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Chapter 11
Discussion Questions
11-1.
Why do we use the overall cost of capital for investment decisions even when
only one source of capital will be used (e.g., debt)?
Though an investment financed by low-cost debt might appear acceptable at
first glance, the use of debt could increase the overall risk of the firm and
eventually make all forms of financing more expensive. Each project must be
measured against the overall cost of funds to the firm.
11-2.
How does the cost of a source of capital relate to the valuation concepts
presented previously in Chapter 10?
The cost of a source of financing directly relates to the required rate of return
for that means of financing. Of course, the required rate of return is used to
establish valuation.
11-3.
In computing the cost of capital, do we use the historical costs of existing debt
and equity or the current costs as determined in the market? Why?
In computing the cost of capital, we use the current costs for the various sources
of financing rather than the historical costs. We must consider what these funds
will cost us to finance projects in the future rather than their past costs.
11-4.
Why is the cost of debt less than the cost of preferred stock if both securities are
priced to yield 10 percent in the market?
Even though debt and preferred stock may be both priced to yield 10 percent in
the market, the cost of debt is less because the interest on debt is a taxdeductible expense. A 10 percent market rate of interest on debt will only cost a
firm in a 35 percent tax bracket an aftertax rate of 6.5 percent. The answer is the
yield multiplied by the difference of (one minus the tax rate).
11-5.
What are the two sources of equity (ownership) capital for the firm?
The two sources of equity capital are retained earnings and new common stock.
11-6.
Explain why retained earnings have an opportunity cost associated?
Retained earnings belong to the existing common stockholders. If the funds are
paid out instead of reinvested, the stockholders could earn a return on them.
Thus, we say retaining funds for reinvestment carries an opportunity cost.
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Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-7.
Why is the cost of retained earnings the equivalent of the firm's own required
rate of return on common stock (Ke)?
Because stockholders can earn a return at least equal to their present
investment. For this reason, the firm's rate of return (Ke) serves as a means of
approximating the opportunities for alternate investments.
11-8.
Why is the cost of issuing new common stock (Kn) higher than the cost of
retained earnings (Ke)?
In issuing new common stock, we must earn a slightly higher return than the
normal cost of common equity in order to cover the distribution costs of the
new security. In the case of the Baker Corporation, the cost of new common
stock was six percent higher.
11-9.
How are the weights determined to arrive at the optimal weighted average cost
of capital?
The weights are determined by examining different capital structures and using
that mix which gives the minimum cost of capital. We must solve a
multidimensional problem to determine the proper weights.
11-10.
Explain the traditional, U-shaped approach to the cost of capital.
The logic of the U-shaped approach to cost of capital can be explained through
Figure 11-1. It is assumed that as we initially increase the debt-to-equity mix
the cost of capital will go down. After we reach an optimum point, the increase
use of debt will increase the overall cost of financing to the firm. Thus we say
the weighted average cost of capital curve is U-shaped.
11-11.
It has often been said that if the company can't earn a rate of return greater than
the cost of capital it should not make investments. Explain.
If the firm cannot earn the overall cost of financing on a given project, the
investment will have a negative impact on the firm's operations and will lower
the overall wealth of the shareholders.
Clearly, it is undesirable to invest in a project yielding 8 percent if the financing
cost is 10 percent.
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-380
11-12.
What effect would inflation have on a company's cost of capital? (Hint: Think
about how inflation influences interest rates, stock prices, corporate profits, and
growth.)
Inflation can only have a negative impact on a firm's cost of capital-forcing it to
go up. This is true because inflation tends to increase interest rates and lower
stock prices, thus raising the cost of debt and equity directly and the cost of
preferred stock indirectly.
