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Question 1 (10 points)
Sampert Industries is attempting to spin off its west coast division, hereafter to be called “WCD,” by selling it to Deer Creek Private Holdings. As a standalone entity WCD is expected to generate free cash flows of $12m at the end of the first year. Free cash flows are expected to grow at 3.5% per year thereafter. The cost of capital for WCD as a stand alone enterprise is 11% per year.
Part A: Given these assumptions, what is the most Deer Creek should be willing to pay for WCD?
The most Deer Creek should pay is $160.00 million.
Solution: The value of the west coast division is simply
FCF m V m r g
Question 2 (15 points)
Lumbar Barrel Stock (LBS) Corporation is a successful company located in London, UK. It currently has 10 million shares outstanding with a current price of GBP 20 per share. It also has debt with a market value of GBP 100 million. Its asset beta is 1.5 and its debt beta is 0.25. Because of recent UK’s law favouring LBS, the company does not pay any taxes.
What is the equity beta of Lumbar Barrel Stock?
LBS’s equity beta is ___ 2.125_____________.
Solution: We can use the formula for asset beta in the absence of taxes. The market value of equity, E, is $200 million. The market value of the firm, D+E, is $300 million. Because
betaA=E/(E+D)betaE+D/(E+D)betaD,
we can write that
1.5=200/300betaE+100/3000.25.
Therefore betaE= 2.
Question 4 (20 points)
Allied Investments (AI) is a diversified company with two operating divisions:
Division Percentage of Firm Value Cosmetics 40% Mining 60%
AI has no debt on its balance sheet. To estimate the cost of capital for each division, AI has identified one principal competitor for each of its two divisions. The competitors are pure-plays, i.e., they are not diversified and operate in only one industry each, and they maintain a constant Debt-Equity ratio at all times. Assume that the debt of the two competitors is riskless.
Competitor Estimated Equity Beta Debt / Equity Debt/(Debt+Equity) Nova Cosmetics 0.9 1/9 0. Blackshaft Mining 1.4 1/4 0.
Finally, assume these betas are accurate estimates and that the CAPM holds.
4A (5 points)
Estimate the asset beta (unlevered beta) for each of AI’s divisions. Show calculations where appropriate.
My estimated asset beta (unlevered beta) for AI cosmetics is 0..
Under the assumptions made, the asset beta is the weighted average of the debt and equity betas. Since the debt of the competitors is riskless, their debt betas are zero:
β β β
β
Assets Equity Debt
Equity
E D
D E D E
E
D E
My estimated asset beta (unlevered beta) for AI mining is 1..
β β β
β
Assets Equity Debt
Equity
E D
D E D E
E
D E
4B (5 points)
Based on your estimates for the betas of AI’s operating divisions, what is your estimate of AI’s equity beta?
My estimated equity beta for AI is 0..
Since AI has not debt on its balance sheet its equity beta equals its asset (or unlevered) beta. AI is a portfolio which consists of two divisions (or assets), and a portfolio beta is the weighted average of the betas of the component assets:
β = β = β = β + β
= +
1 1 2 2 (0.4)(0.81) (0.6)(1.12)
Equity Assets Portfolio w^ w
4C (5 points)
Assume that the risk-free interest rate is 5% and that the expected return on the market portfolio is 12%. What is the cost of capital for each of AI’s divisions? What is the cost of capital for AI as a whole? State your answers and show your calculations below.
My estimated cost of capital for AI cosmetics is 10.67%.
We have assumed that the CAPM holds. Hence the required rate of return is given
by:
( ) =^ +^ β ( ( )− ) = + − =
E r Assets rf (^) Assets E rMarket rf
My estimated cost of capital for AI mining is 12.84%.
( ) =^ +^ β ( ( )− )
= + −
E r Assets rf (^) Assets E rMarket rf
My estimated overall cost of capital for AI is 11.97%.
( ) =^ +^ β ( ( )− ) = + − =
E r Assets rf (^) Assets E rMarket rf
Question 5 (10 points)
Haverton is currently an all-equity firm with 10 million shares outstanding. Its current share price is $60, and its equity cost of capital is 12%. The company is considering a change in its capital structure that will increase its leverage. Two plans are considered:
Debt Plan A : Issue immediately $50 million of debt and maintain this level of debt in perpetuity.
