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연세대학교 경영학과
재무관리 기말고사
SOLUTIONS
Part 1: Short Answer
1. (5 points) If it is the case that the market places the same value on a dollar of dividends as on a dollar of
capital gains, then firms with different dividend payout ratios will appeal to different clienteles of investors.
However, one clientele is as good as any other: a firm can not increase its value by changing dividend
policies. Yet we see strong correlations between payout ratios and other characteristics of firms. For
instance, small rapidly growing firms that have just gone public almost always have dividend payout ratios
of zero. All earnings are reinvested in the business. How would you explain this if dividend policy was
irrelevant?
Answer: Investors value a dollar of dividends = a dollar of capital gains, but if a
growing firm pays out dividends then it would need to return to the capital markets
to obtain additional funds, incurring transaction costs, thus growing firms retain
their earnings.
2. (5 points) Last month, Durham Pulp and Paper, which had been having trouble with its cost overruns at
its timberfarm in Bahama, announced that it would be temporarily suspending its dividend payments due to
cash flow crunch associated with its investment program. The company’s stock price dropped 10% on the
news. How would you interpret this change in the stock price? I.e what caused it?
Answer: the announcement must have contained some information that was not
already in the market. Perhaps the cash flow problems were worse than expected.
3.
(5 points) Smith-Corona typewriter, Inc. has common stock, bonds, and bank loans in its capital
structure. The bank loans are secured by the company’s industrial plant. Its bonds are currently selling
at a discount and offer a rate of return appropriate to a BBB rated bond. They have been incurring
losses lately, and they do not have sufficient cash flow to pay for the the new backspace eraser ribbon
technology that they have ordered for their new line of typewriters. They may be able to get some bank
financing for some of it, but need some long term financing, either by issuing some new common stock
or by issuing some additional bonds. They have accumulated so many losses in recent years, and have
so many tax loss carryforwards that , even if they start to make a profit they will be in the zero percent
tax bracket for years to come.
Their investment banker has advised them that given their losses there is no tax advantage to debt.
He has also stated that, even though the new ribbon technology may be a positive NPV investment, the
current shareholders might be made worse off if they go ahead and finance through an equity offering.
How could it be the case that, even though the project has a positive NPV, financing it through an equity
offering could make the current equity holders worse off?
Answer:
The new equity does increase the value of the firm, but much of that increase goes to
the bond holders, not the equity holders. Now the equity is diluted with the new
shareholders getting a pro rata share of the equity. The new equity holders pay only
what their stake is worth, so any transfer to the bondholders comes at the expense of
the old shareholders.
4. (5 points) You are considering two movie proposals from two writers.
The first movie involves couple
who meet on a plane, fall in love, and then the plane explodes and they die. The second movie involves a
guy on a plane that is hijacked and the guy kills the terrorist and safely lands the plane. The first movie will
cost you $100 m to make today and is expected to have the following payoffs in one years time:
Probability
50%
blockbuster
25%
sleeper
25%
dud
payoff
250m
50m
10m
The second movie also costs $100 is expected to have the following payoffs:
35%
50%
15%
a.
blockbuster
250m
modest success
50m
straight to video 10m
your discount rate is 15%. Which is the better movie? How much would you be willing to pay for
the rights to each script? Assume zero discount rate
Answer:
Sad movie: E (value) = 0.50*250 + 0.25*50 + 0.25 * 10 = 140 –100 = 40
Dopey movie: E (value) = 0.35*250 * 0.5*50 +0.15*10 = 114-100=14
b.
Your assistant, Irving, points out that maybe the second movie is worth more than it appears
because it could create a franchise i.e. allow for a sequel. If the movie is a blockbuster, we can
invest $50m in a schlockola sequel on a boat at t=1 (one year from now) and get payoffs that will
look like this at t=2 (two years from now). Assume zero discount rate.
35%
blockbuster
250m
50%
modest success 50 m
15%
Bad News Bears III 0
The writers for the second movie have said that we can have the sequel rights with the script. Now how
much are we willing to pay? Use Expected value calculation.
Answer: Dopey movie now worth more now:
Value of call = 0.35 [ (0.35*250 + 0.50*50 + 0.15 *0) – 50] = 21.875
Still not worth as much as the doomed love movie.
Part 2: Short problems
1.
(10 points) A local real estate broker has approached you with a proposal. There is an old lady who
currently owns a plot of land near where a bank might be built next year. If the bank is built, her plot
will be worth $305, but if it is not built, the plot will be worth only $55 six months from now. Everyone
agrees that the land is worth $100 now. But your buddy has created a corporation which has obtained
an exclusive option to purchase the land from the lady six months from now for $205. This corporation
was financed by debt which has a face value of 50 due six months from now. The option is the
corporations only asset. He wants to sell you half of the corporation’s equity. How much would you be
willing to pay? Risk free rate is 10%.
Answer: value of land:
305
Value of call option:
100
100
55
0
To get value of call find hybrid position w/ comparable payoff:
Borrow 50 and buy the land and you get:
250
50
so the option must be worth 20
0
The payoff to the bond holders is identical to the payoff to the equity holders,
namely:
50
so they must both be worth 10. Half the
equity is worth 5.