11-13.
What is the concept of marginal cost of capital?
The marginal cost of capital is the cost of incremental funds. After a firm
reaches a given level of financing, capital costs will go up because the firm
must tap more expensive sources. For example, new common stock may be
needed to replace retained earnings as a source of equity capital.
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Copyright © 2005 by The McGraw-Hill Companies, Inc.
Appendix A
Discussion Questions
11A-1.
How does the capital asset pricing model help explain changing costs of
capital?
The capital asset pricing model explains the relationship between risk and
return, and the price adjustment of capital assets to changes in risk and return.
As investors react to their economic environment and their willingness to take
risk, they change the prices of financial assets like common stock, bonds, and
preferred stock. As the prices of these securities adjust to investors' required
returns, the company's cost of capital is adjusted accordingly.
11A-2.
How does the SML react to changes in the rate of interest, changes in the rate of
inflation, and changing investor expectations?
The SML, Security Market Line, reflects the risk-return tradeoffs of securities.
As interest rates increase, the SML moves up parallel to the old SML. Now
investors require a higher minimum return on risk free assets and an equally
higher rate for all levels of risk. A change in the rate of inflation has a similar
impact. The risk free rate goes up to provide the appropriate inflation premium
and there is an upward shift in the SML.
In regard to changing investor expectations, as investors become more risk
averse, the SML increases its slope. The more risk taken, the greater the return
premium that is desired (see figure 11A-4).
Copyright © 2005 by The McGraw-Hill Companies, Inc.
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Problems
Rambo Exterminator Company bought a “Bug Eradicator” in April of 2004 that
provided a return of 7 percent. It was financed by debt costing 6 percent. In
August, Mr. Rambo came up with an “entire bug colony destroying” device that
had a return of 12 percent. The Chief Financial Officer, Mr. Roach, told him it
was impractical because it would require the issuance of common stock at a cost
of 13.5 percent to finance the purchase. Is the company following a logical
approach to using its cost of capital.
11-1.
Solution:
Rambo Exterminator Company
No, each individual project should not be measured against the specific
means of financing that project, but rather against the weighted average
cost of financing all projects for the firm. This principle recognizes that
the availability of one source of financing is dependent on other
sources. Once a common overall cost is determined, the “colony
destroying device” yielding 12 percent is much more likely to be
accepted than the “bug eradicator” only yielding 7 percent.
11-2.
Sullivan Cement Company can issue debt yielding 13 percent. The company is
paying a 36 percent rate. What is the aftertax cost of debt?
Solution:
Sullivan Cement Company
Kd
=
=
=
=
Yield (1 – T)
13% (1 – .36)
13% (.64)
8.32%
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Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-3.
Calculate the aftertax cost of debt under each of the following conditions.
Yield
a. 8.0%
b. 12.0%
c. 10.6%
Corporate Tax Rate
18%
34%
15%
Solution:
Kd
= Yield (1 – T)
(1 – T)
(1 – .18)
(1 – .34)
(1 – .15)
Yield
a. 8.0%
b. 12.0%
c. 10.6%
11-4.
Yield (1 – T)
6.56%
7.92%
9.01%
The Millennium Charitable Foundation, which is tax-exempt, issued debt last
year at 8 percent to help finance a new playground facility in Chicago. This year
the cost of debt is 15 percent higher; that is, firms that paid 10 percent for debt
last year would be paying 11.5 percent this year.
a. If the Millennium Charitable Foundation borrowed money this year, what
would the aftertax cost of debt be, based on their cost last year and the 15
percent increase?
b. If the Foundation was found to be taxable by the IRS (at a rate of 35
percent) because it was involved in political activities, what would the
aftertax cost of debt be?
Solution:
Millennium Charitable Foundation
a. Kd
Yield
Kd
b. Kd
=
=
=
=
Yield (1 – T)
8% x 1.15 = 9.20%
9.2% (1 – 0) = 9.2% (1) = 9.2%
9.2% (1 – 35) = 9.2% (65) = 5.98%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-384
11-5.
Waste Disposal Systems, Inc., has an aftertax cost of debt of 6 percent. With a
tax rate of 33 percent, what can you assume the yield on the debt is?
Solution:
Waste Disposal Systems, Inc.
K d  Yield (1  T)
Yield 
Kd
1  T 
Yield 
6%
6%

