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 tax-deductible
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.
S11-1
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.
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 increased 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.
S11-2
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.
S11-3
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).
S11-4
Chapter 11
Problems
1.
Rambo Exterminator Company bought a “Bug Eradicator” in April of 2008 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.
S11-5
2.
Royal Petroleum Co. can buy a piece of equipment that is anticipated to provide a 9 percent
return and can be financed at 6 percent with debt. Later in the year, the firm turns down
an opportunity to buy a new machine that would yield a 16 percent return but would cost
18 percent to finance through common equity. Assume debt and common equity each
represent 50 percent of the firm’s capital structure.
a. Compute the weighted average cost of capital.
b. Which project(s) should be accepted?
11-2. Solution:
Royal Petroleum Co.
a.
Cost
Debt
Common equity
Weighted average cost of
capital
6%
18%
Weighted
Weights
Cost
50%
50%
3%
9%
12%
b. Only the new machine with a return of 16 percent.
The return exceeds the weighted average cost of capital of
11.0 percent.
S11-6
3.
Sullivan Cement Company can issue debt yielding 13 percent. The company is paying a
36 percent rate. What is the aftertax cost of debt?
11-3. Solution:
Sullivan Cement Company
Kd = Yield (1 – T)
= 13% (1 – .36)
= 13% (.64)
= 8.32%
4.
Calculate the aftertax cost of debt under each of the following conditions.
a.
b.
c.
Yield
8.0%
12.0%
10.6%
Corporate Tax Rate
18%
34%
15%
11-4. Solution:
Kd = Yield (1 – T)
a.
b.
c.
Yield
8.0%
12.0%
10.6%
(1 – T)
(1 – .18)
(1 – .34)
(1 – .15)
S11-7
Yield (1 – T)
6.56%
7.92%
9.01%
5.
Calculate the aftertax cost of debt under each of the following conditions.
Yield
9.0%
10.6
8.5
a.
b.
c.
Corporate Tax Rate
25%
35
0
11-5. Solution:
Kd = Yield (1 – T)
a.
b.
c.
6.
Yield
9.0%
10.6%
8.5%
(1 – T)
(1 – .25)
(1 – .35)
(1 – 0)
Yield(1 – T)
6.75%
6.89%
8.50%
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
after tax cost of debt be, based on its 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?
11-6. Solution:
Millennium Charitable Foundation
a. Kd
Yield
Kd
= Yield (1 – T)
= 8% × 1.15 = 9.20%
= 9.2% (1 – 0) = 9.2% (1) = 9.2%
b. Kd
= 9.2% (1 – .35) = 9.2% (.65) = 5.98%
S11-8
7.
Useless Tool Co. 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?
11-7. Solution:
Useless tool co.
K d  Yield 1  T 
Yield =
Kd
1  T 
6%
6%

 8.95%
1

.33
.67


9% is an acceptable answer.
Yield =
S11-9
8.
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.
11-8. Solution:
Addison Glass Company
Principal payment  Price of the bond
Number of years to maturity
.6 (Price of bond)  .4 (Principal payment)
Annual interest payment 
a.
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%
S11-10
9.
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.
11-9. Solution:
Hewlett Software Corporation
Principal payment  Price of the bond
Number of years to maturity
.6 (Price of bond)  .4 (Principal payment)
Annual interest payment 
a.
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
b. Kd
= Yield (1 – T)
= 10.11% (1 – .35)
= 10.11% (.65)
= 6.57%
S11-11
10.
For Hewlett Software Corporation described in problem 9, 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 9? Explain why.
11-10. Solution:
Hewlett Software Corporation (Continued)
a. Kd = Yield (1 – T)
= 12.00% (1 – .45)
= 12.00% (.55)
= 6.60%
b. The cost has gone up. The increased yield had a greater
impact than the changed tax rate.
11.
McDonald’s Corporation is planning to issue debt that will mature in 2028. In many
respects the issue is similar to currently outstanding debt of the corporation. Using
Table 11-2 of 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 0.20 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?
11-11. Solution:
Mc Donald’s Corporation
a. 5.80%
b. 5.80% + .20% = 6.00%
c. Kd = Yield (1 – T)
= 6.00% (1 – .30)
= 6.00% (.70)
= 4.20%
S11-12
12.
Burger Queen can sell preferred stock for $70 with an estimated flotation cost of $2.50.
It is anticipated 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?
11-12. Solution:
Burger Queen
a.
Kp 

