Chapter 11: Cost of Capital
11-11
Russell Container Corporation (Continued)
a. Kd = Yield (1 – T)
b. It has gone down. Although the before-tax yield is higher,
12. Real-world example and cost of debt (LO3) Kerr-McGee Corp. is planning to issue debt
that will mature in 2027. In many respects the issue is similar to currently outstanding debt
of the corporation. Using Table 11-2, identify:
a. The yield to maturity on similarly outstanding debt for the firm, in terms of maturity.
b. Assume that because the new debt will be issued at par, the required yield to maturity
will be 0.15 percent higher than the value determined in part a. Add this factor to the
answer in a. (New issues at par sometimes require a slightly higher yield than old
issues that are trading below par. There is less leverage and fewer tax advantages.)
c. If the firm is in a 30 percent tax bracket, what is the aftertax cost of debt?
11–12. Solution:
Kerr-McGee Corp. 2027
a. 8.44%
b. 8.44% + .15% = 8.59%
c. Kd = Yield (1 – T)
Chapter 11: Cost of Capital
11-12
13. Cost of preferred stock (LO3) Medco Corporation can sell preferred stock for $80 with
an estimated flotation cost of $3. It is anticipated the preferred stock will pay $6 per share
in dividends.
a. Compute the cost of preferred stock for Medco Corp.
b. Do we need to make a tax adjustment for the issuing firm?
11–13. Solution:
Medco Corporation
a.
p
p
p
D
KPF
$6 $6 7.79%
$80 $3 $77
=
−
= = =
−
corporate recipient).
14. Cost of preferred stock (LO3) The Meredith Corporation issued $100 par value preferred
stock 10 years ago. The stock provided an 8 percent yield at the time of issue. The
preferred stock is now selling for $75. What is the current yield or cost of the preferred
stock? (Disregard flotation costs.)
11–14. Solution:
Meredith Corporation
p
D$8
Yield = 10.67%
P $75
==
15. Comparison of the costs of debt and preferred stock (LO3) The treasurer of Riley Coal
Co. is asked to compute the cost of fixed income securities for her corporation. Even before
making the calculations, she assumes the aftertax cost of debt is at least 2 percent less than
that for preferred stock. Based on the facts below, is she correct?
Chapter 11: Cost of Capital
11-13
Debt can be issued at a yield of 10.6 percent, and the corporate tax rate is 35 percent.
Preferred stock will be priced at $50 and pay a dividend of $4.40. The flotation cost on the
preferred stock is $2.
11–15. Solution:
Riley Coal Inc.
Aftertax cost of debt
d
K Yield (1 T)
=10.6%(1 .35) = 10.6% (.65) = 6.89%
=−
−
Aftertax cost of preferred stock
p
p
p
D$4.40 $4.40
K 9.17%
P F $50 $2 $48
= = = =
−−
versus 9.17%).
16. Costs of retained earnings and new common stock (LO3) Barton Electronics wants you
to calculate its cost of common stock. During the next 12 months, the company expects to
pay dividends (D1) of $1.20 per share, and the current price of its common stock is $30 per
share. The expected growth rate is 9 percent.
a. Compute the cost of retained earnings (Ke). Use Formula 11-6.
b. If a $2 flotation cost is involved, compute the cost of new common stock (Kn). Use
Formula 11-7.
11–16. Solution:
Barton Electronics
a.
1
e
0
D
Kg
P
$1.20
= 9% 4% 9% 13%
$30
=+
+ = + =
Chapter 11: Cost of Capital
b.
1
n
0
D
Kg
PF
$1.20 $1.20
= 9% 9%
$30 $2 $28
4.29% 9% 13.29%
=+
−
+ = +
−
= + =
17. Costs of retained earnings and new common stock (LO3) Compute Ke and Kn under the
following circumstances:
a. D1 = $4.60, P0 = $60, g = 6%, F = $3.00.
b. D1 = $0.25, P0 = $20, g = 9%, F = $1.50.
c. E1 (earnings at the end of period one) = $6, payout ratio equals 30 percent, P0 = $24,
g = 4.5%, F = $1.60.
d. D0 (dividend at the beginning of the first period) = $3, growth rate for dividends and
earnings (g) = 8%, P0 = $50, F = $3.
11–17. Solution:
a.
Chapter 11: Cost of Capital
b.
1
e
0
1
n
0
D
Kg
P
$.25
= 9% 1.25% 9% 10.25%
$20
D
Kg
PF
$.25 $.25
= 9% 9%
$20 $1.50 $18.50
1.35% 9% 10.35%
=+
+ = + =
=+
−
+ = +
−
= + =
11–17. (Continued)
c.
11
D 30% E 30% $6.00 $1.80= = =
1
e
0
1
n
0
D
Kg
P
$1.80
= 4.5% 7.5% 4.5% 12%
$24
D
Kg
PF
$1.80
= 4.5%
$24 $1.60
$1.80 4.5% 8.04% 4.5% 12.54%
$22.40
=+
+ = + =
=+
−
+
−
= + = + =
Chapter 11: Cost of Capital
d.