 8.95%
1  .33 .67
9% is an acceptable answer.
11-6.
Addison Glass Company has a $1,000 par value bond outstanding with 25 years
to maturity. The bond carries an annual interest payment of $88 and is currently
selling for $925. Addison is in a 25 percent tax bracket. The firm wishes to
know what the aftertax cost of a new bond issue is likely to be. The yield to
maturity on the new issue will be the same as the yield to maturity on the old
issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue
and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
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Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-6. Continued
Solution:
Addison Glass Company
a.
Principal payment  Price of the bond
Number of years to maturity
.6 (Price of bond)  .4 (Principal payment)
Annual interest payment 
Y' 
$1,000  $925
25

.6 $925  .4 $1,000
$88 
$75
25

$555  $400
$88 

$88  $3
$955

$91
 9.53%
$955
b. Kd =
=
=
=
Yield (1 – T)
9.53% (1 – .25)
9.53% (.75)
7.15%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-386
11-7.
Hewlett Software Corporation has a $1,000 par value bond outstanding with 20
years to maturity. The bond carries an annual interest payment of $110 and is
currently selling for $1,080 per bond. Hewlett is in a 35 percent tax bracket. The
firm wishes to know what the aftertax cost of a new bond issue is likely to be.
The yield to maturity on the new issue will be the same as the yield to maturity
on the old issue because the risk and maturity date will be similar.
a. Compute the approximate yield to maturity (Formula 11-1) on the old issue
and use this as the yield for the new issue.
b. Make the appropriate tax adjustment to determine the aftertax cost of debt.
Solution:
Hewlett Software Corporation
a.
Principal payment  Price of the bond
Number of years to maturity
.6 (Price of bond)  .4 (Principal payment)
Annual interest payment 
Y' 
$1,000  $1,080
20

.6 $1,080  .4 $1,000
$110 
 $80
20

$648  $400
$110 

$110  $4
$1,048

$106
 10.11%
$1,048
S-387
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-7. Continued
b. Kd = Yield (1 – T)
= 10.11% (1 – .35)
= 10.11% (.65)
= 6.57%
11-8.
For Hewlett Software Corporation, described in problem 7, assume that the
yield on the bonds goes up by 1 percentage point and that the tax rate is now 45
percent.
a. What is the new aftertax cost of debt?
b. Has the aftertax cost of debt gone up or down from problem 7? Explain
why.
Solution:
Hewlett Software Corporation (Continued)
a. Kd = Yield (1 – T)
= 11.11% (1 – .45)
= 11.11% (.55)
= 6.11%
b. It has gone down. Although the before-tax yield is higher, the larger
tax deduction (45 percent versus 35 percent) more than offsets the
higher rate.
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-388
11-9.
Mead Corporation is planning to issue debt that will mature in the year 2025. In
many respects the issue is similar to currently outstanding debt of the
corporation. Using Table 11-2 in the chapter,
a. Identify 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?
Solution:
Mead Corporation
a. 7.51%
b. 7.51% + .15% = 7.66%
c. Kd = Yield (1 – T)
= 7.66% (1 – .30)
= 7.66% (.70)
= 5.36%
S-389
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-10.
Burger Queen can sell preferred stock for $70 with an estimated flotation cost of
$2.50. It is anticipated that the preferred stock will pay $6 per share in
dividends.
a. Compute the cost of preferred stock for Burger Queen.
b. Do we need to make a tax adjustment for the issuing firm?
Solution:
Burger Queen
a. K p 
Dp
Pp  F

$6.00
$70.00  $2.50

$6.00
$67.50
 8.89%
b. No tax adjustment is required. Preferred stock dividends are not a
tax deductible expense for the issuing firm (the dividends, of course,
are 70 percent tax exempt to a corporate recipient).
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-390
11-11.
Wallace Container Company issued $100 par value preferred stock 12 years
ago. The stock provided a 9 percent yield at the time of issue. The preferred
stock is now selling for $72. What is the current yield or cost of the preferred
stock? (Disregard flotation costs.)
Solution:
Wallace Container Company
Yield 
D p $9

 12.5%
Pp $72
11-12.
The treasurer of Bio Science, Inc., 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 following facts, is she correct?
Debt can be issued at a yield of 11 percent, and the corporate tax rate is 30
percent. Preferred stock will be priced at $50, and pay a dividend of $4.80. The
floatation cost on the preferred stock is $2.10.
Solution:
Bio Science, Inc.
Aftertax cost of debt
Kd = Yield (1 – T)
= 11% (1 – .30) = 11% (.70) = 7.70%
Aftertax cost of preferred stock
Kp 