0
2.
(10 points) There are two stocks in the market, Cemex and Pemex. The following data is given:
P0 (cemex) today = $50
The P1 (cemex) tomorrow will be
$40 if the economy is in a recession next year
$55 if the economy is normal next year
$60 if the economy is booming next year
The probablities of recesssion, normalcy, and boom are 0.1, 0.8, and 0.1 respectively.
 (rm) = std. Deviation of the market portfolio = 0.10
E ( r p) = expected return on Pemex = 9%
 (r p ) = std. Dev. Of Pemex returns= 12%
The correlation of Cemex and the market,  cm = 0.8
The correlation of Pemex and the market,  pm = 0.2
The correlation of Cemex and Pemex,  cp = 0.6
a.
If you are a typical risk averse investor, which stock would you prefer, if any? Why ?
Answer: Hard to tell. Cemex gives you rc = 8% with a  = 9.8%, while
Pemex gives you rp = 9% with a  = 12%.
b.
What is the expected return and standard deviation of a portfolio consisting of 70% Cemex and 30%
Pemex?
Answer: E ( r ) = 8.3%
 = 9.47%
from 2 = wc2*2 + wp2*p2 + 2*wc*wp*c*p*cp
= (0.7)2 * (0.098)2 + 0.09*(0.12)2 + 2*(0.7)*(0.3)*(0.898)*(0.12)*(0.6)
= 0.008962
c.
What is the Beta of the portfolio in b above?
Answer: Bc = cm/2m = cm*c*m/m2 = (0.8)(9.8)(0.10)/(0.10)2 = 0.784
Bp = pm/2m = pm*p*m/m2 = (0.2)(9.8)(0.10)/(0.10)2 = 0.240
B (portfolio) = 0.7*(0.784) + 0.3 * (0.240) = 0.6208
3.
(10 points) There are 4 groups of investors with the following wealth and tax rates on interest income
in Sport-land.
Group
Tax rate
Basketball players
Football players
Figure skaters
Curlers
50
40
20
0
Total
wealth
450
1200
200
800
Amount in stock
Amount in bonds
200
1200
0
0
0
0
200
800
Amount in foreign
real estate
250
0
0
0
Corporate bonds and common stock are the only financial assets in the economy. Income from stock is taxfree for all investors. The corporate income tax rate is 40 percent. Corporations as a group have annual
cash flow of $200 m. before interest and taxes. There are no investment tax credits, tax loss carryforwards
or institutional arrangements allowing investors to shelter income in Sportland. All investors can earn a tax
free return of 5% by investing in Caribbean real estate. (assume that neither bonds nor stock nor foreign
real estate has any systematic risk, and that investors simply prefer the investment with the highest after tax
return and prefer domestic to foreign all else equal and will prefer stocks to bonds all else equal.
The interest rate on corporate bonds is_____8.33_________ percent
The total value of corporate securities is ___2400_________ million
The total corporate tax bill is ___46 2/3_____________million per year.
Given your answer to the above questions, could an individual firm change its value by making a small
change to its d/e ratio, assuming that it can make use of its incremental interest deductions?
No
Answer: first you realize that rd (1-Tc) = re
re = 0.05 tc=0.40
This implies that r=8.33 = 0.05/0.6
X = interest payments x/0.08333 = D
since D = 83.33/0.0833 = 1000
x = 83 1/3
(200 –x)(1-TC)/ 0.05 = E = 116.67 (0.6)/0.05 = 1400
D + E = 2400
4. (10 points) You have identified three potential investments with the following characteristics:
Investment
Expected return Beta
Unique risk
Bill Gates IOUs
IBM stock
Microsoft stock
10%
14%
20%
None
None
None
0.0
1.0
1.6
Is there an arbitrage opportunity?
yes
How could you earn profits on a zero investment, zero risk portfolio? In other words, if Xa, Xb, and Xc
represent asset weights on your portfolio, with Xa +Xb+Xc =0, in what security or securities would you
hold a short position?
Answer: go short ibm
Assuming that you invest $1 in microsoft how much money would you put in the other investments?
Answer: Bill Gates 0.60
IBM -1.60
MSFT 1.00
How is equilibrium restored in the market if the above investments were available?
Answer: Arbitrage drives down the price of IBM and bids up the others until their
expected returns are on the SML
5. (10 points) You are Special.com is considering a $2m investment in a web page that generates messages
of self affirmation. This project is expected to generate cash flows of $600,000 a year at the end of the each
of the next six years, with the first positive cash flow received exactly one year after the investment is made.
Rates of return on investments of similar risk are 12%. The NPV of this project is:
Answer: -2m + A (t=6, r=.12 C=600,000) = 466,844
YAS will finance this project entirely by the sale of stock. The costs of floating stock include a fixed cost
of $50,000 plus 5% of the gross proceeds. What value of stock must YAS sell in order to net $2,000,000?
Answer: 2m = 0.95 x – 50,000
X = 2,157,895
What is the APV of the project? (there are no taxes)
Answer: 466,844 – 157,895 = 308,949
6.
