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**Unformatted text preview: **UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
KENAN-FLAGLER BUSINESS SCHOOL
BUSI 408: CORPORATE FINANCE
SOLUTIONS TO REVIEW QUESTIONS
PROF. ARZU OZOGUZ FALL 2008 A. Time Value of Money
1. With graduation only a few days away, you are ready to purchase a new car.
You want to trade in your old Toyota for a Mercedes SLK, which costs
$35,000. One dealer will give you the market value $3,000 for your old car,
and offers a 48-month loan at a 3% APR. You find another dealer that will
give you $8,000 for your old car, if you take their 19% APR, 48-month loan.
Which dealer would you choose?
Option 1: Net price = 35,000
. 3% 0.0025 32,000 3,000 0.25% monthly rate
1 0.0025 Option 2: Net price = 35,000
. 19% 27,000
2. 32,000 0.0158 1
1.0025 8,000 $708.29 27,000 1.58% monthly rate
1 0.0158 1
1.0158 $807.25 If the discount rate is 12.5 percent per annum, would you rather receive
$5000 today, or $1000 per year forever?
PV($1000 per year forever) = 8000 > 5000. . B. Bond Valuation
The electric utility Black-out, Corp. has just issued a new five-year bond with a
$1000 face value and with 7 percent annual coupon, paid semiannually.
a. What is the price of the bond, if the yield to maturity is 12 percent?
35
1
0.06 1
1.06 1000
1.06 815.9 b. Calculate the annual return that an investor would realize, if she buys the
Black-out bonds today, has a three-year holding period, reinvests all the
coupon payments at a 3% semi-annual return, and if she sells the bonds with
two years remaining until maturity. Assume that at the end of three years, the
7% coupon bonds with two years remaining sell at 7 percent yield.
At the end of three years, the bond price’s now becomes:
35
1
0.035 1
1.035 1000
1.035 $1000 Reinvesting the coupons provide at the end of year three:
3
The 3-year gross return she earns is given by
return she therefore earns 1
1.503 1.03 . .
. 1 226.39 =1.503. The annual 14.5% Stock Valuation
The annual earnings of Asheville Skis Inc. will be $4 per share in perpetuity if
the firm makes no new investments. Under such a situation, the firm would
pay out all of its earnings as dividends. Assume that the first dividend will be
received exactly one year from now.
Alternatively, assume that three years from now and in every subsequent year
in perpetuity the firm can invest 25 percent of its earnings in new projects.
Each project will earn 40 percent at year-end in perpetuity. The firm’s
discount rate is 14 percent.
a. What is the price per share of Asheville Skis Inc. stock today without
the company making the new investment?
4
28.57
0.14
b. If Asheville Skis announces that the new investment will be made,
what will the per-share stock price be today?
0.25 0.40 10%
Div1 = $4, Div2 = $4, Div3 =$4(0.75) = $3, Div4 = 3(1+g), …
4
4
4 0.75
1
64.29
1.14
1.14
0.14 0.10 1.14 C. Portfolio Theory
Consider the following distribution of returns:
Probability
30%
40%
30% RA
−20%
5%
40% RB
−5%
10%
15% RM E(R)
σ ?
23.4% ?
8.1% 12%
15% The correlation coefficient between stock A and the market is 0.38, and the correlation
coefficient between stock B and the market is 0.92.
a. Find the expected returns for stock A and stock B.
0.30 20% 0.30 0.40 5% 0.40 5% 0.30 40% 8% 10% 0.30 15% 7% b. Find the covariance and the correlation between A and B.
,
0.30
20% 8%
5% 7%
0.40
5% 8% 10% 7%
0.30
40% 8% 15%
0.0174 7% 0.30 20% 8%
0.0546 0.40
5%
0.2336 8% 0.30 40% 8% 0.30 5% 7%
0.0066 0.40
10%
0.081 7% 0.30 15% 7% , , 0.0174
0.2336 0.081 0.919 c. What is the expected return of a portfolio with 40% in A, 40% in B, and 20% in
M?
0.4 0.08 0.4 0.07 0.2 0.12 0.084 d. What is the standard deviation of a portfolio with 60% in A and 40% in B?
0.60 0.2336
0.40 0.081
2 0.60 0.40 0.919 0.2336 0.081 0.029 0.17 e. What is the risk-free rate implied by CAPM, given the above data? (Round to one
digit after the decimal in your calculations.)
0.38 0.2336 0.15
0.15
8% 0.59 12% 0.59 2.24% D. Capital Asset Pricing Model
Assume that CAPM holds, and the expected return on the market is 15 percent, and
the return on T-bills is 5%.
a. Graph the Security Market Line, clearly label the axes and identify the slope and
intercept. Plot the market portfolio.
b. What is the market risk premium, and how is it related to slope of the Security
Market Line?
E. Net Present Value
French Wines Company is taking on a new project. The project itself requires a net
investment of 10 million euros, and is expected to generate 2 million euros every
year, growing at 2 percent in perpetuity. French Wines’ debt is rated A, which means
it can borrow at 8 percent. The object of the proposed is to make organic wine.
OrgWine, the dominant player in the industry, is a single product company, making
organic wine exclusively. OrgWine is all-equity financed, and it has a beta of 1.5.
The risk free rate is 5 percent, and the market risk premium is 10 percent. The
corporate tax rate is 34 percent.
a. What is the NPV of the project if French Wine finances it all-equity?
