This will be a timed exam with 5 detailed questions and the expert will have 3 hours total to complete it.
Caiden
fin508solutionweek7.pdf
FIN 508 Assignment 7 _____________________________________________________________________________
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7.1. Sicily Pharmaceuticals has $10 million in debt and $70 million in equity. Its tax rate is 30%, cost of debt 8%, and beta 1.5. The riskless rate is 5% and the expected return on
the market 12%. Sicily would like to start a newspaper using its existing capital. Sardinia
Times is a daily newspaper. Sardinia has $12 million in debt and $40 million in equity,
with tax rate of 32% and beta 1.25. Find the required rate of return for Sicily in the new
venture. 12.07% ♥
First, consider Sardinia Times, which publishes a newspaper. Its unleveraged beta is
given by (11.3) as
βU(Sardinia) = βL
1 + (1 − t) B/S =
1.25
1 + (1 − .32)(12/40) = 1.038205980
This gives a measure of the risk inherent in the newspaper business. Next, releverage it
using Sicily’s financial data.
βL(Sicily) = βU [1 + (1 − t) B
S ] = 1.038205980 [1 + (1 − 0.3)(10/70)] = 1.142026578
Use CAPM, equation (7.7) to find the cost of equity for Sicily,
ke = .05 + 1.142026578 (.12 − .05) = .1299418605
Finally, find the risk-adjusted WACC of Sicily for this venture. Use (9.5),
WACC = (1 − .3)(.08)(10/80) + .1299418605 (70/80) = .1206991279 = 12.07% ♥
7.2. Consider the financial information of Cyprus Hotels and Corsica Inns, the two hotel chains.
Company Debt/Assets β Cost of debt Tax rate
Cyprus Hotels 21% 1.73 10% 33%
Corsica Inns 29% ? 10% 35%
At present, the risk-free rate is 3% and the expected return on the market 11%. Find the
weighted average cost of capital for Corsica. 14.57% ♥
First, find the debt/equity ratio for Cyprus. Since debt is 21%, equity must be 79%.
Therefore, B/S = .21/.79 = 21/79.
Next, find the unleveraged beta of Cyprus, which represents the risk of the hotel industry.
βU(Cyprus) = βL
1 + (1 − t) B/S =
1.73
1 + (1 − .33)(21/79) = 1.468464596
You can use this as the unleveraged beta of Corsica. For Corsica, debt is 29% and equity
71%, and thus B/S = 29/71. Find the leveraged β for Corsica,
FIN 508 Assignment 7 _____________________________________________________________________________
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βL(Corsica) = βU [1 + (1 − t) B
S ] = 1.468464596 [1 + (1 − 0.35)(29/71)] = 1.858331605
Use CAPM, equation (7.7) to find the cost of equity for Corsica.
ke = .03 + 1.858331605 (.11 − .03) = .1786665284
Finally, find the WACC of Corsica.
WACC = (1 − .35)(.10)(.29) + .1786665284 (.71) = .1457032352 = 14.57% ♥
7.3. The following table provides the financial information of two companies in different businesses, with the dollar amounts in millions:
Company Debt Cost of debt Equity Cost of equity Tax rate Business
Crete Co. $33 11% $107 18% 33% Chemicals
Majorca Co. $12 9% $66 17% 29% Retail stores
At present, the risk-free rate is 4% and the expected return on the market 12%. If Crete
Company wants to start a retail store chain as a side business, using its existing capital,
what is the minimum acceptable rate of return on the new venture? From your analysis,
can you deduce which is the riskier business, chemicals or retail stores?
