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Chapter 9
The Cost of Capital
Instructor’s Resources
Overview
This chapter introduces the student to an important financial concept, the cost of capital. The mechanics of
computing the sources of capital debt, preferred stock, common stock, and retained earnings are reviewed. These
individual costs are then combined into a weighted average cost of capital. Students are encouraged to devote time
and effort to learning Chapter 9’s materials because acceptable projects encountered in their professional life or
investment decisions made in their personal life will be correct if they earn a return higher than the cost of capital.
Suggested Answers to Opener-in-Review Questions
In the chapter opener you learned that Alcoa’s weighted average cost of capital was around 12 percent, but
its investments were earning returns closer to 5 percent. From 2010 to 2012, Alcoa invested roughly $1
billion in capital expenditures. Suppose Alcoa spends $1 billion expanding its manufacturing facilities today,
and that investment produces a net cash flow of $50 million (5 percent of $1 billion) every year in perpetuity.
Calculate the NPV of that investment using a 12 percent discount rate. How much value does the $1 billion
investment create or destroy? Does it seem that Alcoa should be pursuing growth in this market?
NPV = CF ÷ r
Hence, NPV of the investment = $50 million ÷ 12% = $416.67 million
Answers to Review Questions
1. The cost of capital represents the firm’s cost of financing in percentage terms. A firm’s cost of capital is the
2. The cost of capital provides a benchmark against which the potential rate of return on an investment is
© 2015 Pearson Education, Inc.
Chapter 9 The Cost of Capital 179
3. Capital structure consists of long-term sources of financing, coming from bondholders and stockholders. The
4. The four basic long-term sources of capital available to firms are long-term debt, preferred stock, common
5. The net proceeds from the sale of a bond are the funds received from its sale after all underwriting and
6. The three approaches to finding the before-tax cost of debt are the following:
a. The quotation approach that uses the current market value of a bond to determine the yield-to-maturity
b. The calculation approach finds the before-tax cost of debt by calculating the internal rate of return (IRR)
c. The approximation approach uses the following formula to approximate the before-tax cost of the debt.
[($1,000 )]
( $1,000)
2
d
d
d
N
In
rN
-
+
=+
7. The before-tax cost is converted to an after-tax debt cost (ri) by using the following equation:
ri rd (1 T), where T is the firm’s tax rate.
8. Answers will vary for question because values are algorithmically generated in MyFinanceLab.
9. The cost of preferred stock is found by dividing the annual preferred stock dividend by the net proceeds from
p
p
p
D
rN
=
© 2015 Pearson Education, Inc.
Chapter 9 The Cost of Capital 180
10. The assumptions underlying the constant-growth valuation (Gordon) model are
11. The CAPM technique directly considers a firm’s risk, through the inclusion of “beta,” in determining the
12. The cost of retained earnings is technically less than the cost of new common stock because by using retained
13. The weighted average cost of capital (WACC), ra, is an average of the firm’s cost of long-term financing. It is
14. The weighted average cost of capital (WACC), ra, is highly dependent upon the firm’s target capital structure.
15. Using target capital structure weights, a firm is trying to develop a capital structure that is optimal for the
Suggested Answer to Focus on Ethics Box: The Ethics of Profit
The Vioxx recall increased Merck’s cost of capital. What effect would an increased cost of capital have on a
firm’s future investments?
Suggested Answer to Focus on Practice Box: Uncertain Times Make for
an Uncertain Weighted Average Cost of Capital
Why don’t firms generally use both short- and long-run weighted average costs of capital?
Firms maximize shareholder wealth through investment in fixed assets. Capital budgeting is the process of
evaluating and selecting these assets, which are utilized for more than a year. Mismatching of asset life and
financing duration increases financial risk.
© 2015 Pearson Education, Inc.
Chapter 9 The Cost of Capital 181
Answers to Warm-Up Exercises
E9-1. Weighted average cost of capital
Answer: N 10, PV $20,000 (1 0.02) $19,600, PMT 0.08 $20,000 $1,600, FV $20,000
E9-2. Cost of preferred stock
Answer: The cost of preferred stock is the ratio of the preferred stock dividend to the firm’s net proceeds from
E9-3. Cost of common stock equity
Answer: The cost of common stock equity can be found by dividing the dividend expected at the end of year 1
by the current price of the stock and adding the expected growth rate.
