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Question 1

GBU Corporation stock is currently trading at $40 per share. There are 20 millionshares outstanding, and the company has no debt. You are a partner in a firm thatspecializes in leveraged buyouts. Your analysis indicates that the management ofthis corporation could be improved considerably. If the managers were replaced

with more capable ones, you estimate that the value of the company would in-crease by 50%. You decide to initiate a leveraged buyout and issue a tender offerfor at least a controlling interest, which is 50% of the outstanding shares.

(a) Explain how a leveraged buyout works.

In a leveraged buyout (LBO), a group of private investors purchases all theequity of a public corporation using borrowed funds, pledging the to-be-purchased shares as collateral for the loan. The investors make a tenderofferto buy a majority in the firm. It it succeeds, you can attach the debt to

the firm, essentially gaining control for free.

(b) What is the maximum amount of value you can extract and still completethe deal?

Currently, the value of the firm is $4020 million = 800 million. If you bor-row $400 million and your tender offer (at $40/share) succeeds, you will takecontrol of the firm, and the firm will be worth 50% more, that is, $1.2 billion.You attach the debt of 400 million to the firm, and therefore the firms equity

will be worth $1.2 billion - $400 million = $800 million. You now own sharesworth $400 million and you extracted all of the value you added by changingthe mangement.

(c) What is the maximum amount of value you can extract if you use a toeholdof 10% instead of the leveraged buyout.

Suppose you could acquire the toehold for the pre-annoucement sharepriceof $40. To gain the control, you have to purchase another 40% of the firm atthe new value of $60 per share. In total you pay $402 million + $608 million= $560 million to gain control of the firm. After you change managment, yourstake will be worth $600 million. This means you only extract $40 million ofthe total value of $400 million you created by changing management.

Question 2

Tybo Corporation adjusts its debt so that its interest expenses are 20% of its free

cash flow. Tybo is considering an expansion that will generate free cash flows of$2.5 million this year and is expected to grow at a rate of 4% per year from thenon. Suppose Tybos marginal corporate tax rate is 40%.

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(a) If the unlevered cost of capital for this expansion is 10%, what is the unlev-ered value of the expansion?

Unlevered valueVU =FCF/ (rU g) = 2.5/ (10% 4%) = $41.67million

(b) What is the levered value of the expansion. Use the APV method.

This is an example of APV with constant interest coverage (p. 594): VL =(1 +ck) V

U = (1 + 0.4 0.2)41.67 = 45million

(c) If Tybo pays 5% interest on its debt, what amount of debt will it take oninitially for the expansion.

Interest = 20% of FCF = $0.5 million. Interest is also 5% of outstanding debt,therefore 0.5 = 0.05D, which implies that D = $10 million.

(d) What is the debt-to-value ratio for this expansion? What is its WACC?

Debt-to-value = D/VL = 10/45 = 0.222. From equation 18.11: rwacc = rU dcr= 9.556%.

(e) What is the levered value of the expansion using the WACC method?

Levered valueVL =FCF/ (rwacc g) = 2.5/ (9.556% 4%) = $45million

Question 3

You are a manager at Perforated Fiber, which is considering expanding its oper-

ations in synthetic fiber manufacturing. The expansion project would require anup-front investment of $20 million and produce extra sales of $32 million per yearfor the next ten years.

Assume that gross profits are 40% of sales, that Selling and AdministrativeExpenditures will be $2 million with the project, but only $1 million without theproject, that the firm uses straight-line depreciation over the life of the project,and that the corporate income tax rate is 35%.

(a) Prepare a pro-forma income statement for the project over the next 10 years.

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(in thousands) t=1 ... t=10

Sales 32,000 32,000Gross Profit 12,800 12,800

Selling&Admin 1,000 1,000Depreciation 2,000 2,000

EBIT 9,800 9,800Income tax 3.430 3.430

Unlevered NI 6,370 6,370

Note: Selling and Administrative expenses are only 1 million because this istheopportunity cost!