15.41%, chemicals ♥
First, look at Majorca. Its leveraged beta is given by CAPM, equation (7.7),
.17 = .04 + βL(.12 − .04)
or βL = .17 − .04
.12 − .04 = 1.625
Its unleveraged beta, which represents the risk of retail store business, is given by (11.3)
as
βU = 1.625
1 + (1 − .29)(12/66) = 1.439210950 1.4392 (retail store business)
This is also the unleveraged beta of Crete for its new retail store venture. Leveraging it
for the parameters of Crete, we get by using (11.3),
βL = 1.439210950 [1 + (1 − .33)(33/107)] = 1.736603044
Use CAPM, equation (7.7), to find the cost of equity for Crete
ke = .04 + 1.736603044 (.12 − .04) = .1789282435
FIN 508 Assignment 7 _____________________________________________________________________________
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Next, find the WACC for Crete for this venture. The total value of Crete is 33 + 107 =
$140 million
WACC = (1 − .33)(.11)
33
140 + (.1789282435)
107
140 = .1541244433 = 15.41% ♥
The βL for Crete as a publishing company is given by CAPM
.18 = .04 + βL(.12 − .04)
This gives βL = .18 − .04
.12 − .04 = 1.75
The βU for Crete as a publishing company is
βU = 1.75
1 + (1 − .33)(33/107) = 1.450313686 1.4503 (chemicals)
Comparing the unleveraged betas, we find chemicals business to be slightly more risky. ♥
7.4. Rhodes Company has beta 1.55, debt/assets ratio 25%, and tax rate 31%. The cost of debt for Rhodes is 10%, and of equity 16%. The riskless rate is 5%. Find the WACC of
Rhodes. If its debt/assets ratio is increased to 30% while its cost of debt remains
unchanged, what is the new WACC? Which leverage ratio is better?
WACC(1) = 13.725%, WACC(2) = 13.681%, second is better ♥
The current WACC of Rhodes is
WACC(2) = (1 − .31)(.1)(.25) + .16 (.75) = .13725
Use CAPM to find E(Rm). Using data for Rhodes,
.16 = .05 + 1.55[E(Rm) − .05]
Solving for E(Rm), E(Rm) = (.16 − .05)/1.55 + .05 = .1209677419
The current B/V = .25. If B = .25, then S = .75. Thus B/S = .25/.75 = 1/3. Its unleveraged
beta is
βU = βL
1 + (1 − t) B/S =
1.55
1 + (1 − 0.31)(1/3) = 1.260162602
The new B/V = .3. If B = .3, then S = .7. Thus B/S = 3/7.
The new leveraged beta of Rhodes is
βL = βU[1 + (1 − t) B/S] = 1.260162602 [1 + (1 − .31)(3/7)] = 1.632810686
FIN 508 Assignment 7 _____________________________________________________________________________
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The new cost of equity for Rhodes is
ke = .05 + 1.632810686 (.1209677419 − .05) = .1658768873
The new WACC of Rhodes is
WACC(2) = (1 − .31)(.1)(.3) + .1658768873 (.7) = .1368138211 .13681
Comparing, WACC(1) = .13725, WACC(2) = .13681, second is slightly better. ♥
7.5. Minorca Company has $125 million of bonds outstanding, with a coupon of 6%, selling at 95. It has 2.5 million shares of $3 preferred stock and 20 million shares of
common stock. Minorca has EBIT of $75 million this year, and it has income tax rate of
32%. Minorca must also pay a principal payment of $10 million to the bondholders. The
company has decided to have a dividend payout ratio of 35%. What dividend should
Minorca declare on the common stock per share? 49.7¢ ♥
The dividend per share, DPS is given by
DPS = [(EBIT – I)(1 – t) − SF – PD]DPR
N
In this case, EBIT = $75 million, I = .06*125 = $7.5 million, t = .32, SF = $10 million,
PD = 3*2.5 = $7.5 million, DPR = .35, and N = 20 million. Therefore,
DPS =
(75 – 7.5)(1 – .32) – 10 – 7.5
20 (.35) = $0.497 ♥
7.6. Corfu Company expects to have $70 million in EBIT next year, with standard deviation $15 million. The company has $120 million in long-term bonds with coupon
7%, and it has to pay $5 million in preferred dividends. Corfu has dividend payout ratio
45%, and 20 million shares of common stock. The income tax rate of the company is
33%. Find the probability that the dividend next year is more than 75¢ per share.
61.50% ♥
Suppose the company needs x in EBIT in order to pay 60¢ per share in dividends.
Calculate the earnings after taxes for the company, using
EAT = (EBIT – I)(1 – t) – PD
Let EBIT = x, I = 7% on $120 million in debt = $8.4 million, t = .33, and PD = $5
million. This gives
EAT = (x – 8.4)(1 − .33) – 5
Next, find the earnings per share by dividing the above quantity by the number of shares,
20 million,
FIN 508 Assignment 7 _____________________________________________________________________________
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EPS = [(x – 8.4)(1 − .33) – 5]/20
Find the dividend per share by multiplying it by the dividend payout ratio, .45, and equate
it to the given dividend, $0.75. This gives
DPS = [(x – 8.4)(1 − .33) – 5]/10*.45 = .75
You can solve it at WolframAlpha as follows
((x-8.4)*(1-.33)-5)/20*.45=.75
Solving for x, we have x = $65.6139 million. This is the minimum EBIT to pay the
required dividend.