2
2% 10 The appropriate discount rate should reflect the project risk. We look at a pureplay wine company OrgWine, that is similar in risk, to get the discount rate.
OrgWine’s all-equity beta reflects the business risk involved in wine. Therefore:
0.05 1.5 0.10 20% The NPV of the project if all-equity financed:
10 2
0.20 0.02 1.11 b. What is the NPV of the project if French Wine issues 4 million euro debt to make
the investment?
If the project is financed using debt, we need to find the overall cost of capital for
the project which should reflect the cost of equity and the cost of debt. Note,
however, that the cost of equity now needs to be the cost of equity for levered
French Wines.
1
To find :
0.20 4
1
6 0.34 0.08 4
10 1
0.252
0.252 6
10 10 1 2
0.172 0.02 0.34 0.20 0.08 0.172 3.15 F. Free Cash Flow
“Ice-Cream Unlimited, Inc.” plans to operate a fleet of 100 mobile ice-cream selling
vans in France. The entire fleet costs 9 million euros, and will be depreciated on a
straight-line basis to a salvage value of zero over 3 years of economic life. Annual
operating costs are estimated to amount to 5 million euros, and working capital
requirements are expected to be 30% of the sales revenue. All cash flows occur at the
end of the year. The company is subject to a corporate tax rate of 50%. The
company’s opportunity cost of capital is 10%.
What is the minimal annual sales revenue required to break even (that is, with a zero
NPV) if this project lasts for three years only? What revenue does this imply for each
van?
You can use the following table for your calculations. The sales revenue is denoted
by the variable Z. Year
0 Year 1 Year 2 Year 3 Sales $Z $Z $Z Costs −5m −5m −5m $Z−5m $Z−5m $Z−5m −3m −3m −3m $Z−5m−3m $Z−5m−3m $Z−5m−3m Operating
Profit
Depreciation
EBIT
Taxes −0.5($Z−8m) −0.5($Z−8m) −0.5($Z−8m) Net Income 0.5($Z−8m) 0.5($Z−8m) 0.5($Z−8m) Depreciation +3m 0 0.3Z −9m WCR
Free
Flow +3m −0.3Z Capital Exp. +3m Cash −9m 0.5($Z−8m)+3m−0.3Z 0
9 1.10
For each van, this implies 9
0.2
. 0.5($Z−8m)+3m 0.2$Z 1m
1.10 1 1.10
1.592
3.31
$0.096 0.5$Z 1m
1.10 0.5($Z−8m)+3m+0.3Z 0.8$Z 1m
1.10 0.5Z 1 1.10
0.8Z 1
1.592
15.289
9.60 to break even. Capital Budgeting
ABC Company is considering replacing its heating and cooling system. The old
system cost $7 million 5 years ago. It has a remaining life of five years and is being
straight-line depreciated to zero over seven years. The current market value is $2.5
million.
The newer, more efficient system would cost $10 million. Annual operating expenses
would fall from $3 million to $800,000. The new system would last for five years
and would be depreciated to zero evenly over this period. The salvage value at the
end of the five years is $3 million.
The firm is currently all-equity financed, with a market value of $50 million. ABC
will issue debt to fund the entire project. Assume that proceeds from the sale of the old system can be immediately applied against the cost of the new system. This
project is similar in risk to the firm as a whole. The firm has a 40% tax rate, a 15%
cost of equity, and can issue debt at 8%.
a. How much debt would the firm need to issue?
We need to find the net amount the new machine would cost, that is $10m less the
after-tax gain on the old machine:
7
2.5 5 7
7 2 0.4 2.5 2 2.3 Therefore, the firm needs to issue:
$10 $2.3 7.7 b. What cost of capital should the firm use to evaluate the project?
Since the firm is currently all-equity, the cost of equity is the firm’s cost of
capital. Project risk is the same as the firm, so use 15%.
c. Should the firm replace the old system?
Equivalent annual cost of new machine
0.8 1
2 5.73
5.73 0.40 0.15 1 1
1.15 0.48 0.8 1
1.15 0.48 0.8
1
0.15 7.7 0.40 3 1 0.4
1.15 1.7 Keeping the old machine one more year:
3
1 1 0.40 1.7 0.4 1.8
3.7 1.15 0.40 0.4 1.8 2.3 3.7 G. Capital Structure
A firm has 1 million shares trading at $60 and 10,000 bonds with $1000 par. The
bonds have a yield to maturity of 10%, an 8% annual coupon rate paid semiannually,
and 10 years until maturity. The firm has EBIT of $16.8 million and pays all of its
residual cash flow as dividends. Assume the earnings and the interest continue in
perpetuity. The firm has a 40% tax rate. All-equity firms that are otherwise similar
have a cost of capital of 14%.
a) What is the WACC?
1
40
1
0.05 60 60
10,000 1
1.05 875.37 1000
1.05 10,000 875.37 8.7537
1 To find :
1 0.14 0.1435
1
0.1328 8.75
1
60 0.1435
13.28% 60
68.75 0.4 0.14 0.10 1 0.10 0.4 8.75
68.75 b) Suppose the firm refinances to have a D/E ratio of 0.5. What is the new cost of
equity?
:
To find the new
1
0.152 0.14 0.5 1 0.4 0.14 0.10 ...

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