(b) The project requires extra net working capital equal to one-year sales up-front. The extra working capital will be fully recovered in year 10. Estimatethe free cash flows of the project in years 0-10.

(in thousands) t=0 t=1 ... t=9 t=10

Unlevered NI 0 6,370 6,370 6,370+Depreciation 0 2,000 2,000 2,000

-NWC -32,000 0 0 +32,000-Capital Expend. -20,000 0 0 0Free CFs -52,000 8,370 8,370 40,370

(c) Assuming a cost of capital of 15%, should the project be done? Ignore taxshield effects.

NPV(Free CFs, discounted at 15%) = $-2.08 million. The project should notbe done.

(d) How would your answer in (c) change if the firm could increase its debtcapacity because of the project? Explain in words.

With increased debt capacity, the firm might increase debt and therefore in-crease its tax shield. The savings in taxes may make this project desirable(but it depends on the amount of debt).

Question 4

The current price of W Corporation stock is $70. In each of the next two years,this stock price can either go up by 6% or go down by 5%. The stock pays no

dividends. The one-year risk-free interest rate is 3% and will remain constant.

(a) Draw the event tree. At t=2, what are the possible values the stock pricecan take on?

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At t=1: Su= 74.2,Sd= 66.5

At t=2: Suu= 78.652,Sud =Sdu = 70.49,Sdd = 63.175

(b) Calculate the price of a two-year European call option on W stock with an

strike price of $75.

At t=2: Cuu= 3.6520,Cud = Cdu= 0,Cdd = 0

The risk-neutral up-probability isp = 0.7273,1 p= 0.2727

At t=1: Cu = 1.031 (0.7273 3.6520 + 0.2727 0) = 2.5786, Cd =

1.031 (0.7273 0 + 0.2727 0) = 0

At t=0: C= 1.031 (0.7273 2.5786 + 0.2727 0) = 1.8208

(c) Using put-call parity, calculate the price of a two-year European put optionon W stock with an strike price of $75.

P=C+ P V(K) S= 1.8208 + (1.03)2 75 70 = 2.5154

(d) How do your answers to (b) and (c) change if the options are American-styleinstead of European-style?

The price of the Call does not change. The put may be exercised early, which

is what happens here if the stock price goes down to 66.5 in one period.P= 3.0939

Question 5

Answer all questions:

(a) How does the volatility of an equally weighted portfolio change as morestocks are added to it? Explain briefly.

An equally weighted portfolio is a portfolio in which the same amount is in-vested in each stock. Ifnis the number of stocks in this portfolio, the varianceof the portfolio can be written as:

V ar(Rp) = 1

n(Average Variance of the Stocks) +

1 1n

(Average Covariance between the Stocks).

(See p. 333 in the book)

Adding a stock stock to the portfolio could increase or decrease depending onhow it influences the Average Variance and the Average Covariance. In gen-eral it will decrease asn increases. For large n, only the covariance matters.

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(b) In the year 2000, short-term U.S. government bond rates were about 5.8%and the rate of inflation was about 3.4%. In 2003, interest rates were about1% and inflation was about 1.9%. What was the real interest rate in 2000and 2003?

2000: rr = 0.058

1+0.034 1 = 2.32%2003: rr =

0.011+0.019

1 = 0.88%

(c) How does the option to wait affect the capital budgeting decision? Explainin a few sentences.

By waiting before committing to an investment, a firm can obtain more in-formation about the investments returns. By correctly choosing the time tocommit to an investment, it can add value. As a result, given the option towait, an investment that currently has a negative NPV can have a positivevalue.

(d) With perfect capital markets, does the risk of default reduce the value of thefirm? Does the Modigliani-Miller Proposition I still hold? Explain.

With perfect capital markets, MM Proposition I applies: the total value to allinvestors does not depend on the firms capital structure. Investors as a groupare not worse off because a firm has leverage. In particular, investors antici-pate the probability of default and discount the value of debt accordingly.

(e) Explain the IRR rule of capital budgeting? How does it differ from the NPVrule and which rule is better?

see book

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