10
1
e
0
1
n
0
D D (1 g) $3.00 (1.08) $3.24
D
Kg
P
$3.24 8% 6.48% 8% 14.48%
$50
D
Kg
PF
$3.24 $3.24
8% 8%
$50 $3 $47
6.89% 8% 14.89%
= + = =
=+
= + = + =
=+
−
= + = +
−
= + =
18. Growth rates and common stock valuation (LO3) O’Neal’s Men’s Shops, Inc.,
specializes in large-size clothing. Business has been good, as indicated by the six-year
growth in earnings per share. The earnings have grown from $1.00 to $1.87.
a. Use Appendix A at the back of the text to determine the compound annual rate of
growth in earnings (n = 6).
b. Based on the growth rate determined in part a, project earnings for next year (E1).
(Round to two places to the right of the decimal point.)
c. Assume the dividend payout ratio is 40 percent. Compute (D1). (Round to two places
to the right of the decimal point).
d. The current price of the stock is $18. Using the growth rate (g) from part a and D1
from part c, compute Ke.
e. If the flotation cost is $1.50, compute the cost of new common stock (Kn).
11–18. Solution:
O’Neal’s Men’s Shops, Inc.
1.00 = = =
Chapter 11: Cost of Capital
b.
10
E E (1 g)
$1.87 (1.11)
$2.08
=+
=
=
c.
11
D E 40%
$2.08 40%
$.83
=
=
=
d.
1
e
o
D
Kg
P
$.83 11%
$18
4.61% 11%
15.61%
=+
=+
=+
=
11–18. (Continued)
e.
1
n
o
D
Kg
PF
$.83 11%
$18 $1.50
$.83 11%
$16.50
5.03% 11% 16.03%
=+
−
=+
−
=+
= + =
Chapter 11: Cost of Capital
19. Weighted average cost of capital (LO1) United Business Forms’ capital structure is as
follows:
Debt …………………….. 35%
Preferred stock ………. 15
Common equity ……… 50
The aftertax cost of debt is 7 percent; the cost of preferred stock is 10 percent; and the cost
of common equity (in the form of retained earnings) is 13 percent.
Calculate United Business Forms’ weighted average cost of capital in a manner similar
to Table 11-1.
11–19. Solution:
United Business Forms
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ………………………..…
Preferred stock (Kp) ………………..
Common equity (Ke)
(retained earnings) …………..……..
Weighted average cost of
capital (Ka) ……………………..……
7.0%
10.0
13.0
35%
15
50
2.45%
1.50
6.50
10.45%
20. Weighted average cost of capital (LO1) As an alternative to the capital structure shown
in Problem 19 for United Business Forms, an outside consultant has suggested the
following modifications.
Debt …………………….. 65%
Preferred stock ………. 5
Common equity ……… 30
Under this new, more debt-oriented arrangement, the aftertax cost of debt is 9.8 percent;
the cost of preferred stock is 12 percent, and the cost of common equity (in the form of
retained earnings) is 15.5 percent.
Recalculate United Business Forms’ weighted average cost of capital. Which plan is
optimal in terms of minimizing the weighted average cost of capital?
11–20. Solution:
Chapter 11: Cost of Capital
United Business Forms (Continued)
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ………………………..…
Preferred stock (Kp) ………………..
Common equity (Ke)
(retained earnings) …………..……..
Weighted average cost of
capital (Ka) ……………………..……
9.8%
12.0
15.5
65%
5
30
6.37%
0.60
4.65
11.62%
The plan presented in Problem 11-19 is the better alternative.
21. Weighted average cost of capital (LO1) Sauer Milk, Inc. wants to determine the
minimum cost of capital point for the firm. Assume it is considering the following financial
plans:
Cost
(aftertax)
Weights
Plan A
Debt …………………………….…
5.0%
20%
Preferred stock …………………
10.0
10
Common equity ……………..…
14.0
70
Plan B
Debt …………………………….…
5.5%
30%
Preferred stock …………………
10.5
10
Common equity ……………..…
15.0
60
Plan C
Debt …………………………….…
6.0%
40%
Preferred stock …………………
10.7
10
Common equity ……………..…
15.8
50
Plan D
Debt …………………………….…
8.0%
50%
Preferred stock …………………
11.2
10
Common equity ……………..…
17.5
40
Chapter 11: Cost of Capital
11-20
a. Which of the four plans has the lowest weighted average cost of capital? (Round to
two places to the right of decimal point.)
b. Briefly discuss the results from Plan C and Plan D, and why one is better than
the other.
11–21. Solution:
Sauer Milk, Inc.
a. Cost Weighted
(after tax) Weights Cost
Plan A
Debt
5.0%
20%
1.00%
Preferred stock
10.0
10
1.00
Common equity
14.0
70
9.80
11.80%
Plan B
Debt
5.5%
30%
1.65%
Preferred stock
10.5
10
1.05
Common equity
15.0
60
9.00
11.70%
Plan C
Debt
6.0%
40%
2.4
Preferred stock
10.7
10
1.07
Common equity
15.8
50
7.90
11.37%
Plan D
Debt
8.0%
50%
4.00%
Preferred stock
11.2
10
1.12
Common equity
17.5
40
7.00
12.12%
Plan C has the lowest weighted average cost of capital.