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next dollar of total new financing. Break points rep- the marginal return on its investment equals its
resent the level of total new financing at which the weighted marginal cost of capital.

SELF-TEST PROBLEM (Solution in Appendix B)
ST 10â€“1 Specific costs, WACC, WMCC, and IOS Humble Manufacturing is interested
LG2 LG3 LG4
in measuring its overall cost of capital. The firm is in the 40% tax bracket. Cur-
rent investigation has gathered the following data:
LG6
LG5
Debt The firm can raise an unlimited amount of debt by selling \$1,000-par-
value, 10% coupon interest rate, 10-year bonds on which annual interest pay-
ments will be made. To sell the issue, an average discount of \$30 per bond must
be given. The firm must also pay flotation costs of \$20 per bond.

Preferred stock The firm can sell 11% (annual dividend) preferred stock at its
\$100-per-share par value. The cost of issuing and selling the preferred stock is
expected to be \$4 per share. An unlimited amount of preferred stock can be sold
under these terms.
Common stock The firmâ€™s common stock is currently selling for \$80 per share.
The firm expects to pay cash dividends of \$6 per share next year. The firmâ€™s div-
idends have been growing at an annual rate of 6%, and this rate is expected to
continue in the future. The stock will have to be underpriced by \$4 per share,
and flotation costs are expected to amount to \$4 per share. The firm can sell an
unlimited amount of new common stock under these terms.

Retained earnings The firm expects to have \$225,000 of retained earnings
available in the coming year. Once these retained earnings are exhausted, the
firm will use new common stock as the form of common stock equity
financing.
a. Calculate the specific cost of each source of financing. (Round to the nearest
0.1%.)
411
CHAPTER 10 The Cost of Capital

b. The firm uses the weights shown in the following table, which are based on
target capital structure proportions, to calculate its weighted average cost of
capital. (Round to the nearest 0.1%.)

Source of capital Weight

Long-term debt 40%
Preferred stock 15
Common stock equity 45
Total 100%

(1) Calculate the single break point associated with the firmâ€™s financial situa-
tion. (Hint: This point results from the exhaustion of the firmâ€™s retained
earnings.)
(2) Calculate the weighted average cost of capital associated with total new
financing below the break point calculated in part (1).
(3) Calculate the weighted average cost of capital associated with total new
financing above the break point calculated in part (1).
c. Using the results of part b along with the information shown in the following
table on the available investment opportunities, draw the firmâ€™s weighted
marginal cost of capital (WMCC) schedule and investment opportunities
schedule (IOS) on the same set of axes (total new financing or investment on
the x axis and weighted average cost of capital and IRR on the y axis).

Internal
Investment rate of return Initial
opportunity (IRR) investment

A 11.2% \$100,000
B 9.7 500,000
C 12.9 150,000
D 16.5 200,000
E 11.8 450,000
F 10.1 600,000
G 10.5 300,000

d. Which, if any, of the available investments do you recommend that the firm

PROBLEMS
10â€“1 Concept of cost of capital Wren Manufacturing is in the process of analyzing
LG1
its investment decision-making procedures. The two projects evaluated by the
firm during the past month were projects 263 and 264. The basic variables sur-
rounding each project analysis, using the IRR decision technique, and the result-
ing decision actions are summarized in the following table.
412 PART 4 Long-Term Financial Decisions

Basic variables Project 263 Project 264

Cost \$64,000 \$58,000
Life 15 years 15 years
IRR 8% 15%
Least-cost financing
Source Debt Equity
Cost (after-tax) 7% 16%
Decision
Action Accept Reject
Reason 8% IRR 7% cost 15% IRR 16% cost

a. Evaluate the firmâ€™s decision-making procedures, and explain why the accep-
tance of project 263 and rejection of project 264 may not be in the ownersâ€™
best interest.
b. If the firm maintains a capital structure containing 40% debt and 60%
equity, find its weighted average cost using the data in the table.
c. Had the firm used the weighted average cost calculated in part b, what
actions would have been indicated relative to projects 263 and 264?
d. Compare and contrast the firmâ€™s actions with your findings in part c. Which
decision method seems more appropriate? Explain why.

