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Chapter 11: Cost of Capital
11-31
11-28. (Continued)
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...................
Preferred stock (Kp) ..
New common stock
(Kn) ...........................
Marginal cost of capital
(Kmc) .........................
5.60%
9.00
13.20
45%
15
40
2.52%
1.35
5.28
9.15%
Amount of lower cost debt
d. Z % of debt within the capital structure
$18 million $40 million
.45
=
==
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ................................
Preferred stock (Kp) ....................
New common stock
(Kn) .............................................
Marginal cost of capital
(Kmc) ...........................................
7.20%
9.00
13.20
45%
15
40
3.24%
1.35
5.28
9.87%
Chapter 11: Cost of Capital
29. Marginal cost of capital (LO5) The McGee Corporation finds it is necessary to determine
its marginal cost of capital. McGee’s current capital structure calls for 40 percent debt, 5
percent preferred stock, and 55 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, 7.4 percent; preferred stock, 10.0 percent;
retained earnings, 13.0 percent; and new common stock, 14.4 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 $27.5 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 55 percent of the capital structure, but will all be in the form of new
common stock, Kn.)
d. The 7.4 percent cost of debt referred to above applies only to the first $32 million of
debt. After that the cost of debt will be 8.6 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.)
11-29. Solution:
The McGee Corporation
a.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ................................
Preferred stock (Kp) ....................
Common equity (Ke)
(retained earnings) ......................
Weighted average cost of
capital (Ka) ................................
7.40%
10.00
13.00
40%
5
55
2.96%
.50
7.15
10.61%
b.
Retained earnings
X% of retained earnings within the capital structure
$27.5 million $50 million
=
Chapter 11: Cost of Capital
11-33
11-29. (Continued)
c.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...................
Preferred stock (Kp) ...
New common stock
(Kn) ............................
Marginal cost of capital
(Kmc) ..........................
7.40%
10.00
14.40
40%
5
55
2.96%
.50
7.92
11.38%
d.
Amount of lower cost debt
Z% of debt within the capital structure
$32 million $80 million
.40
=
==
e.
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...................
Preferred stock (Kp) ...
New common stock
(Kn) ............................
Marginal cost of capital
(Kmc) ..........................
8.60%
10.00
14.40
40%
5
55
3.44%
.50
7.92
11.86%
Chapter 11: Cost of Capital
30. Capital asset pricing model and dividend valuation model (LO3) Eaton Electronic
Company’s treasurer uses both the capital asset pricing model and the dividend valuation
model to compute the cost of common equity (also referred to as the required rate of return
for common equity).
Assume:
Rf = 5%
Km = 10%
β = 1.2
D1 = $.80
Po = $20
g = 7%
a. Compute Ki (required rate of return on common equity based on the capital asset
pricing model).
b. Compute Ke (required rate of return on common equity based on the dividend
valuation model).
11-30. Solution:
Eaton Electronic Company
a. Kj = Rf.+ β(Km – Rf)
1
e
0
D
b. K = g
P
$.80
= 7%
$20
4% 7% 11%
+
+
=+=
Although the values are equal in this example, that is not always
the case.
Chapter 11: Cost of Capital
11-35
COMPREHENSIVE PROBLEM
Comprehensive Problem 1.
Southern Textiles (marginal cost of capital and investment returns) (LO5) Southern Textiles
is in the process of expanding its productive capacity to introduce a new line of products. Current
plans call for a possible expenditure of $100 million on four projects of equal size ($25 million),
but different returns. Project A will increase the firm’s processed yarn capacity and has an
expected return of 15 percent after taxes. Project B will increase the capacity for woven fabrics
and carries a return of 13.5 percent. Project C, a venture into synthetic fibers, is expected to earn
11.2 percent, and Project D, an investment into dye and textile chemicals, is expected to show a
10.5 percent return.
The firm’s capital structure consists of 40 percent debt and 60 percent common equity and
this will continue in the future. There is no preferred stock.
Southern Textile has $15 million in retained earnings. After a capital structure with $15
million in retained earnings is reached (in which retained earnings represent 60 percent of the
financing), all additional equity financing must come in the form of new common stock.
Common stock is selling for $30 per share and underwriting costs are estimated at $3 if new
shares are issued. Dividends for the next year will be $1.50 per share (D1), and earnings and
dividends have grown consistently at 9 percent per year.
The yield on comparative bonds has been hovering at 11 percent. The investment banker
feels that the first $20 million of bonds could be sold to yield 11 percent while additional debt
might require a 2 percent premium and be sold to yield 13 percent. The corporate tax rate is 34
percent.
a. Based on the two sources of financing, what is the initial weighted average cost of capital?
(Use Kd and Ke.)
b. 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?
d. 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?
f. Based on the information about potential returns on investments in the first paragraph and
information on marginal cost of capital (in parts a, c, and e), how large a capital investment
budget should the firm use?
g. Graph the answer determined in part f.
CP 11-1. Solution: Marginal Cost of
Capital and Investment Returns
Southern Textiles
a. Kd = Yield (1 – T)
Chapter 11: Cost of Capital
11-36
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...........................
7.26%
40%
2.90%
Common equity (Ke)
(retained earnings) ..........
14.00
60
8.40
Weighted average cost
of capital (Ka) .................
11.30%
b.
Retained earnings
X% of retained earnings in the capital structure
$15 million $25 million
.60
=
==
c. First compute Kn
Kn = (D1/(P0 – F)) + g
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...........................
7.26%
40%
2.90%
New common stock
(Kn) ................................
14.56
60
8.74
Marginal cost of capital
(Kmc) ...............................
11.64%
CP 11-1. (Continued)
d.
Amount of lower cost debt
Z% of debt in the capital structure
$20 million $50 million
.40
=
==
Chapter 11: Cost of Capital
11-37
e. First compute the new value for Kd
Kd = Yield (1 – T)
Cost
(aftertax)
Weights
Weighted
Cost
Debt (Kd) ...........................
8.58%
40%
3.43%
New common stock
(Kn) ................................
14.56
60
8.74
Marginal cost of capital
(Kmc) ...............................
12.17%
f. The answer is $50 million.
Return on
Investment
Marginal Cost
of Capital
1st $25 million
15.0%
>
11.30%
$25 million - $50 million
13.5%
>
11.63%
$50 million - $75 million
11.2%
<
12.17%
$75 million - $100 million
10.5%
<
12.17%
