Chapter 11: Cost of Capital
11-21
50 percent debt level.
22. Weighted average cost of capital (LO1) Given the following information, calculate the
weighted average cost of capital for Hamilton Corp. Line up the calculations in the order
shown in Table 11-1.
Percent of capital structure:
Debt …………………….. 30%
Preferred stock ………. 15
Common equity ……… 55
Additional information:
Bond coupon rate………………………… 13%
Bond yield to maturity …………………. 11%
Dividend, expected common…………. $ 3.00
Dividend, preferred……………………… $10.00
Price, common……………………………. $50.00
Price, preferred …………………………... $98.00
Flotation cost, preferred ……………….. $ 5.50
Growth rate ……………………………….. 8%
Corporate tax rate ……………………….. 30%
11–22. Solution:
The Hamilton Corp.
Kd = Yield (1 – T)
The bond yield of 11% is used rather than the coupon rate of
Chapter 11: Cost of Capital
p
p
p
1
e
0
D
KPF
$10.00 $10.00 10.81%
$98 $5.50 $92.50
D
Kg
P
$3 8% 6% 8% 14%
$50
=
−
= = =
−
=+
= + = + =
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) …………………………..
Preferred stock (Kp) ………………..
Common equity (Ke)
(retained earnings) ……………..…..
Weighted average cost of
capital (Ka) ………………………..…
7.70%
10.81
14.00
30%
15
55
2.31%
1.62
7.70
11.63%
23. Weighted average cost of capital (LO1) Given the following information, calculate the
weighted average cost of capital for Hadley Corporation. Line up the calculations in the
order shown in Table 11-1.
Percent of capital structure:
Preferred stock ……………. 10%
Common equity …………… 60
Debt ………………………….. 30
Additional information:
Chapter 11: Cost of Capital
11-23
Corporate tax rate ……………………….. 34%
Dividend, preferred……………………… $9.00
Dividend, expected common…………. $3.50
Price, preferred …………………………... $102.00
Growth rate ……………………………….. 6%
Bond yield …………………………………. 10%
Flotation cost, preferred ……………….. $3.20
Price, common……………………………. $70.00
11–23. Solution:
Hadley Corporation
Kd = Yield (1 – T)
Kp = Dp/(Pp – F)
Ke = (D1/P0) + g
Chapter 11: Cost of Capital
11–23. (Continued)
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) …………………………..
Preferred stock (Kp) ………………..
Common equity (Ke)
(retained earnings) ……………..…..
Weighted average cost of
capital (Ka) ………………………..…
6.60%
9.11
11.00
30%
10
60
1.98%
0.91
6.60
9.49%
24. Changes in costs and weighted average cost of capital (LO1) Brook’s Window Shields,
Inc., is trying to calculate its cost of capital for use in a capital budgeting decision. Mr.
Glass, the vice-president of finance, has given you the following information and has asked
you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 11.2 percent coupon rate and
another bond with an 7.5 percent coupon rate. The firm has been informed by its
investment banker that bonds of equal risk and credit rating are now selling to yield 12.4
percent.
The common stock has a price of $54 and an expected dividend (D1) of $2.70 per share.
The firm’s historical growth rate of earnings and dividends per share has been 14.5 percent,
but security analysts on Wall Street expect this growth to slow to 12 percent in the future
years.
The preferred stock is selling at $50 per share and carries a dividend of $4.75 per share.
The corporate tax rate is 35 percent. The flotation cost is 2.8 percent of the selling price for
preferred stock. The optimum capital structure is 35 percent debt, 10 percent preferred
stock, and 55 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure, and
then calculate the weighted average cost of capital (similar to Table 11-1).
11–24. Solution:
Brook’s Window Shields, Inc.
Kd = Yield (1 – T)
Chapter 11: Cost of Capital
Kp = Dp/(Pp – F)
Ke = (D1/P0) + g
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ………………………..…
Preferred stock (Kp) ………….……..
Common equity (Ke)
(retained earnings) …………………..
Weighted average cost of
capital (Ka) ……………………..……
8.06%
9.77
17.00
35%
10
55
2.82%
0.98
9.35
13.15%
25. Changes in cost and weighted average cost of capital (LO1) A-Rod Manufacturing
Company is trying to calculate its cost of capital for use in making a capital budgeting
decision. Mr. Jeter, the vice-president of finance, has given you the following information
and has asked you to compute the weighted average cost of capital.
The company currently has outstanding a bond with a 10.6 percent coupon rate and
another bond with a 8.2 percent rate. The firm has been informed by its investment banker
that bonds of equal risk and credit rating are now selling to yield 11.5 percent. The
common stock has a price of $60 and an expected dividend (D1) of $1.80 per share. The
historical growth pattern (g) for dividends is as follows.
$1.35
1.49
1.64
1.80
Compute the historical growth rate, round it to the nearest whole number, and use it for g.
The preferred stock is selling at $80 per share and pays a dividend of $7.60 per share.
The corporate tax rate is 30 percent. The flotation cost is 2.5 percent of the selling price for
preferred stock. The optimum capital structure for the firm is 25 percent debt, 10 percent
preferred stock, and 65 percent common equity in the form of retained earnings.
Compute the cost of capital for the individual components in the capital structure, and
then calculate the weighted average cost of capital (similar to Table 11-1).