10â€“2 Cost of debt using both methods Currently, Warren Industries can sell 15-year,
LG2
\$1,000-par-value bonds paying annual interest at a 12% coupon rate. As a
result of current interest rates, the bonds can be sold for \$1,010 each; flotation
costs of \$30 per bond will be incurred in this process. The firm is in the 40% tax
bracket.
a. Find the net proceeds from sale of the bond, Nd.
b. Show the cash flows from the firmâ€™s point of view over the maturity of the
bond.
c. Use the IRR approach to calculate the before-tax and after-tax costs of debt.
d. Use the approximation formula to estimate the before-tax and after-tax costs
of debt.
e. Compare and contrast the costs of debt calculated in parts c and d. Which
approach do you prefer? Why?

10â€“3 Cost of debt using the approximation formula For each of the following
LG2
\$1,000-par-value bonds, assuming annual interest payment and a 40% tax rate,
calculate the after-tax cost to maturity using the approximation formula.

Discount ( ) or
Bond Life Underwriting fee premium ( ) Coupon interest rate

A 20 years \$25 \$20 9%
B 16 40 10 10
C 15 30 15 12
D 25 15 Par 9
E 22 20 60 11
413
CHAPTER 10 The Cost of Capital

10â€“4 Cost of preferred stock Taylor Systems has just issued preferred stock.
LG2
The stock has a 12% annual dividend and a \$100 par value and was sold
at \$97.50 per share. In addition, flotation costs of \$2.50 per share must
be paid.
a. Calculate the cost of the preferred stock.
b. If the firm sells the preferred stock with a 10% annual dividend and nets
\$90.00 after flotation costs, what is its cost?

10â€“5 Cost of preferred stock Determine the cost for each of the following preferred
LG2
stocks.

Preferred stock Par value Sale price Flotation cost Annual dividend

A \$100 \$101 \$9.00 11%
B 40 38 \$3.50 8%
C 35 37 \$4.00 \$5.00
D 30 26 5% of par \$3.00
E 20 20 \$2.50 9%

10â€“6 Cost of common stock equityâ€”CAPM J&M Corporation common stock
LG3
has a beta, b, of 1.2. The risk-free rate is 6%, and the market return
is 11%.
a. Determine the risk premium on J&M common stock.
b. Determine the required return that J&M common stock should provide.
c. Determine J&Mâ€™s cost of common stock equity using the CAPM.

10â€“7 Cost of common stock equity Ross Textiles wishes to measure its cost of com-
LG3
mon stock equity. The firmâ€™s stock is currently selling for \$57.50. The firm
expects to pay a \$3.40 dividend at the end of the year (2004). The dividends for
the past 5 years are shown in the following table.

Year Dividend

2003 \$3.10
2002 2.92
2001 2.60
2000 2.30
1999 2.12

After underpricing and flotation costs, the firm expects to net \$52 per share on a
new issue.
a. Determine the growth rate of dividends.
b. Determine the net proceeds, Nn, that the firm actually receives.
c. Using the constant-growth valuation model, determine the cost of retained
earnings, kr.
d. Using the constant-growth valuation model, determine the cost of new com-
mon stock, kn.
414 PART 4 Long-Term Financial Decisions

10â€“8 Retained earnings versus new common stock Using the data for each firm
LG3
shown in the following table, calculate the cost of retained earnings and
the cost of new common stock using the constant-growth valuation
model.

Projected
Current market Dividend dividend per Underpricing Flotation cost
Firm price per share growth rate share next year per share per share

A \$50.00 8% \$2.25 \$2.00 \$1.00
B 20.00 4 1.00 0.50 1.50
C 42.50 6 2.00 1.00 2.00
D 19.00 2 2.10 1.30 1.70

10â€“9 WACCâ€”Book weights Ridge Tool has on its books the amounts and
LG4
specific (after-tax) costs shown in the following table for each source of
capital.