Debt Plan B : Issue immediately $80 million in debt, then pay $20 million of the principal in one year and another $20 in two years. This means that the total value of debt will be $ million in one year and $40 million in two years. Once these two reductions in the value of debt outstanding are made, maintain $40 million of debt in perpetuity.
Assume that in both plans Haverton will be able to borrow at the risk-free interest rate of 5%. In both plans the proceeds of the debt issues will be paid out to equity holders. In Plan B the reductions of debt will be financed by issuing equity. Suppose the corporate tax rate is 35%, and ignore personal taxes and all other imperfections associated with financing. Which of these two plans would you recommend to Haverton? Mark your answer and explain below.
I would recommend Plan A over Plan B under these assumptions.
The difference between the plans can only be due to difference in the present value of the tax shield generated by the interest. For Plan A, the present value of the tax shield is
D ××××T (^) c (^) ==== $50 m ×××× 0.35 (^) ====$17.5m_. For Plan B we have_
××××^ ××××
==== ×××× ++++ ++++ ====
( ) 0.35 $14.984m 1.05 1.05 1.
PV TS
Since Plan A has a larger tax shield, it is the better plan under the conditions of the question.
Question 6 (10 points)
Donald Trump is starring in yet another television show. In this show he has three young and very eager investment managers vying for the chance to manage his wealth. He has assigned each of the contestants the task of researching the market opportunities for making investments. He has also asked each of the contestants to report back to him the expected return and standard deviation of the portfolio they would form for him. Assume that all securities are priced according to the CAPM (Capital Asset Pricing Model) and that the riskless rate is 2% and the expected return on the market portfolio is 8.5%. Assume that the variance of the market portfolio is 0.0225. The table below gives the reports made by the three contestants.
The table shows that Alex K., the first contestant, is claiming that he can form a portfolio with an expected return of 12.25% and a standard deviation of 22.50%. According to the rules of the show, Donald must fire any contestant who reports back an expected return and standard deviation combination that is either (1) inefficient or (2) infeasible. Check the box that applies below for each of the contestants:
Alex K.:
Donald should fire Alex K. because his reported portfolio is inefficient.
Donald should fire Alex K. because his reported portfolio is infeasible.
Donald should not fire Alex K. because his reported portfolio is neither
inefficient nor infeasible.
Pamela W.:
Donald should fire Pamela W. because her reported portfolio is inefficient.
Donald should fire Pamela W. because her reported portfolio is infeasible.
Donald should not fire Pamela W. because her reported portfolio is neither
inefficient nor infeasible.
Sanjay B.:
Donald should fire Sanjay B. because his reported portfolio is inefficient.
Donald should fire Sanjay B. because his reported portfolio is infeasible.
Donald should not fire Sanjay B. because his reported portfolio is neither
inefficient nor infeasible.
Contestant Expected Return Standard Deviation
Alex K. 12.25% 22.50% Pamela W. 16.80% 36.00% Sanjay B. 21.50% 45.00%
Question 7 (20 points)
You are the CEO of Green Paper Inc., a producer of high-end printing paper with an emphasis on environmentally friendly production methods. One of your employees has proposed a significant expansion of your product line. The expansion would require an initial investment of $8m into Property, Plant, and Equipment (PPE) and into Net Working Capital (NWC). The expansion is expected to generate Earnings before Interest and Taxes (EBIT) of $1.1m in the first year. The EBIT from the expansion is expected to grow at a rate of 3% per year in perpetuity. Future investments into PPE and NWC caused by the expansion are expected to equal depreciation in each year. The cash flows from the expansion have the same risk characteristics as the cash flows from your already existing products.
The corporate tax rate of Green Paper Inc. is 35%. Ignore personal taxes and all other imperfections associated with debt financing. You have estimated an equity cost of capital for Green Paper of 13.5% and a debt cost of capital of 7%. Green Paper has always maintained a constant debt-equity ratio of 0.3.
7A (10 points)
Assume that the expansion project is financed in the same manner as the rest of Green Paper. This means that the project will be financed so that the Debt/Equity ratio of Green Paper will remain at 0.3. What is the NPV of the project under this assumption?
The NPV is $476,.
