Problem Set Ch09 and Solutions`

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Problem Set on Chapter 9.

CAPM, beta, and WACC

1.

1. BrBradadshshaw Staw Steeel hael has s a a cacapipitatal l ststruructcturure e wiwith 30 peth 30 perrcecennt t ddebebtt (all long-term bonds) and 70 percent common equity. The yield (all long-term bonds) and 70 percent common equity. The yield to maturity on the company’s long-term bonds is 8 percent, and to maturity on the company’s long-term bonds is 8 percent, and th

the e fifirm rm esestitimamatetes s ththat at itits s ovovereralall l cocompmposositite e WAWACC CC is is 1010 perc

percent. The ent. The riskrisk-fre-free e rate of rate of inteinterest is rest is 5.5 percent5.5 percent, , thethe market risk premium is 5

market risk premium is 5 percent, and the company’s tax rate ispercent, and the company’s tax rate is 40

40 perpercencent. t. BraBradshdshaw aw useuses s the CAPM the CAPM to to detdetermermine its ine its coscost t ofof equity. What is the beta on Bradshaw’s stock?

equity. What is the beta on Bradshaw’s stock?

Beta risk

2.

2. Su

Sun St

n Stat

ate

e Mi

Mini

ning In

ng Inc.

c., an all

, an all-e

-equ

quit

ity fir

y firm

m, is con

, is consi

side

deri

ring th

ng the for

e form

mat

atio

ion

n of a

of a

new division that will increase the assets of the firm by 50 percent. Sun State

currently has a required rate of return of 18 percent, U. S. Treasury bonds

yield 7 percent, and the market risk premium is 5 percent. If Sun State wants

to reduce its required rate of return to 16 percent, what is the maximum beta

coefficient the new division could have?

Risk-adjusted discount rate

3.

3. As

Assu

sume y

me you a

ou are t

re the d

he dir

irec

ecto

tor of c

r of cap

apit

ital b

al bud

udge

geti

ting f

ng for a

or an al

n all-

l-eq

equi

uity f

ty fir

irm. T

m. The

he

firm’s current cost of equity is 16 percent; the risk-free rate is 10 percent; and

the market risk premium is 5 percent. You are considering a new project that

has 50 percent more beta risk than your firm’s assets currently have, that is, its

beta

beta is

is 50

50 percent

percent larger

larger than

than the f

the firm’s e

irm’s existing

xisting beta.

beta. The

The expected

expected return

return on

on

the new project is 18 percent. Should the project be accepted if beta risk is the

appropriate risk measure?

Pure play method

4.

4. In

Inte

ters

rsta

tate Tr

te Tran

ansp

spor

ort ha

t has a

s a ta

targ

rget ca

et capi

pita

tal st

l stru

ruct

ctur

ure of 50 pe

e of 50 perc

rcen

ent deb

t debt and 5

t and 50

0 percent

percent common

common equity.

equity. The

The firm

firm is

is considering

considering a

a new

new independent

independent project

project

that has an expected return of 13 percent and is not related to transportation.

How

Howev

ever,

er, a

a pur

pure

e pla

play

y pro

proxy

xy fir

firm

m ha

has

s bee

been

n ide

ident

ntifi

ified

ed tha

that

t is

is exc

exclu

lusiv

sively

ely

engaged in the new line of business. The proxy firm has a beta of 1.38. Both

firms have a marginal tax rate of 40 percent, and Interstate’s before-tax cost of

deb

debt

t is

is 12

12 pe

perce

rcent. The

nt. The ri

risk-

sk-fre

free

e rat

rate

e is

is 10

10 per

percen

cent

t and the

and the ma

marke

rket

t ri

risk

sk

premium is 5 percent. What s

premium is 5 percent. What should the firm do?

hould the firm do?

5.