Source of capital Book value Specific cost

Long-term debt \$700,000 5.3%
Preferred stock 50,000 12.0
Common stock equity 650,000 16.0

a. Calculate the firmâ€™s weighted average cost of capital using book value
weights.
b. Explain how the firm can use this cost in the investment decision-making
process.

10â€“10 WACCâ€”Book weights and market weights Webster Company has compiled
LG4
the information shown in the following table.

Source of capital Book value Market value After-tax cost

Long-term debt \$4,000,000 \$3,840,000 6.0%
Preferred stock 40,000 60,000 13.0
Common stock equity 1,060,000 3,000,000 17.0
Totals \$5,100,000 \$6,900,000

a. Calculate the weighted average cost of capital using book value weights.
b. Calculate the weighted average cost of capital using market value weights.
c. Compare the answers obtained in parts a and b. Explain the differences.

10â€“11 WACC and target weights After careful analysis, Dexter Brothers has deter-
LG4
mined that its optimal capital structure is composed of the sources and target
market value weights shown in the following table.
415
CHAPTER 10 The Cost of Capital

Target market
Source of capital value weight

Long-term debt 30%
Preferred stock 15
Common stock equity 55
Total 100%

The cost of debt is estimated to be 7.2%; the cost of preferred stock is estimated to
be 13.5%; the cost of retained earnings is estimated to be 16.0%; and the cost of
new common stock is estimated to be 18.0%. All of these are after-tax rates. The
companyâ€™s debt represents 25%, the preferred stock represents 10%, and the com-
mon stock equity represents 65% of total capital on the basis of the market values
of the three components. The company expects to have a significant amount of
retained earnings available and does not expect to sell any new common stock.
a. Calculate the weighted average cost of capital on the basis of historical mar-
ket value weights.
b. Calculate the weighted average cost of capital on the basis of target market
value weights.

10â€“12 Calculation of specific costs, WACC, and WMCC Dillon Labs has asked its
LG2 LG3 LG4
financial manager to measure the cost of each specific type of capital as well as
the weighted average cost of capital. The weighted average cost is to be mea-
LG5
sured by using the following weights: 40% long-term debt, 10% preferred stock,
and 50% common stock equity (retained earnings, new common stock, or both).
The firmâ€™s tax rate is 40%.

Debt The firm can sell for \$980 a 10-year, \$1,000-par-value bond paying
annual interest at a 10% coupon rate. A flotation cost of 3% of the par value is
required in addition to the discount of \$20 per bond.

Preferred stock Eight percent (annual dividend) preferred stock having a par
value of \$100 can be sold for \$65. An additional fee of \$2 per share must be
paid to the underwriters.

Common stock The firmâ€™s common stock is currently selling for \$50 per share.
The dividend expected to be paid at the end of the coming year (2004) is \$4. Its
dividend payments, which have been approximately 60% of earnings per share in
each of the past 5 years, were as shown in the following table.

Year Dividend

2003 \$3.75
2002 3.50
2001 3.30
2000 3.15
1999 2.85
416 PART 4 Long-Term Financial Decisions

It is expected that in order to sell, new common stock must be underpriced \$5
per share, and the firm must also pay \$3 per share in flotation costs. Dividend
payments are expected to continue at 60% of earnings.
a. Calculate the specific cost of each source of financing. (Assume that
kr ks.)
b. If earnings available to common shareholders are expected to be \$7
million, what is the break point associated with the exhaustion of retained
earnings?
c. Determine the weighted average cost of capital between zero and the break
point calculated in part b.
d. Determine the weighted average cost of capital just beyond the break point
calculated in part b.