Dp
Pp  F
$4.80
$4.80

 10.02%
$50  $2.10 $47.90
Yes, the treasurer is correct. The difference is 2.32% (7.70% versus
10.02%).
S-391
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-13.
Murray Motor Company wants you to calculate its cost of common stock.
During the next 12 months, the company expects to pay dividends (D1) of $2.50
per share, and the current price of its common stock is $50 per share. The
expected growth rate is 8 percent.
a. Compute the cost of retained earnings (Ke). Use Formula 11-6.
b. If a $3 floatation cost is involved, compute the cost of new common stock
(Kn). Use Formula 11-7.
Solution:
Murray Motor Co.
a. K e 

b. K n 

D1
g
P0
$2.50
 8%  5%  8%  13%
$50
D1
g
P0  F
$2.50
$2.50
 8% 
 8%
$50  $3
$47
 5.32%  8%  13.32%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-392
11-14.
Compute Ke and Kn under the following circumstances:
a. D1 = $4.20, P0 = $55, g = 5%, F = $3.80.
b. D1 = $0.40, P0 = $15, g = 8%, F = $1.
c. E1 (earnings at the end of period one) = $8, payout ratio equals 25 percent,
P0 = $32, g = 5%, F = $2.
d. D0 (dividend at the beginning of the first period) = $3, growth rate for
dividends and earnings (g) = 9%, P0 = $60, F = $3.50.
Solution:
a. K e 

Kn 

D1
g
P0
$4.20
 5%  7.64%  5%  12.64%
$55
D1
g
P0  F
$4.20
$4.20
 5% 
 5%
$55  $3.80
$51.20
 8.20%  5%  13.20%
b. K e 

D1
g
P0
$0.40
 8%  2.66%  8%  10.66%
$15
S-393
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-14. Continued
Kn 
D1
g
P0  F

$.40
 8%
$15  $1

$.40
 8%  2.86%  8%  10.86%
$14
c. D1  25%  E1  25%  $8.00  $2.00
Ke 

Kn 
D1
g
P0
$2.00
 5%  6.25%  5%  11.25%
$32
D1
g
P0  F

$2.00
 5%
$32  $2

$2.00
 5%  6.67%  5%  11.67%
$30
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-394
11-14. Continued
d. D1  D 0 1  g   $3.00  1.09  $3.27
Ke 

Kn 
11-15.
D1
g
P0
$3.27
 9%  5.45%  9%  14.45%
$60
D1
g
P0  F

$3.27
 9%
$60  $3.50

$3.27
 9%  5.79%  9%  14.79%
$56.50
Business has been good for Keystone Control Systems, as indicated by the fouryear growth in earnings per share. The earnings have grown from $1.00 to
$1.63.
a. Use Appendix A at the back of the text to determine the compound annual
rate of growth in earnings (n = 4).
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 $50. Using the growth rate (g) from part a
and (D1) from part c, compute Ke.
e. If the floatation cost is $3.75, compute the cost of new common stock (Kn).
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Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-15. Continued
Solution:
Keystone Control Systems
a.
$1.63
 FVIF1.63n  4i  13%
1.00
b. E1 = Eo (1 + g)
= $1.63 (1.13)
= $1.84
c. D1 = E1 x 40%
= $1.84 x 40%
= $.74
d. Ke =
=
D1
g
Po
$.74
 13%
$50
= 1.48% + 13%
= 14.48%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-396
11-15. Continued
e. K n 
D1
g
Po  F

$.74
 13%
$50  $3.75

$.74
 13%
$46.25
 1.6%  13%  14.60%
S-397
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-16.
Global Technology’s capital structure is as follows:
Debt ........................................
Preferred stock .......................
Common equity......................
35%
15
50
The aftertax cost of debt is 6.5 percent; the cost of preferred stock is 10 percent;
and the cost of common equity (in the form of retained earnings) is 13.5
percent.
Calculate Global Technology’s weighted average cost of capital in a manner
similar to Table 11-1.
Solution:
Global Technology
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Cost
(aftertax)
6.5%
10.0
13.5
Weighted
Weights
Cost
35%
2.27%
15
1.50
50
6.75
10.52%
S-398
11-17.
As an alternative to the capital structure shown in problem 16 for Global
Technology, an outside consultant has suggested the following modifications.
Debt .................................................
Preferred stock ................................
Common equity...............................
60%
5
35
Under this new, more debt-oriented arrangement, the aftertax cost of debt is 8.8
percent; the cost of preferred stock is 11 percent; and the cost of common equity
(in the form of retained earnings) is 15.6 percent.
Recalculate Global’s weighted average cost of capital. Which plan is optimal in
terms of minimizing the weighted average cost of capital?
Solution:
Global Technology (Continued)
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Cost
(aftertax)
8.8%
11.0
15.6
Weighted
Weights
Cost
60%
5.28%
5
0.55
35
5.46
11.29%
The plan presented in Problem 11-12 is the better alternative. Even
though the second plan has more relatively cheap debt, the increased
costs of all forms of financing more than offset this factor.
S-399
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-18.
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 .................................................
Preferred stock ................................
Common equity...............................
30%
15
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%
Solution:
The Hamilton Corp.
Kd =
=
=
=
Yield (1 – T)
11% (1 – 0.30)
11% (.70)
7.7%
The bond yield of 11% is used rather than the coupon rate of 13%
because bonds are priced in the market according to competitive yields
to maturity. The new bond would be sold to reflect yield to maturity.
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-400
11-18. Continued
Kp 