11–25. Solution:
Chapter 11: Cost of Capital
A-Rod Construction Company
Kd = Yield (1 – T)
Kp = Dp/(Pp – F)
Ke = (D1/P0) + g
D1 = $1.80
P0 = $60
g = 10% (see below)
Ke = (D1/P0) + g
11–25. (Continued)
Bring the above values together to compute the weighted average cost of
capital
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) …………………….
Preferred stock (Kp)………
Common equity (Ke)
(retained earnings)………..
8.05%
9.74
13.00
25%
10%
65%
2.01%
0.97
8.45
Weighted average cost of capital (Ka)……..
11.43%
Chapter 11: Cost of Capital
11-27
26. Impact of credit ratings on cost of capital (LO3) Northwest Utility Company faces
increasing needs for capital. Fortunately, it has an Aa3 credit rating. The corporate tax rate
is 35 percent. Northwest’s treasurer is trying to determine the corporation’s current
weighted average cost of capital in order to assess the profitability of capital budgeting
projects.
Historically the corporation’s earnings and dividends per share have increased about
6.2 percent annually and this should continue in the future. Northwest’s common stock is
selling at $60 per share, and the company will pay a $4.50 per share dividend (D1).
The company’s $100 preferred stock has been yielding 8 percent in the current market.
Flotation costs for the company have been estimated by its investment banker to be $2.00
for preferred stock.
The company’s optimum capital structure is 50 percent debt, 10 percent preferred stock,
and 40 percent common equity in the form of retained earnings. Refer to the table below on
bond issues for comparative yields on bonds of equal risk to Northwest.
Data on Bond Issues
Issue
Moody’s
Rating
Price
Yield to
Maturity
Utilities:
Southwest Electric Power––7¼ 2023 …..……..
Aa2
$ 875.18
8.24%
Pacific Bell––7⅜ 2025 ……………………….….
Aa3
887.25
8.43
Pennsylvania Power & Light––8½
2022 …………………………………………….……..
A2
950.66
8.99
Industrials:
Johnson & Johnson––6¾ 2023 …………….……..
Aaa
840.24
8.14%
Dillard’s Department Stores––71/8
2023 …………………………………………….……..
A2
920.92
8.44
Marriott Corp.––10 2015 …………………………..
B2
1,015.10
9.99
Compute the answers to the following questions from the information given.
a. Cost of debt, Kd (Use the accompanying table––relate to the utility bond credit rating
for yield.)
b. Cost of preferred stock, Kp.
c. Cost of common equity in the form of retained earnings, Ke.
d. Weighted average cost of capital.
Chapter 11: Cost of Capital
11–26. Solution:
Northwest Utility Company
a. The student must realize that the cost of debt is related to the
cost of debt for other debt issues of the same risk class.
Although, in actuality, the rate Northwest might pay will
b. Kp = Dp/(Pp – F)
c. Ke = (D1/P0) + g
d.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) …………………
Preferred stock (Kp)…..
Common equity (Ke)
(retained earnings) ….
Weighted average cost
of capital (Ka) …………
5.48%
8.16
13.70
50%
10
40
2.74%
.82
5.48
9.04%
Chapter 11: Cost of Capital
11-29
27. Marginal cost of capital (LO5) Delta Corporation has the following capital structure:
Cost
(aftertax)
Weights
Weighted
Cost
Debt ……………………………………………………….
6.1%
25%
1.53%
Preferred stock (Kp) ……………………………………………………
7.6
10
.76
Common equity (Ke)
(retained earnings) …………………………….……………………
15.1
65
9.82
Weighted average cost of capital (Ka) ……….………………….
12.11%
a. If the firm has $26 million in retained earnings, at what size capital structure will the
firm run out of retained earnings?
b. The 7.1 percent cost of debt referred to above applies only to the first $13 million of
debt. After that the cost of debt will go up. At what size capital structure will there be
a change in the cost of debt?
11–27. Solution:
Delta Corporation
a.
Retained Earnings
X% of retained earnings in the capital structure
$26million /.65 $40million
=
==
b.
Amount of lower cost debt
Z% of debt in the capital structure
$13 million /.25 $52 million
=
==
Chapter 11: Cost of Capital
28. Marginal cost of capital (LO5) The Nolan Corporation finds it is necessary to determine
its marginal cost of capital. Nolan’s current capital structure calls for 45 percent debt, 15
percent preferred stock, and 40 percent common equity. Initially, common equity will be in
the form of retained earnings (Ke) and then new common stock (Kn). The costs of the
various sources of financing are as follows: debt, 5.6 percent; preferred stock, 9 percent;
retained earnings, 12 percent; and new common stock, 13.2 percent.
a. What is the initial weighted average cost of capital? (Include debt, preferred stock, and
common equity in the form of retained earnings, Ke.)
b. If the firm has $12 million in retained earnings, at what size capital structure will the
firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point? (Equity will
remain at 40 percent of the capital structure, but will all be in the form of new
common stock, Kn.)
d. The 5.6 percent cost of debt referred to above applies only to the first $18 million of
debt. After that the cost of debt will be 7.2 percent. At what size capital structure will
there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point? (Consider the
facts in both parts c and d.)
11–28. Solution:
Nolan Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ……………….
Preferred stock (Kp) ………………..
Common equity (Ke)
(retained earnings) …………..……..
Weighted average cost of
capital (Ka) ……………………..……
5.60%
9.00
12.00
45%
15
40
2.52%
1.35
4.80
8.67%
Retained earnings
b. X % of retained earnings within the capital structure
$12 million $30 million
.40
=
==