10â€“13 Calculation of specific costs, WACC, and WMCC Lang Enterprises is inter-
LG2 LG3 LG4
ested in measuring its overall cost of capital. Current investigation has gathered
the following data. The firm is in the 40% tax bracket.
LG5

Debt The firm can raise an unlimited amount of debt by selling \$1,000-par-
value, 8% coupon interest rate, 20-year bonds on which annual interest
payments will be made. To sell the issue, an average discount of \$30 per bond
would have to be given. The firm also must pay flotation costs of \$30 per bond.

Preferred stock The firm can sell 8% preferred stock at its \$95-per-share
par value. The cost of issuing and selling the preferred stock is expected to be
\$5 per share. An unlimited amount of preferred stock can be sold under these
terms.

Common stock The firmâ€™s common stock is currently selling for \$90 per share.
The firm expects to pay cash dividends of \$7 per share next year. The firmâ€™s
dividends have been growing at an annual rate of 6%, and this is expected to
continue into the future. The stock must be underpriced by \$7 per share, and
flotation costs are expected to amount to \$5 per share. The firm can sell an
unlimited amount of new common stock under these terms.

Retained earnings When measuring this cost, the firm does not concern itself
with the tax bracket or brokerage fees of owners. It expects to have available
\$100,000 of retained earnings in the coming year; once these retained earnings
are exhausted, the firm will use new common stock as the form of common
stock equity financing.

a. Calculate the specific cost of each source of financing. (Round answers to the
nearest 0.1%.)

Source of capital Weight

Long-term debt 30%
Preferred stock 20
Common stock equity 50
Total 100%
417
CHAPTER 10 The Cost of Capital

b. The firmâ€™s capital structure weights used in calculating its weighted average
cost of capital are shown in the table at the bottom of page 416. (Round
(1) Calculate the single break point associated with the firmâ€™s financial situa-
tion. (Hint: This point results from exhaustion of the firmâ€™s retained
earnings.)
(2) Calculate the weighted average cost of capital associated with total new
financing below the break point calculated in part (1).
(3) Calculate the weighted average cost of capital associated with total new
financing above the break point calculated in part (1).

10â€“14 Integrativeâ€”WACC, WMCC, and IOS Cartwell Products has compiled the
LG4 LG5 LG6
data shown in the following table for the current costs of its three basic sources
of capitalâ€”long-term debt, preferred stock, and common stock equityâ€”for vari-
ous ranges of new financing.

Source of capital Range of new financing After-tax cost

Long-term debt \$0 to \$320,000 6%
\$320,000 and above 8

Preferred stock \$0 and above 17%

Common stock equity \$0 to \$200,000 20%
\$200,000 and above 24

The companyâ€™s capital structure weights used in calculating its weighted
average cost of capital are shown in the following table.

Source of capital Weight

Long-term debt 40%
Preferred stock 20
Common stock equity 40
Total 100%

a. Determine the break points and ranges of total new financing associated with
each source of capital.
b. Using the data developed in part a, determine the break points (levels of total
new financing) at which the firmâ€™s weighted average cost of capital will change.
c. Calculate the weighted average cost of capital for each range of total new
financing found in part b. (Hint: There are three ranges.)
d. Using the results of part c, along with the following information on the
available investment opportunities, draw the firmâ€™s weighted marginal
cost of capital (WMCC) schedule and investment opportunities schedule
(IOS) on the same set of axes (total new financing or investment on the
x axis and weighted average cost of capital and IRR on the y axis).
418 PART 4 Long-Term Financial Decisions