Ke 

Dp
Pp  F
$10.00
$10.00

 10.81%
$98  $5.50 $92.50
D1
g
P0
$3
 8%  6%  8%  14%
$50
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Cost
(aftertax)
7.70%
10.81
14.00
Weighted
Weights
Cost
30%
2.31%
15
1.62
55
7.70
11.63%
S-401
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-19.
Given the following information, calculate the weighted average cost of capital
for Digital Processing, Inc. Line up the calculations in the order shown in Table
11-1.
Percent of capital structure:
Preferred stock ................................
Common equity...............................
Debt .................................................
15%
40%
45%
Additional information:
Corporate tax rate ............................
34%
Dividend, preferred .........................
$8.50
Dividend, expected common ..........
$2.50
Price, preferred ................................ $105.00
Growth rate .....................................
7%
Bond yield .......................................
9.5%
Flotation cost, preferred ..................
$3.60
Price, common ................................ $75.00
Solution:
Digital Processing, Inc.
Kd =
=
=
=
Yield (1 – T)
9.5% (1 – .34)
9.5% (.66)
6.27
Kp = Dp/(Pp – F)
= $8.50/($105 – 3.60) = $8.50/$101.40 = 8.38%
Ke = (D1/P0) + g
= ($2.50/$75) + 7% = 3.33% + 7% = 10.33%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-402
11-19. Continued
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
11-20.
Cost
(aftertax)
6.27%
8.38
10.33
Weighted
Weights
Cost
45%
2.82%
15
1.26
40
4.13
8.21%
Carr Auto Parts is trying to calculate its cost of capital for use in a capital
budgeting decision. Mr. Horn, 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 12 percent coupon rate
and a convertible bond with an 8.1 percent coupon rate. The firm has been
informed by its investment banker, Axle, Wiell, and Axle, that bonds of equal
risk and credit rating are now selling to yield 14 percent. The common stock has
a price of $30 and an expected dividend (D1) of $1.30 per share. The firm's
historical growth rate of earnings and dividends per share has been 15.5 percent,
but security analysts on Wall Street expect this growth to slow to 12 percent in
future. The preferred stock is selling at $60 per share and carries a dividend of
$6.80 per share. The corporate tax rate is 30 percent. The flotation costs are 3
percent of the selling price for preferred stock.
The optimum capital structure for the firm seems to be 45 percent debt, 5
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).
S-403
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-20. Continued
Solution:
Carr Auto Parts
Kd = Yield (1 – T)
= 14% (1 – .30) = 9.80%
Kp = Dp/(Pp – F)
= $6.80/($60 – $1.80*) = $6.80/$58.20 = 11.68%
*3% x $60 = $1.80
Ke = (D1/Po) + g
= ($1.30/$30.00) + 12% = 4.33 + 12% = 16.33%
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Cost
(aftertax)
9.80%
11.68
16.33
Weighted
Weights
Cost
45%
4.41%
5
.58
55
8.98
13.97%
S-404
11-21.
First Tennessee Utility Company faces increasing needs for capital. Fortunately,
it has an Aa2 credit rating. The corporate tax rate is 36 percent. First
Tennessee’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 earning and dividends per share have
increased at about 6 percent annual rate.
First Tennessee’s common stock is selling at $60 per share, and the company
will pay a $4.80 per share dividend (D1). The company's $100 preferred stock
has been yielding 9 percent in the current market. Flotation costs for the
company have been estimated by its investment banker to be $1.50 for preferred
stock. The company's optimum capital structure is 40 percent debt, 10 percent
preferred stock, and 50 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 First Tennessee. Compute the answer to questions a, b, c, and d
from the information given.
Data on Bond Issues
Issue
Utilities:
Balt, G&E 8 ⅜s 2010
New York Tel. Co. 7 1/2s 2009
Miss. Pow. 9.62s 2011
Industrials:
IBM 9 ⅜s 2016
May Department St. 7.95s 2010
General Mills 9 ⅜s 2009
Moody's
Rating
Price
Yield to
Maturity
Aa1
Aa2
A1
$ 975.25
850.75
960.50
8.60%
9.11
9.67
Aaa
Aa3
A2
$1,050.50 8.50
940.00 11.81
1,030.75 9.05
Compute the answers to the following questions from the information given.
a. Cost of debt, Kd. (Use the above 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.
S-405
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-21. Continued
Solution:
First Tennessee Utility Company
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 First Tennessee might pay will not be exactly equal to New
York Telephone Company, it should be close enough to serve as an
approximation.
a. Kd = Yield (1 – T)
= 9.11% (1 – .36) = 9.11% (.64) = 5.83%
b. Kp = Dp/(Pp – F)
= $9.00/($100 – $1.50) = $9.00/$98.50 = 9.14%
c. Ke = (D1/Po) + g
= ($4.80/$60.00) + 6% = 8% + 6% = 14.00%
d.
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Cost
(aftertax)
5.83%
9.14
14.00
Weighted
Weights
Cost
40%
2.33%
10
.91
50
7.00
10.24%
S-406
11-22.
Eaton International Corporation has the following capital structure:
Debt (Kd) ................................
Preferred stock (Kp) ...............
Common equity (Ke)
(retained earnings) ...............
Weighted average cost
of capital (Ka) .......................
Cost
(aftertax)
7.1%
8.6
14.1
Weights
25%
10
Weighted
Cost
2.66%
.86
65
9.17
12.69%
a. If the firm has $19.5 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 $14
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?
Solution:
Eaton International Corporation
a.
X
Retained Earnings
% of retained earnings in the capital structure
 $19.5 million/.65  $30 million
b.
Z
Amount of lower cost debt
% of debt in the capital structure
 $14 million/.25  $56 million
S-407
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-23.
The Evans Corporation finds it is necessary to determine its marginal cost of
capital. Evan'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, 6.2 percent;
preferred stock, 9.4 percent; retained earnings, 12.0 percent; and new common
stock, 13.4 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 $20 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 6.2 percent cost of debt referred to above applies only to the first $36
million of debt. After that the cost of debt will be 7.8 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.)
Solution:
The Evans Corporation
a.
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
b. X 