Dp
Pp  F
$6.00
$6.00

 8.89%
$70.00  $2.50 $67.50
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).
13.
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.)
11-13. Solution:
Wallace Container Company
Yield =
Dp
Dp

$9
 12.5%
$72
S11-13
14.
The treasurer of BioScience, 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 pays a dividend of $4.80. The flotation cost on
the preferred stock is $2.10.
11-14. Solution:
Bio Science, Inc.
Aftertax cost of debt
K d  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%).
S11-14
15.
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 flotation cost is involved, compute the cost of new common stock (Kn).
Use Formula 11-7.
.
11-15. Solution:
Murray Motor Co.
a.
Ke 
=
b.
Kn 
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%
=
S11-15
16.
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.
11-16. Solution:
a.
Ke 
D1
g
P0
$4.20
 5%  7.64%  5%  12.64%
$55
D1
Kn 
g
P0  F
=
$4.20
$4.20
 5% 
 5%
$55  $3.80
$51.20
 8.20%  5%  13.20%
=
b.
Ke 
D1
g
P0
$0.40
 8%  2.66%  8%  10.66%
$15
D1
Kn 
g
P0  F
=
$.40
 8%
$15  $1
$.40

 8%  2.86%  8%  10.86%
$14
=
S11-16
11-16. (Continued)
c.
D1  25%  E1  25%  $8.00  $2.00
D
Ke  1  g
P0
$2.00
 5%  6.25%  5%  11.25%
$32
D1
Kn 
g
P0  F
=
$2.00
 5%
$32  $2
$2.00

 5%  6.67%  5%  11.67%
$30
=
d.
D1  D0 (1  g)  $3.00  (1.09)  $3.27
Ke 
D1
g
P0
$3.27
 9%  5.45%  9%  14.45%
$60
D1
Kn 
g
P0  F

$3.27
 9%
$60  $3.50
$3.27

 9%  5.79%  9%  14.79%
$56.60

S11-17
17.
Business has been good for Keystone Control Systems, as indicated by the four-year
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 flotation cost is $3.75, compute the cost of new common stock (Kn).
11-17. Solution:
Keystone Control Systems
$1.63
 FVIF
1.00
From Appendix A, FVIF = 1.63 for (n = 4, i = 13%).
a.
b.
E1  E 0 (1  g)
 $1.63 (1.13)
 $1.84
c.
D1  E1  40%
 $1.84  40%
 $.74
d. K e 
D1
g
Po
$.74
 13%
$50
 1.48%  13%
 14.48%

S11-18
11-17. (Continued)
e.
Kn 
D1
g
Po  F
$.74
 13%
$50  $3.75
$.74

 13%
$46.25
 1.6%  13%  14.60%

18.
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.
11-18. Solution:
Global Technology
Cost
(aftertax) Weights
Debt (Kd) ......................................
6.5%
35%
Preferred stock (Kp)......................
10.0
15
Common equity (Ke)
(retained earnings) ......................
13.5
50
Weighted average cost
of capital (Ka) .............................
S11-19
Weighted
Cost
2.27%
1.50
6.75
10.52%
19.
As an alternative to the capital structure shown in problem 18 for Global Technology, an
outside consultant has suggested the following modifications.
Debt ............................
Preferred stock ...........
Common equity..........
60%
5
35
Under this new and 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?
11-19. Solution:
Global Technology (Continued)
Cost
(aftertax) Weights
Debt (Kd) ......................................
8.8%
60%
Preferred stock (Kp)......................
11.0
5
Common equity (Ke)
(retained earnings) ......................
15.6
35
Weighted average cost
of capital (Ka) .............................
Weighted
Cost
5.28%
0.55
5.46
11.29%
The plan presented in Problem 11-18 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.
S11-20
20.
Mary Ott Hotels wants to determine the minimum cost of capital point for the firm.
Assume it is considering the following financial plans:
Cost (aftertax)
Plan A
Debt .......................................
Preferred stock ......................
Common equity .....................
Plan B
Debt .......................................
Preferred stock ......................
Common equity .....................
Plan C
Debt .......................................
Preferred stock ......................
Common equity .....................
Plan D
Debt .......................................
Preferred stock ......................
Common equity .....................
a.
b.
Weights
6.0%
10.0
13.0
20%
10
70
6.5%
10.5
13.5
30%
10
60
7.0%
10.7
14.2
40%
10
50
9.0%
11.2
16.0
50%
10
40
Which of the four plans has the lowest weighted average cost of capital? (Round to
two places to the right of decimal point.)
Briefly discuss the results from Plan C and Plan D, and why one is better than
the other.
S11-21
11-20. Solution:
a.
Cost
(after tax)
Weights
Weighted
Cost
Plan A
Debt
Preferred stock
Common equity
6.0%
10.0
13.0
20%
10
70
1.20%
1.00
9.10
11.30%
Plan B
Debt
Preferred stock
Common equity
6.5%
10.5
13.5
30%
10
60
1.95%
1.05
8.10
11.10%
Plan C
Debt
Preferred stock
Common equity
7.0%
10.7
14.2
40%
10
50
2.80%
1.07
7.10
10.97%
Plan D
Debt
Preferred stock
Common equity
9.0%
11.2
16.0
50%
10
40
4.50%
1.12
6.40
12.02%
Plan C has the lowest weighted average cost of capital
b. Plan D is higher than Plan C because all components in the
capital structure increased sharply after the firm hit the
50 percent debt level.
S11-22
21.
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%
S11-23
11-21. 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.
Kp 
Dp
Pp  F
$10.00
$10.00

