its debt-to-equity ratio of 1.90. For this, equation
10.6 can be used:
where RF = 5 percent is the risk-free rate, RM – RF = 4 percent is the market risk premium, and
βDivision = 1.33 is the division’s equity beta coefficient.
kE = 5% + 1.33 4 % = 10.32%