Cost
(aftertax)
6.2%
9.4
12.0
Weighted
Weights
Cost
45%
2.79%
15
1.41
40
9.00%
Retained earnings
% of retained earnings within th e capital structure
$20 million
 $50 million
.40
Copyright © 2005 by The McGraw-Hill Companies, Inc.
4.80
S-408
11-23. Continued
c.
Debt (Kd)......................................
Preferred stock (Kp) .....................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
d. Z 

Cost
(aftertax)
6.2%
9.4
13.4
Weighted
Weights
Cost
45%
2.79%
15
1.41
40
5.36
9.56%
Amount of lower cost debt
% of debt withi n the capital structure
$36 million
 $80 million
.45
e.
Debt (Kd)......................................
Preferred stock (Kp) .....................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
Cost
(aftertax)
7.8%
9.4
13.4
Weighted
Weights
Cost
45%
3.51%
15
1.41
40
5.36
10.28%
S-409
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11-24.
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.)
Solution:
The McGee Corporation
a.
Cost
(aftertax)
7.40%
10.00
Debt (Kd)......................................
Preferred stock (Kp) .....................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
b. X 

13.00
Weighted
Weights
Cost
40%
2.96%
5
.50
55
10.61%
Retained earnings
% of retained earnings within th e capital structure
$27.5 million
 $50 million
.55
Copyright © 2005 by The McGraw-Hill Companies, Inc.
7.15
S-410
11-24. Continued
c.
Debt (Kd)......................................
Preferred stock (Kp) .....................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
d. Z 