 10.81%
$98  $5.50 $92.50
D
Ke  1  g
P0


$3
 8%  6%  8%  14%
$50
Cost
(aftertax)
Debt (Kd) ......................................7.70%
Preferred stock (Kp)......................
10.81
Common equity (Ke)
(retained earnings)......................
14.00
Weighted average cost
of capital (Ka) .............................
S11-24
Weighted
Weights
Cost
30%
2.31%
15
1.62
55
7.70
11.63%
22.
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
11-22. 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%
S11-25
23.
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 the 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).
11-23. 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% × $60 = $1.80
Ke = (D1/P0) + g
= ($1.30/$30.00) + 12% = 4.33% + 12% = 16.33%
Cost
(aftertax)
Debt (Kd) .....................................9.80%
Preferred stock (Kp) .....................
11.68
Common equity (Ke)
(retained earnings) .....................
16.33
Weighted average cost
of capital (Ka) ............................
S11-26
Weighted
Weights
Cost
45%
4.41%
5
.58
50
8.17
13.16%
24.
McNabb Construction Company is trying to calculate its cost of capital for use in making a
capital budgeting decision. Mr. Reid, 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 9.5 percent coupon rate and
another bond with a 7.8 percent rate. The firm has been informed by its investment banker
that bonds of equal risk and credit rating are now selling to yield 10.5 percent. The
common stock has a price of $98.44 and an expected dividend (D1) of $3.15 per share.
The historical growth pattern (g) for dividends is as follows.
$2.00
2.24
2.51
2.81
Compute the historical growth rate, round it to the nearest whole number, and use it for g.
The preferred stock is selling at $90 per share and pays a dividend of $8.50 per share.
The corporate tax rate is 30 percent. The flotation cost is 2 percent of the selling price for
preferred stock. The optimum capital structure for the firm is 30 percent debt, 10 percent
preferred stock, and 60 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).
S11-27
11-24. Solution:
McNabb Construction Co.
Kd = Yield (1 – T)
= 10.5% (1 – .30) = 10.5% (.70) = 7.35%
Kp = Dp/(Pp – F)
= $8.50/($90 – $1.80) = $8.50/$88.20 = 9.64%
Ke = (D1/P0) + g
D1 = $3.15
P0 = $98.44
g = 12% (see below)
$24/2.00 = 12%
$27/2.24 = 12.05%
$30/2.51 = 11.95%
Round to 12% or $2.81/2.00 = 1.405 n=3, FVIF = 1.405 (APP.A)
g = 12%
Ke = (D1/P0) + g
= $3.15/$98.44 + 12% = 3.20% + 12% = 15.20%
Bring the above values together to compute the weighted average
cost of capital
Debt (Kd) .........................
Preferred stock (Kp) .........
Common equity (Ke)
(retained earnings) .........
Weighted average cost
of capital (Ka) ................
Cost
(aftertax)
7.35%
9.64
15.20
S11-28
Weights
30%
10%
65%
Weighted
Cost
2.205%
.964
9.120
12.289%
or 12.29%
25.
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 earnings and
dividends per share have increased at about a 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 answers to questions a, b, c,
and d from the information given.
Issue
Data on Bond Issues
Moody’s
Rating
Utilities:
Balt, G&E 8⅜s 2010 .........................................Aa1
New York Tel. Co. 7½s 2009 ...........................Aa2
Miss. Pow. 9.62s 2011 ......................................A1
Industrials:
IBM 9⅜s 2016 ..................................................Aaa
May Department St. 7.95s 2010 .......................Aa3
General Mills 9⅜s 2009 ....................................A2
a.
b.
c.
d.
Price
Yield to
Maturity
$ 975.25
850.75
960.50
8.60%
9.11
9.67
$1,050.50
940.00
1,030.75
8.50%
11.81
9.05
Cost of debt, Kd (Use the table above—relate to the utility bond credit rating for
yield.)
Cost of preferred stock, Kp.
Cost of common equity in the form of retained earnings, Ke.
Weighted average cost of capital.
S11-29
11-25. 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) = 5.38%
b. Kp = Dp/(Pp – F)
= $9.00/($100 – $1.50) = $9.00/$98.50 = 9.14%
c. Ke = (D1/P0) + g
= ($4.80/$60.00) + 6% = 8% + 6% = 14.00%
d.
Cost
(aftertax)
Debt (Kd) ............................ 5.83%
Preferred stock (Kp)............ 9.14
Common equity (Ke)
(retained earnings) ............ 14.00
Weighted average cost
of capital (Ka) ...................
S11-30
Weights
40%
10
50
Weighted
Cost
2.33%
.91
7.00
10.24%
26.
Eaton International Corporation has the following capital structure:
Cost
(aftertax) Weights
Debt (Kd) ...............................................................................
7.1%
25%
Preferred stock (Kp)...............................................................
8.6
10
Common equity (Ke)
(retained earnings) ............................................................
14.1
65
Weighted average cost of capital (Ka)...................................
Weighted
Cost
2.66%
.86
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?
11-26. Solution:
Eaton International Corporation
a.
X
Retained Earnings
% of retained earnings in the capital structure
 $26 million / .65  $40 million
b.
Amount of lower cost debt
% of debt in the capital structure
 $14 million / .25  $56 million
Z 
S11-31
27.
The Evans Corporation finds it is necessary to determine its marginal cost of capital.
Evans’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.
b.
c.
d.
e.
What is the initial weighted average cost of capital? (Include debt, preferred stock,
and common equity in the form of retained earnings, Ke.)
If the firm has $20 million in retained earnings, at what size capital structure will the
firm run out of retained earnings?
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.)
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?
What will the marginal cost of capital be immediately after that point? (Consider the
facts in both parts c and d.)
11-27. Solution:
The Evans Corporation
a.
Cost
(aftertax)
Debt (Kd) ...................
6.2%
Preferred stock (Kp)......................
9.4
Common equity (Ke)
(retained earnings) ......................
12.0
Weighted average cost
of capital (Ka) .............................
b. X 