(10 points) Instalid is a corporation with profitable ongoing operations. They have asked you to
evaluate their proposed project for the production of injection molded plastic turbans. Calculate the
NPV of this project at a 5% real discount rate. Show your cash flow computations.
Physical
production
Plastic input, in
pounds
Energy input, in
Mw
Year 1
100 cases
Year 2
200 cases
Year 3
200 cases
Year 4
150 cases
2000
2000
2000
2000
200
200
200
200
The required investment on January 1, 2000 is $40,000. The firm faces a 40% tax rate, and uses straight
line depreciation. The salvage value of the investment will be zero. Plastic costs will be $12/pound at the
start of year 2000 and will increase at 2% a year in real terms. The price of the Instalids will be $300/case
and will stay constant in real terms. Energy costs will be $5/Mw in January of 2000 and will increase at 5%
/year in real terms. The inflation rate is 10%. Reveneue is received and costs are paid at years end.
After tax cash flows:
1.1.2000
Answer:
(real terms)
-40,000
1.1.2001
1.1.2002
1.1.2003
1.1.2004
+ 6318
+ 23,662
+23,029
+13,416
The NPV is
18,409
Answer: in real terms
1.1.00
Investment
Revenue
Real Depn
Plastic
Energy
Taxable
income
Taxes
Ncf
Pv real
1.1.01
1.1.02
1.1.03
1.1.04
0
30,000
9091
24,480
1050
-4621
60,000
8264
24,970
1102
25,664
60,000
7513
25,469
1158
25,860
45,000
6830
25,978
1216
10,976
-40,000
-40,000
-1848
6318
6017
10,266
23,662
21,462
10,344
23,029
19,893
4390
13,416
11,037
-40,000
7. (10 points) Triangle Trinkets manufactures styrofoam beer can coolers with the insignia of two local
ACC schools: Tar Heels and Blue Devils. The Tar Heel division’s customers are primarily casual fans and
erratic drinkers and are somewhat sensitive to the business cycle; the tar heel division’s beta is 1.0. The
Blue Devil division’s customers are more loyal and so this division’s beta is only 0.5. The Tar Heel
Division’s expected net cash flow is currently $200,000 per year, and is expected to grow at 3% per year in
real terms. The Blue Devil division’s expected net cash flow is $90,000 per year, and its real growth rate is
4% per year in real terms. TT has no other growth opportunities, it is an all equity firm, there is no
inflation, the real risk free rate of interest is 3%, and the risk premium on the market is 8%. TT has annual
overhead expenses, which are not allocated to either division, of $45,000 per year, and these are expected to
remain constant in real terms. Furthermore, the overhead expenses have no systematic risk. Assume that all
cash flows occur at year end. Analyze TT as a combination of “pure plays” i.e the firm is a combination of
its divisions. All of the above expenses and net cash flows are net of taxes.
What is the Beta of the company?
Answer:
PV (tar heels) = 200,000/ 0.11 – 0.03 = 2,500,000
Pv (blue devils) = 90,000/0.07-0.04 = 3,000,000
PV (overhead) = -45,000/0.03 = -1.5m
PV (entire co.) = 4,000,000
B (company) = B (tar heels) * PV(tar heels)/PV (co.) + B(blue devils) * PV (Blue devils)/PV (co.)
= 1.0 * (2.5/4.0) + 0.5 (3.0/4.0) = 1.0
What is the market value of the company?
Answer:
PV (co) = 4m.
8. (10 points) Because of the large cash inflows from sales of Brealey and Myers Principles of Corporate
Finance, the McGRaw Hill corporation has decided to retire all of its outstanding debt and become an allequity corporation. The debt is “permanent” debt, i.e. the maturity date is indefinitiely far away, and it is
considered risk free. The debt has a book value of $3,000,000 and it has a 10% coupon rate. However
since market interest rates on long term bonds increased to 15%, the market value of the bonds is only
$2,000,000. All of the debt is held by a single institution, which would be willing to sell it back to McGraw
Hill for $2m. in cash, with no transaction costs. (assume no tax consequences as well). If McGraw Hill did
not retire it, it would use the $2,000,000 in cash to buy back some of its stock on the open market, also with
no transaction costs. Investors expect McGraw Hill to buy back some of their stock and thus will be
completely surprised when the debt retirement plan is announced. Furthermore, when McGraw Hill
becomes all equity, it plans to remain unlevered forever. The required rate of return of the equity holders
after M-H becomes all equity is 20% in real terms. The expected annual income before interest and taxes
for the firm is $1,100,000 and is expected to remain constant. The NPV of growth opportunities is zero,
and the company is subject to a 50% tax rate. Assume that the M&M propositions with taxes hold, and that
there is no inflation.
a.
What was the market value of the company before the debt repurchase was announced?
Answer: $3,750,000
2,000,000 in debt
1,750,000 in equity
b.
Value = all equity firm + Tc*D
By how much does the required rate of return of equity holders change?
Answer: 2.67%
Re = $400,000/1,750,000 = 22 6/7%
$400,000 = ($1,100,000 - $300,000) (1-Tc)