Investment Internal rate of Initial
opportunity return (IRR) investment

A 19% \$200,000
B 15 300,000
C 22 100,000
D 14 600,000
E 23 200,000
F 13 100,000
G 21 300,000
H 17 100,000
I 16 400,000

e. Which, if any, of the available investments do you recommend that the firm

CHAPTER 10 CASE Making Star Productsâ€™
Financing/Investment Decision

S tar Products Company is a growing manufacturer of automobile accessories
whose stock is actively traded on the over-the-counter exchange. During
2003, the Dallas-based company experienced sharp increases in both sales and
earnings. Because of this recent growth, Melissa Jen, the companyâ€™s treasurer,
wants to make sure that available funds are being used to their fullest. Manage-
ment policy is to maintain the current capital structure proportions of 30%
long-term debt, 10% preferred stock, and 60% common stock equity for at least
the next 3 years. The firm is in the 40% tax bracket.
Starâ€™s division and product managers have presented several competing
investment opportunities to Ms. Jen. However, because funds are limited,
choices of which projects to accept must be made. The investment opportunities
schedule (IOS) is shown in the following table.

Investment Opportunities Schedule (IOS)
for Star Products Company

Investment Internal rate of Initial
opportunity return (IRR) investment

A 15% \$400,000
B 22 200,000
C 25 700,000
D 23 400,000
E 17 500,000
F 19 600,000
G 14 500,000
419
CHAPTER 10 The Cost of Capital

To estimate the firmâ€™s weighted average cost of capital (WACC), Ms. Jen con-
tacted a leading investment banking firm, which provided the financing cost data
shown in the following table.

Financing Cost Data
Star Products Company

Long-term debt: The firm can raise \$450,000 of addi-
tional debt by selling 15-year, \$1,000-par-value, 9%
coupon interest rate bonds that pay annual interest. It
expects to net \$960 per bond after flotation costs.
Any debt in excess of \$450,000 will have a before-tax
cost, kd, of 13%.

Preferred stock: Preferred stock, regardless of the
amount sold, can be issued with a \$70 par value and a
14% annual dividend rate and will net \$65 per share
after flotation costs.

Common stock equity: The firm expects dividends
and earnings per share to be \$0.96 and \$3.20, respec-
tively, in 2004 and to continue to grow at a constant
rate of 11% per year. The firmâ€™s stock currently sells
for \$12 per share. Star expects to have \$1,500,000 of
retained earnings available in the coming year. Once
the retained earnings have been exhausted, the firm
can raise additional funds by selling new common
stock, netting \$9 per share after underpricing and
flotation costs.

Required
a. Calculate the cost of each source of financing, as specified:
(1) Long-term debt, first \$450,000.
(2) Long-term debt, greater than \$450,000.
(3) Preferred stock, all amounts.
(4) Common stock equity, first \$1,500,000.
(5) Common stock equity, greater than \$1,500,000.
b. Find the break points associated with each source of capital, and
use them to specify each of the ranges of total new financing over
which the firmâ€™s weighted average cost of capital (WACC) remains
constant.
c. Calculate the weighted average cost of capital (WACC) over each of the
ranges of total new financing specified in part b.
d. Using your findings in part c along with the investment opportunities
schedule (IOS), draw the firmâ€™s weighted marginal cost of capital (WMCC)
and IOS on the same set of axes (total new financing or investment on
the x axis and weighted average cost of capital and IRR on the y axis).
e. Which, if any, of the available investments would you recommend that the
420 PART 4 Long-Term Financial Decisions

WEB EXERCISE Go to the St. Louis Federal Reserve Bank Web site www.stls.frb.org. Click on
WW Economic Research; click on Fred; click on Monthly Interest Rates; and then
W
click on Bank Prime Loan Rate Changesâ€”Historic Dates of Changes and
Ratesâ€”1929.

1. What was the prime interest rate in 1934?
2. What is the highest the prime interest rate has been? When was that?
3. What has been the highest prime interest rate since you were born?
4. What is the present prime interest rate?
5. Over the past 10 years, what was the lowest prime interest rate? What has
been the highest prime interest rate over the past 10 years?

Now go to Barraâ€™s Web site www.barra.com and click on Research Indexes
and then on S&P/Barra U.S. Equity Indexes.

6. What was the average annual 10-year return on large-cap stocks, as mea-
sured by growth in the S&P 500 (annualized 10-year return)? How does this