Given that the risk of the project cash flows is the same as the risk in Green
Paper’s already existing cash flows, and given that the project is being financed
with the same debt-equity mix as Green Paper, we can use Green Paper’s overall
WACC to evaluate the expansion project:
( ) (^) ( )
= ^ − +^ ^
+^ +
Debt Equity
D E
WACC r t r D E D E
The Free Cash Flow in the first year is given by:
FCF = (^) ( $1.1m (^) )( 1 − 0.35 )=$0.715m
Hence the expansion project’s NPV is:
m NPV m m
7B (5 points)
How much additional debt will Green Paper need to borrow initially because of the expansion project, if it is financed in the same manner as the rest of Green Paper?
The amount of additional debt would be $1.9562m.
The debt-to-value ratio for the expansion project is:
D D
V D E
The total value of the project is:
V = $8 m + $0.4769876 m =$8.4769876m
Hence the amount of debt Green Paper will need to borrow initially is:
D = (23.0769%)($8.4769876 m ) =$1.9562m
7C (5 points)
Assume instead that the expansion project is financed solely by issuing new equity to investors. This means that the Debt-Equity ratio of Green Paper will decrease. What is the NPV of the project under this assumption? If this differs from your answer in Part A, explain why.
The NPV is –$55,.
My answer differs from Part A because:
The NPV of the project is significantly lower than in Part A because it is now all
equity financed and hence does not benefit from the tax shield generated by debt
financing. Since the expansion project is financed solely by issuing new equity, we
need to discount the FCFs at the all-equity cost of capital. The all-equity cost of
capital can be calculated as the WACC with a tax rate of zero (since in that case
the all-equity cost of capital and the WACC coincide):
( ) (^) ( )
=
= = ^ − +^ ^
= ^ ^ − +^
_ 0 (1^ )
All Equity^ t^ Debt^ Equity
D E
r WACC r t r D E D E
Question 8 (10 points)
Consider the following information:
(i) The current stock price of Blayde Inc. is $50.00 a share. Blayde will not pay any dividends in the next year. (ii) The price of a European call option on Blayde stock that expires in one year and has an exercise price of $40 is $16. (iii) The price of a European put option on Blayde stock that expires in one year and has an exercise price of $42 is $4. (iv) The one-year riskless borrowing and lending rate (EAR) is 4%.
8A (5 points)
Given this information, is there is an arbitrage opportunity? If there is an arbitrage opportunity, describe how you would take advantage of it.
The prices given permit arbitrage. To take advantage of the opportunity I would:
(1) Buy the put with X = $42; (2) sell the call with X = $40; (3) buy Blayde stock; and (4) borrow PV(40) = 38.4615.
According to put-call parity, the value of a European put with exercise price of 40$
is given by
Put Price Call Price (40) Stock Price 16 50 $4.
PV
According to (iii) above, we can buy a European put with exercise price of $42,
which is more valuable than a put with exercise price of $40, at a price of $4. Thus,
an arbitrage position would be created if we buy the put with X = $42 and “sell” the
put with X = $40, which entails selling the call with X = $40, borrowing PV(40) =
$38.4614 for one year, and buying Blade stock for $50. The overall arbitrage
position yields a cash flow of 4.4615 – 4 = $0.4615 today (per share of Blayde). At
expiration this position creates zero cash flows if the stock price of Blayde is
above $42. However, if the stock price of Blayde is between $40 and $42, then
this position generate additional positive cash flows, because you can exercise the
put you bought (with X = $42), but the put you wrote (with X = $40) expires out of
the money. If the stock price of Blayde is below $40 your payoff is $2.
8B (5 points)
Suppose all the information above is the same except that the call and the put options are actually American options, not European. Is there an arbitrage opportunity in this case? If there is an arbitrage opportunity, how would you take advantage of it?
The prices given permit arbitrage. To take advantage of the opportunity I would (do
the same as in part (A)):
(1) Buy the put with X = $42; (2) sell the call with X = $40; (3) buy Blayde stock; and (4) borrow PV(40) = 38.4615.
The American call has equal value to the European call with the same exercise price,
because without dividends, it is never exercised early. The American put is more
valuable than the European put with the same exercise price. Since in the arbitrage
position we are buying the put with X = $42 at the quoted price of $4, if the put is
actually American and its price is $4, it is even more valuable. Clearly, the same
arbitrage profits can be made by ignoring the early exercise option of the put that
is bought.