E9-4. Weighted average cost of capital
E9-5. Weighted average cost of capital
Solutions to Problems
P9-1. Concept of cost of capital
LG 1; Basic
a. Project North is expected to earn an 8% return. If the analyst expects the cost of debt to be 7%, he
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Chapter 9 The Cost of Capital 182
b. Project South is expected to earn 15%, but if the analyst believes that it will be financed with equity
c. These decisions may not be in the best interest of a firm’s investors because the firm uses a blend of
d. The weighted average cost is (0.4 × 7%) + (0.6 × 16%) = 12.4%.
e. If both analysts used 12.4% as the hurdle rate for the investments, then North would be rejected, and
f. When the analysts focus on a single source of financing rather than the blend that the firm actually
P9-2. Cost of debt using both methods
LG 3; Intermediate
a. Net proceeds: Nd $1,010 $30
b. Cash flows: T CF
0 $ 980
c. Cost to maturity:
d. Approximate before-tax cost of debt
($1,000 $980)
$120 15
($980 $1,000)
2
d
r
-
+
=+
rd $121.33 $990
rd 12.26%
Approximate after-tax cost of debt 12.26% (10.4) 7.36%
e. The advantages of the calculator method are evident. There are fewer keypunching strokes, and one
P9-3. Before-tax cost of debt and after-tax cost of debt
LG 3; Easy
a. N 10, PV 930 (an expenditure), PMT 0.6(1,000) 60, FV 1,000
b. Use the model: After-tax cost of debt before-tax cost of debt (1 tax bracket)
P9-4. Cost of debt using the approximation formula:
© 2015 Pearson Education, Inc.
Chapter 9 The Cost of Capital 183
LG 3; Basic
$1,000
$1,000
2
d
d
d
N
In
rN
-
+
=+
ri rd (1T)
Bond A
$1,000 $955
$90 $92.25
20 9.44%
$955 $1,000 $977.50
2
d
r
-
+
= = =
+
Bond B
$1,000 $970
$100 $101.88
16 10.34%
$970 $1,000 $985
2
d
r
-
+
= = =
+
ri 10.34% (10.40) 6.20%
Bond C
$1,000 $955
$120 $123
15 12.58%
$955 $1,000 $977.50
2
d
r
-
+
= = =
+
ri 12.58% (10.40) 7.55%
Bond D
$1,000 $985
$90 $90.60
25 9.13%
$985 $1,000 $992.50
2
d
r
-
+
= = =
+
Bond E
$1,000 $920
$110 $113.64
22 11.84%
$920 $1,000 $960
2
d
r
-
+
= = =
+
P9-5. Cost of debt using the approximation formula
LG 3; Intermediate
Chapter 9 The Cost of Capital 184
$1,000
$1,000
2
d
d
d
N
In
rN
-
+
=+
ri rd (1T)
Alternative A
$1,000 $1,220
$90 $76.25
16 6.87%
$1,220 $1,000 $1,110
2
d
r
-
+
= = =
+
Alternative B
$1,000 $1,020
$70 $66.00
56.53%
$1,020 $1,000 $1,010
2
d
r
-
+
= = =
+
Alternative C
$1,000 $970
$60 $64.29
76.53%
$970 $1,000 $985
2
d
r
-
+
= = =
+
Alternative D
$1,000 $895
$50 $60.50
10 6.39%
$895 $1,000 $947.50
2
d
r
-
+
= = =
+
P9-6. After-tax cost of debt
Chapter 9 The Cost of Capital 185
LG 3; Intermediate
a. The after-tax cost of borrowing from the motorcycle dealer is the same as the pretax cost, 5%.
P9-7. Cost of preferred stock: rp Dp Np
LG 2; Basic
a.
$12.00 12.63%
$95.00
p
r= =
b.
$10.00 11.11%
$90.00
p
r= =
P9-8. Cost of preferred stock: rp Dp Np
LG 4; Basic
Preferred Stock Calculation
Arp$11.00 $92.00 11.96%
P9-9. Cost of common stock equity—capital asset pricing model (CAPM)
LG 5; Intermediate
rs RF [b (rm RF)]
a. Risk premium 6%
b. Rate of return 12%
c. After-tax cost of common equity using the CAPM 12%
P9-10. Cost of common stock equity:
1
n
D g
nN
k
+
=
LG 5; Intermediate
a. N 4 (2015 2011), PV (initial value) $2.12, FV (terminal value) $3.10
b. Nn $52 (given in the problem)
c. rr (Next Dividend Current Price) growth rate
d. rr ($3.40 $52) 0.0997
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Chapter 9 The Cost of Capital 186
P9-11. Retained earnings versus new common stock
LG 5; Intermediate
1
0
r
D
r g
P
= +
1
n
n
D
r g
N
= +
Firm Calculation
Arr ($2.25 $50.00) 8% 12.50%
Brr ($1.00 $20.00) 4% 9.00%
Crr ($2.00 $42.50) 6% 10.71%
Drr ($2.10 $19.00) 2% 13.05%
P9-12. Effect of tax rate on WACC
LG 3, 4, 5, 6; Intermediate
a. WACC (0.40)(6%)(1 0.40) (0.10)(8%) (0.50)(10%)
b. WACC (0.40)(6%)(1 0.35) (0.10)(8%) (0.50)(10%)
c. WACC (0.40)(6%)(1 0.25) (0.10)(8%) (0.50)(10%)
d. As the tax rate falls, the weighted-average cost of capital goes up. The lower the tax rate, the lower
© 2015 Pearson Education, Inc.