Since the company expects to make $70 million in EBIT, it is more than 50% probable
that the company will meet its goal. Next, find
z = (65.6139 – 70)/15 = −.2924
Draw a normal probability curve, with z = 0 at the center. For the minimum required
EBIT, z = −.2924, and it is somewhat to the left of center. The area to the right of x,
which is somewhat more than 50%, will give the probability that the company will be
able to pay the 75¢ dividend.
From the tables, we get
Probability (Div > .75) = .5 + [.1141 + .24(.1179 − .1141)] = .6150 = 61.50% ♥
You can verify the answer by using Excel.
EXCEL =1-NORMDIST(65.6139,70,15,TRUE)
7.7. Ibiza Corporation has the following capital structure: $100 million in bonds, selling at par with coupon 8%; 40 million shares of common stock, priced at $20.50 each; and 1
million shares of preferred stock with an annual dividend of $4 each. Next year, the
company expects to have EBIT of $80 million out of which it wants to keep $10 million
in retained earnings. The tax rate of the company is 35%. Find the dividend that it should
declare on the common stock. What is the dividend yield of this stock?
FIN 508 Assignment 7 _____________________________________________________________________________
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82¢ per share, 4% ♥
Suppose the common dividend is x per share. Using Figure 10.2, page 177, as a guide, we
pay from EBIT, the interest, taxes, preferred dividends, and common dividends, in that
order, to arrive at the retained earnings. We write this as an equation,
(80 − .08*100)(1 − .35) – 1*4 − 40x = 10
The above equation is set up as follows.
(80 − .08*100) (1 − .35) − 4 − 40x = 10
EBIT − interest − taxes − preferred dividends
− common dividends
= retained earnings
Use WolframAlpha, to solve the equation
(80-.08*100)*(1-.35)-4-40*x=10
The answer is x = .82, or 82¢ per share ♥
The dividend yield of a stock is dividend per share divided by the price per share. In this
case it is .82/20.5 = .04 = 4% ♥
7.8. Malta Company follows the residual theory of dividends. It has 5 million shares of common stock, and it maintains its optimal debt/assets ratio at 35%. Its EBIT next year is
expected to be $15 million, with a standard deviation of $5 million. The income tax rate
of Malta is 30% and it has to pay $2 million in interest. It would like to finance $10
million in new projects from retained earnings and new borrowings. Find the probability
that it will be able to give a dividend of at least 80¢ next year.
34.46% ♥
To follow the residual theory of dividends, the company (a) identifies profitable projects,
(b) finances them while (c) maintaining an optimal capital structure. It has $10 million in
new projects, which should be financed with 35% debt and 65% in equity. It needs
.35*10 = $3.5 million in new debt, acquired by selling new bonds.
The remaining .65*10 = $6.5 million is equity. To have this money in retained earnings,
the company should have at least x in EBIT. Since the company has to pay $2 million in
interest and 30% in taxes, the after-taxes earnings from this EBIT are
EAT = (x − 2)(1 − .3)
Out of this EAT, the company pays .8*5 = $4 million in dividends and has $6.5 million
in retained earnings. Thus
(x − 2)(1 − .3) − 4 = 6.5
FIN 508 Assignment 7 _____________________________________________________________________________
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Solving for x, we get x = (6.5 + 4)/(1 − .3) + 2 = $17 million
The company should have $17 million in EBIT to pay a dividend of $0.80 per share.
Since the company expects to have only $15 million in EBIT, the probability of an 80¢
dividend is somewhat less than 50%. Next, find z = (17 − 15)/5 = .4.
Draw a normal probability curve, with z = 0 at the center. For the required EBIT, z = .4 is
somewhat to the right of center. The area further to the right of that point gives the
required probability. Check the tables to find the probability as
P(DPS > $0.80) = .5 – .1554 = .3446 = 34.46% ♥
To verify the answer at Excel, use the following
EXCEL =1-NORMDIST(17,15,5,TRUE)