Weighted
Weights
Cost
45%
2.79%
15
1.41
40
4.80
9.00%
Retained earnings
% of retained earnings within the capital structure
$20 million
 $50 million
.40
S11-32
11-27. (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 within the capital structure
$36 million
 $80 million
.40
e.
Cost
(aftertax)
Debt (Kd) ......................................
7.8%
Preferred stock (Kp) .....................
9.4
New common stock
(Kn) .............................................
13.4
Marginal cost of capital
(Kmc) ...........................................
S11-33
Weighted
Weights
Cost
45%
3.51%
15
1.41
40
5.36
10.28%
28.
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.
b.
c.
d.
e.
What is the initial weighted average cost of capital? (Include debt, preferred stock, and
common equity in the form of retained earnings, Ke.)
If the firm has $27.5 million in retained earnings, at what size capital structure will the
firm run out of retained earnings?
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.)
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?
What will the marginal cost of capital be immediately after that point? (Consider the
facts in both parts c and d.)
11-28. Solution:
The McGee Corporation
a.
Cost
(aftertax)
Debt (Kd) ......................................7.40%
Preferred stock (Kp) .....................
10.00
Common equity (Ke)
(retained earnings) .....................
13.00
Weighted average cost
of capital (Ka) .............................
b.
Weighted
Weights
Cost
40%
2.96%
5
.50
55
7.15
10.61%
Retained earnings
% of retained earnings within the capital structure
$27.5 million

 $50 million
.55
X
S11-34
11-28. (Continued)
c.
Debt (Kd)....................
Preferred stock (Kp) ...
New common stock
(Kn) ..........................
Marginal cost of capital
(Kmc).........................
Cost
(aftertax)
7.40%
40.00
14.40
Weights
40%
5
55
Weighted
Cost
2.96%
.50
7.92
11.38%
Amount of lower cost debt
% of debt within the capital structure
$32 million