Cost
(aftertax)
7.40%
10.00
14.40
Weighted
Weights
Cost
40%
2.96%
5
.50
55
7.92
11.38%
Amount of lower cost debt
% of debt withi n the capital structure
$32 million
 $80 million
.40
e.
Debt (Kd)......................................
Preferred stock (Kp) .....................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
Cost
(aftertax)
8.60%
10.00
14.40
Weighted
Weights
Cost
40%
3.44%
5
.50
55
7.92
11.86%
S-411
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Comprehensive Problems
CP 11-1.
Medical Research Corporation is expanding its research and production
capacity to introduce a new line of products. Current plans call for the
expenditure of $100 million on four projects of equal size ($25 million each),
but different returns. Project A is in blood clotting proteins and has an expected
return of 18 percent. Project B relates to a hepatitis vaccine and carries a
potential return of 14 percent. Project C, dealing with a cardiovascular
compound, is expected to earn 11.8 percent, and Project D, an investment in
orthopedic implants, is expected to show a 10.9 percent return.
The firm has $15 million in retained earnings. After 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 $25 per share and underwriting costs are estimated
at $3 if new shares are issued. Dividends for the next year will be $.90 per share
(D1), and earnings and dividends have grown consistently at 11 percent per
year.
The yield on comparative bonds has been hovering at 11 percent. The
investment banker feels that the first $20 million of bonds could be sold to yield
11 percent while additional debt might require a 2 percent premium and be sold
to yield 13 percent. The corporate tax rate is 30 percent. Debt represents 40
percent of the capital structure.
a. Based on the two sources of financing, what is the initial weighted average
cost of capital? (Use Kd and Ke.)
b. At what size capital structure will the firm run out of retained earnings?
c. What will the marginal cost of capital be immediately after that point?
d. At what size capital structure will there be a change in the cost of debt?
e. What will the marginal cost of capital be immediately after that point?
f. Based on the information about potential returns on investments in the first
paragraph and information on marginal cost of capital (in parts a, c, and e),
how large a capital investment budget should the firm use?
g. Graph the answer determined in part f.
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-412
CP 11-1. Continued
Solution:
Marginal Cost of
Capital and Investment Returns
Medical Research Corporation
a. Kd = Yield (1 – T)
= 11% (1 – .30) = 11% (.70) = 7.70%
Ke = (D1/Po) + g
= ($.90/$25.00) + 11.0% = 3.6% + 11.0% = 14.60%
Debt (Kd)......................................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
b. X 

Cost
(aftertax)
7.70%
Weighted
Weights
Cost
40%
3.08%
14.60
60
8.76
11.84%
Retained earnings
% of retained earnings in the capital structure
$15 million
 $25 million
.60
c. First compute Kn
Kn = (D1/(Po – F)) + g
= ($.90/($25 – $3)) + 11%
= ($.90/$22) + 11% = 4.09% + 11% = 15.09%
S-413
Copyright © 2005 by The McGraw-Hill Companies, Inc.
CP 11-1. Continued
Debt (Kd)......................................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
d. Z 