Longstreet Corporation has a target capital structure that consists of 30 percent debt, 50Longstreet Corporation has a target capital structure that consists of 30 percent debt, 50 percent

percent common common equity, equity, and and 20 20 percent percent preferred preferred stock. stock. The The tax tax rate rate is is 30 30 percent. percent. TheThe company has projects in which it would like to invest with costs that total $1,500,000. company has projects in which it would like to invest with costs that total $1,500,000. Longstreet will retain $500,000 of net income this year. The last dividend was $5, the current Longstreet will retain $500,000 of net income this year. The last dividend was $5, the current stock price is $75, and the growth rate of the company is 10 percent. If the company raises stock price is $75, and the growth rate of the company is 10 percent. If the company raises capital through a new equity issuance, the flotation costs are 10 percent. The cost of preferred capital through a new equity issuance, the flotation costs are 10 percent. The cost of preferred stock is 9 percent and the cost of debt is 7 percent. (Assume debt and preferred stock have no stock is 9 percent and the cost of debt is 7 percent. (Assume debt and preferred stock have no

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flotation costs.) What is the weighted average cost of capital at the firm’s optimal capital budget?

6.

Lamonica Motors just reported earnings per share of $2.00. The stock has a price earnings ratio of 40, so the stock’s current price is $80 per share. Analysts expect that one year from now the company will have an EPS of $2.40, and it will pay its first dividend of $1.00 per share. The stock has a required return of 10 percent. What price earnings ratio must the stock have one year from now so that investors realize their expected return?

7.

Heavy Metal Corp. is a steel manufacturer that finances its operations with 40 percent debt, 10 percent preferred stock, and 50 percent equity. The interest rate on the company’s debt is 11 percent. The preferred stock pays an annual dividend of $2 and sells for $20 a share. The company’s common stock trades at $30 a share, and its current dividend (D0) of $2 a share is

expected to grow at a constant rate of 8 percent per year. The flotation cost of external equity is 15 percent of the dollar amount issued, while the flotation cost on preferred stock is 10 percent. The company estimates that its WACC is 12.30 percent. Assume that the firm will not have enough retained earnings to fund the equity portion of its capital budget. What is the company’s tax rate?

8.

Anderson Company has four investment opportunities with the following costs (paid at t = 0) and expected returns:

Expected Project Cost Return

A $2,000 16.0%

B 3,000 14.5

C 5,000 11.5

D 3,000 9.5

The company has a target capital structure that consists of 40 percent common equity, 40 percent debt, and 20 percent preferred stock. The company has $1,000 in retained earnings. The company expects its year-end dividend to be $3.00 per share (D1= $3.00). The dividend

is expected to grow at a constant rate of 5 percent a year. The company’s stock price is currently $42.75. If the company issues new common stock, the company will pay its investment bankers a 10 percent flotation cost.

The company can issue corporate bonds with a yield to maturity of 10 percent. The company is in the 35 percent tax bracket. How large can the cost of preferred stock be (including flotation costs) and it still be profitable for the company to invest in all four projects?

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Solutions to Problem Set Ch. 10

1. CAPM, beta, and WACC

Data given:

w

d

= 0.3; w

c

= 0.7; k

d

= 8%; T = 0.4; k

RF

= 5.5%, k

M

- k

RF

= 5%.

Step 1:

Determine the firm’s cost of equity using the WACC equation:

WACC

= w

d×

k

d×

(1 - T) + w

c×

k

s

10% = 0.3

×

8%

×

(1 - 0.4) + 0.7

×

k

s

8.56%= 0.7

×

k

s

k

s

= 12.2286%.

Step 2:

Calculate the firm’s beta using the CAPM equation:

k

s

= k

RF

+ (k

M

- k

RF

)b

12.2286% = 5.5% + (5%)b

6.7286% = 5%b

b = 1.3457

≈

1.35.

2. Beta risk

Old assets = 1.0. New assets = 0.5. Total assets = 1.5.

Old required rate: New required rate:

18% = 7% + (5%)b 16% = 7% + (5%)b

beta = 2.2. beta = 1.8.