 $80 million
.40
d. Z 
e.
Debt (Kd)....................
Preferred stock (Kp) ...
New common stock
(Kn) ..........................
Marginal cost of capital
(Kmc).........................
Cost
(aftertax)
8.60%
10.00
14.40
Weights
40%
5
55
Weighted
Cost
3.44%
.50
7.92
11.86%
S11-35
COMPREHENSIVE PROBLEM
Comprehensive Problem 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 potentital 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 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 $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 $20 million of bonds could be sold to yield 11 percent while additional debt
might require a 2 percent premium and be sold to yield 13 percent. The corporate tax rate is 30
percent. Debt represents 40 percent of the capital structure.
a.
b.
c.
d.
e.
f.
g.
Based on the two sources of financing, what is the initial weighted average cost of capital?
(Use Kd and Ke.)
At what size capital structure will the firm run out of retained earnings?
What will the marginal cost of capital be immediately after that point?
At what size capital structure will there be a change in the cost of debt?
What will the marginal cost of capital be immediately after that point?
Based on the information about potential returns on investments in the first paragraph and
information on marginal cost of capital (in parts a, c, and e), how large a capital investment
budget should the firm use?
Graph the answer determined in part f.
S11-36
CP 11-1. Solution:
Medical Research Corporation
a. Kd = Yield (1 – T)
= 11% (1 – .30) = 11% (.70) = 7.70%
Ke = (D1/P0) + g
= ($.90/$25.00) + 11.0% = 3.6% + 11.0% = 14.60%
Cost
(aftertax)
Debt (Kd) ............................. 7.70%
Common equity (Ke)
14.60
(retained earnings) ...........
Weighted average cost
of capital (Ka) ..................
b.
Weights
40%
60
Weighted
Cost
3.08%
8.76
11.84%
Retained earnings
% of retained earnings in the capital structure
$15 million

 $25 million
.60
X
c. First compute Kn
Kn = (D1/(P0 – F)) + g
= ($.90/($25 – $3)) + 11%
= ($.90/$22) + 11% = 4.09% + 11% = 15.09%
Cost
(aftertax)
Debt (Kd) ............................. 7.70%
New common stock
15.09
(Kn) ..................................
Marginal cost of capital
(Kmc) ................................
S11-37
Weights
40%
60
Weighted
Cost
3.08%
9.05
12.13%
CP 11-1. (Continued)
d.
Amount of lower cost debt
% of debt in the capital structure
$20 million

 $50 million
.40
Z
e. First compute the new value for Kd
Kd = Yield (1 – T)
= 13% (1 – .30) = 13% (.70) = 9.10%
Cost
(aftertax)
Debt (Kd) ............................. 9.10%
New common stock
15.09
(Kn) ..................................
Marginal cost of capital
(Kmc) ................................
f.
Weights
40%
60
Weighted
Cost
3.64%
9.05
12.69%
The answer is $50 million.
1st $25 million
$25 million - $50 million
$50 million - $75 million
$75 million - $100 million
Return on
Investment
18.0%
14.0%
11.8%
10.9%
S11-38
>
>
<
<
Marginal Cost
of Capital
11.84%
12.13%
12.69%
12.69%
CP 11-1. (Continued)
g. Top bar represents return on investment
Dotted line represents marginal cost of capital (Kmc)
Invest up to $50 million
Percent (return)
18%
14%
Kmc
12.69%
12.13%
11.8%
11.84%
10.9%
0
25
50
75
Amount of Capital ($ millions)
S11-39
100
Comprehensive Problem 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 percent series .......................
$50 million of 7 percent series ...........................
$75 million of 5 percent series ..........................
2021
2015
2011
The vice-president of finance is planning to sell $75 million of bonds next year to replace the
debt due to expire in 2008. Present market yields on similar Baa-rated 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.
S11-40
CP 11-2. Solution
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/P0) + g
= ($1.90/$40.00) + 8.0% = 4.75% + 8.0% = 12.75%
d. Kn = (D1/P0 – F) + g
= ($1.90/($40 – $2.20)) + 8%
= ($1.90/$37.80) + 8% = 5.03% + 8% = 13.03%
S11-41
CP 11-2. (Continued)
e. Only those sources of capital that are expected to be used
as long-run 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.
Cost
Weighted
(aftertax) Weights
Cost
Debt (Kd) ............................. 7.26%
50%
3.63%
Common equity (Ke)
(retained earnings)............. 12.75
50
6.37
Weighted average cost
of capital (Ka) ....................
10.00%
S11-42
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
11A-1
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 (4%)
5% + 10.45%
15.45%
S11-43
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.
11A-2.
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%
S11-44