Cost
(aftertax)
7.70%
15.09
Weighted
Weights
Cost
40%
3.08%
60
9.05
12.13%
Amount of lower cost debt
% of debt in the capital structure
$20 million
 $50 million
.40
e. First compute the new value for Kd
Kd = Yield (1 – T)
= 13% (1 – .30) = 13% (.70) = 9.10%
Debt (Kd)......................................
New common stock
(Kn) ............................................
Marginal cost of capital
(Kmc) ..........................................
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Cost
(aftertax)
9.10%
15.09
Weighted
Weights
Cost
40%
3.64%
60
9.05
12.69%
S-414
CP 11-1. Continued
f. The answer is $50 million.
Return on
Investment
18.0%
14.0%
11.8%
10.9%
1st $25 million
$25 million - $50 million
$50 million - $75 million
$75 million - $100 million
>
>
<
<
Marginal Cost
of Capital
11.84%
12.13%
12.69%
12.69%
g. Top bar represents return on investment
Dotted line represents marginal cost of capital (Kmc)
Invest up to $50 million
Percent (return)
18%
14%
12.69%
Kmc
12.13%
11.8%
11.84%
10.9%
0
25
50
75
100
Amount of Capital ($ millions)
S-415
Copyright © 2005 by The McGraw-Hill Companies, Inc.
CP 11-2.
Masco Oil and Gas Company is a very large company with common stock
listed on the New York Stock Exchange and bonds traded over the counter. As
of the current balance sheet, it has three bond issues outstanding:
$150 million of 10% series
$50 million of 7% series
$75 million of 5% series
Expiration
2015
2009
2006
The vice president of finance is planning to sell $75 million of bonds next year
to replace the debt due to expire in 2006. Present market yields on similar Baarated bonds are 12.1 percent. Masco also has $90 million of 7.5 percent
noncallable preferred stock outstanding, and it has no intentions of selling any
preferred stock at any time in the future. The preferred stock is currently priced
at $80 per share, and its dividend per share is $7.80.
The company has had very volatile earnings, but its dividends per share have
had a very stable growth rate of 8 percent and this will continue. The expected
dividend (D1) is $1.90 per share, and the common stock is selling for $40 per
share. The company's investment banker has quoted the following flotation
costs to Masco: $2.50 per share for preferred stock and $2.20 per share for
common stock.
On the advice of its investment banker, Masco has kept its debt at 50 percent of
assets and its equity at 50 percent. Masco sees no need to sell either common or
preferred stock in the foreseeable future as it has generated enough internal
funds for its investment needs when these funds are combined with debt
financing. Masco’s corporate tax rate is 40 percent.
Compute the cost of capital for the following:
a.
b.
c.
d.
e.
Bond (debt) (Kd).
Preferred stock (Kp).
Common equity in the form of retained earnings (Ke).
New common stock (Kn)
Weighted average cost of capital.
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-416
CP 11-2. Continued
Solution:
Cost of Capital with
Changing Financial Needs
Masco Oil and Gas Company
a. The before tax cost of debt will be equal to the market rate of
12.1%. The student must realize that the historical cost of the three
bonds does not influence the cost of debt.
Kd = Yield (1 – T)
= 12.1% (1 – .4) = 12.1% (.6) = 7.26%
b. The fact that the preferred stock carries a coupon rate of 7.5% does
not influence Kp, which is dependent upon current prices and the
dividend.
Kp = (Dp)/(Pp – F)
= ($7.80)/($80 – $2.50) = ($7.80)/($77.50) = 10.06%
c. Ke = (D1/Po) + g
= ($1.90/$40.00) + 8.0% = 4.75% + 8.0% = 12.75%
d. Kn = (D1/Po – F)) + g
= ($1.90/($40 – $2.20)) + 8%
= ($1.90/$37.80) + 8% = 5.03% + 8% = 13.03%
S-417
Copyright © 2005 by The McGraw-Hill Companies, Inc.
CP 11-2. Continued
e. Only those sources of capital that are expected to be used as longrun optimum components of the capital structure should be included
in the weighted average cost of capital. The firm states that all their
funds can be supplied by retained earnings (50%), therefore, we do
not need to include new common stock or preferred stock in our
calculation of the weighted cost of capital.
Debt (Kd)......................................
Common equity (Ke)
(retained earnings) .....................
Weighted average cost
of capital (Ka) ............................
Copyright © 2005 by The McGraw-Hill Companies, Inc.
Cost
(aftertax)
7.26%
12.75
Weighted
Weights
Cost
50%
3.63%
50
6.37
10.00%
S-418
Appendix
11A-1.
Assume that Rf = 5 percent and Km = 10.5 percent. Compute Kj for the
following betas, using Formula 11A-2.
a. 0.6
b. 1.3
c. 1.9
Solution:
a. Kj
=
=
=
=
=
Rf + β (Km – Rf)
5% + .6 (10.5% – 5%)
5% + .6 (5.5%)
5% + 3.3%
8.3%
b. Kj
=
=
=
=
5% + 1.3 (10.5% – 5%)
5% + 1.3 (5.5%)
5% + 7.15%
12.15%
c. Kj
=
=
=
=
5% + 1.9 (10.5% – 5%)
5% + 1.9 (5.5%)
5% + 10.45%
15.45%
S-419
Copyright © 2005 by The McGraw-Hill Companies, Inc.
11A-2.
In the preceding problem, assume an increase in interest rates changes Rf to 6.0
percent, and the market risk premium (Km – Rf) changes to 7.0 percent.
Compute Kj for the three betas of 0.6, 1.3, and 1.9.
Solution:
a. Kj
= 6% + .6 (7%)
= 6% + 4.2%
= 10.2%
b. Kj
= 6% + 1.3 (7%)
= 6% + 9.1%
= 15.1%
c. Kj
= 6% + 1.9 (7%)
= 6% + 13.3%
= 19.3%
Copyright © 2005 by The McGraw-Hill Companies, Inc.
S-420