New b must not be greater than 1.8, therefore 1.5 1 (2.2) + 1.5 0.5 (b) = 1.8 0.3333(b) = 0.3333 b = 1.0.

Therefore, beta of the new division cannot exceed 1.0.

3. Risk-adjusted discount rate

Calculate the beta of the firm, and use to calculate project beta:

ks = 0.16 = 0.10 + (0.05)bFirm. bFirm = 1.2.

bProject = (bFirm)1.5. (bProject is 50% greater than current bFirm)

bProject = (1.2)1.5 = 1.8.

Calculate required return on project, kProject, and compare to

expected return:

Project: kProject = 0.10 + (0.05)1.8 = 0.19 = 19%. Expected

return = 0.18 = 18%. Since the required return is one percentage point greater than the expected return, the firm should not accept the new project.

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4. Pure play method

Calculate the required return, ks, and use to calculate the

WACC:

ks = 10% + 1.38(5%) = 16.9%.

WACC = 0.5(12.0%)(0.6) + 0.5(16.9%) = 12.05%.

Compare expected project return,

kˆProject

, to WACC:

But

kˆProject

= IRR = 13.0%.

Accept the project since IRRProject > WACC: 13.0% > 12.05%.

5. WACC

First, calculate the aftertax component cost of debt as 7%(1 -0.3) = 4.9%. Next, calculate the retained earnings breakpoint as $500,000/0.5 = $1,000,000. Thus, to finance its optimal capital budget, Longstreet must issue some new equity and flotation costs of 10% will be incurred. The cost of new equity is then [$5(1.10%)/$75(1 - 0.1)] + 10% = 8.15% + 10% = 18.15%. Finally, the WACC = 4.9%(0.3) + 9%(0.2) + 18.15%(0.5) = 12.34%. 6

.

Expected return and P/E ratio

Data given: EPS = $2.00; P/E = 40×; P0= $80; D1= $1.00; k s= 10%; EPS1= $2.40.

Step 1: Calculate the price of the stock one year from today: k s = D1/P0+ (P1- P0)/P0

0.10 = $1/$80 + (P1- $80)/$80

8 = $1 + P1- $80

$87 = P1.

Step 2: Calculate the P/E ratio one year from today: P/E = $87/$2.40 = 36.25×. 7. WACC Capital structure: 40% D, 10% P, 50% E. WACC = 12.30% (given). kd = 11% (given). WACC = 0.4(kd)(1 - T) + 0.1(kp) + 0.5(ke).

Because the firm has insufficient retained earnings to fund the equity portion of the firm’s capital budget, use ke in the WACC

calculation. a. Calculate ke: ke = $30(0.85) $2(1.08) + 8% = 8.47% + 8% = 16.47%. b. Calculate k p: kp = P D N p = $20(0.9) $2 = 11.11%.

c. Find T by substituting values for kd , k p, and ke in the WACC

equation:

0.1230 = 0.4(0.11)(1 - T) + 0.1(0.1111) + 0.5(0.1647) 0.1230 = 0.044(1 - T) + 0.0111 + 0.0824

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0.0295 = 0.044(1 - T) 0.6713 = 1 - T

0.3287 = T.

8. WACC and cost of preferred

We need to find k p at the point where all 4 projects are accepted. In other words, the capital

budget = $2,000 + $3,000 + $5,000 + $3,000 = $13,000. The WACC at that point is equal to IRR D= 9.5%.

Step 1: Find the retained earnings break point to determine whether k s or k e is used in the

WACC calculation: BPRE=

0.4 $1,000

= $2,500.

Since the capital budget > the retained earnings break point, k e is used in the

WACC calculation. Step 2: Calculate k e: k e= ) $42.75(0.9 $3.00 + 5% = 12.80%. Step 3: Find k p: 9.5% = 0.4(10%)(0.65) + 0.2(k ps) + 0.4(12.80%) 9.5% = 2.60% + 0.2(k ps) + 5.12% 1.78% = 0.2k p 8.90% = kp.