Calculate the face value and promised interest rate of the

Question

Section A-

Question 1: The previously publicly traded firm Wisconsin Railroad ("WR") has gone through a leveraged buyout, instigated by a team of railroad executives ("The Management Group") in conjunction with the buyout firm Herkshire. The buyout was for a total consideration of $180M, of which $140M was used to buy 10 million shares of WR at $14 per share (a $4 premium over the pre-buyout share price of $10), $30M was used to pay off the outstanding debt, and $10M was paid in legal- and investment banking fees. The $180M was financed in the following way:

• $150M of bank debt, at 8% interest
• $10M equity infusion from Herkshire, for a 40% equity ownership
• $10M equity infusion from the management group, for a 60% equity ownership (they get more equity since they will manage the company!)
• The remaining $1 OM was financed by paying out the $1 OM of excess cash that WR had prior to the buyout.

a) Was this a good purchase from the perspective of the management group? From the perspective of Herkshire? In order to answer this question, you need to calculate the value of both the management group's and Herkshire's equity post buyout, using the APV method. Use the extra information given below, and clearly state any additional assumptions you make.

• The pre-buyout balance sheet of WR looked like this (all in million USD):

Assets		Liabilities
Cash, Excess	10	Non-Debt current liabilities	20
Other Current Assets	20	Debt	30
Net Property, Plant, and Equipment	45	Book Value Equity	25
Total Assets	75	Total Liabilities	75

• The pre-buyout equity beta of WR was 1.2 and the pre-buyout debt beta was zero
• The long-term risk free rate is 6% and the risk premium on the market is 6%
• The corporate tax-rate is 40%
• After the buyout, Year I EBIT (Earnings Before Interest and Taxes) is expected to be $20M, which is then expected to grow at 5% forever (which is the expected rate of inflation)
• Current assets (including working cash) and non-interest bearing current liabilities are expected to be of equal size going forward
• Net PPE (which is Property, Plant, and Equipment minus accumulated depreciation) will have to be increased by $5M in Year 1, after which net PPE will also grow at 5% forever
• Some non-core land assets (not part of PPE) will be sold off for $2M after tax in Year I
• The debt is expected to be kept constant the first 2 years, and will then be increased by 5% per year.

b) Will the firm be able to pay the interest on the debt during the first two years without borrowing more or using up any working cash?

c) Briefly explain the factors a firm should take into consideration when deciding on whether to become highly levered or not.

Question 2: Alpha Cars is a firm specialised in dealing sports cars. Its total enterprise value at the end of the year depends on the general state of the economy. The economy can either be in a good state or in a bad state. Each state is equally probable. Alpha Cars will be worth 250 million in the good state and 90 million in the bad state. Alpha Cars needs to issue debt today to raise 140 million. These new funds will be used to fully repay the previous debt of the firm. There is a perfectly competitive market of financiers, everyone is risk neutral and the net discount rate is zero.

a) Calculate the face value and promised interest rate of the debt that Alpha Cars needs to issue. Calculate the value of the equity of Alpha Cars.

b) Discuss the following statement "In a world with risk neutral preferences, the interest rate on debt is always the risk free rate"

Delta Trucks is a dealer in second-hand trucks. Second-hand trucks sell well during bad times. For this reason, its total enterprise value at the end of the year will be 50 million in the good state and 150 million in the bad state. It currently has debt with face value of 100 million, which matures at the end of the year. In case of default, Delta Trucks will incur bankruptcy costs of 30 million that need to be subtracted from its enterprise value.

c) Calculate the current enterprise value, debt value and equity value of Delta Trucks.

Right after issuing its new debt, Alpha Cars initiated talks about a possible merger with Delta Trucks. The new company should be called Alpha-Delta. The management of both firms expects to generate substantial synergies in the form of cost savings. They calculate that the synergies between both firms have a net present value at the end of the year of 30 million regardless of the state of the economy. The rest of the cash flows of each firm will remain unchanged.

d) Calculate the current enterprise value, debt value and equity value of Alpha-Delta. Should the firms go ahead with the merger?

The management of both firms re-calculated the value of the synergies and they now believe that they will have a net present value of 80 million at the end of the year.

e) Calculate the enterprise value, debt value and equity value of Alpha-Delta under this new synergy value. Should the firms go ahead with the merger?

f) Carefully explain the main economic phenomenon driving your answers in parts d) and e). Analyze how value is created and distributed in this merger. Propose solutions that would help the maximization of shareholder value.

Question 3: BankWest is a commercial bank in a world where the assumptions of the Modigliani-Miller theorem hold. Its assets have a market value of £100 billion and generate £7 billion per year in perpetuity. It is funded with £90 billion of debt that requires a rate of return of 6%, and £10 billion of equity.

The board of BankWest intends to issue £5 billion of equity to buy back some debt. The resulting debt level of the bank will still require a 6% rate. However the CEO of BankWest is worried, she claims that this recapitalization will bring down the return on equity and discourage investors from investing in the bank".

a) Find the expected return on assets and expected return on equity of BankWest before the recapitalization.

b) Find the expected return on assets and expected return on equity of BankWest after the recapitalization. Is the statement of the CEO correct?

Now suppose, alternatively, that BankWest operates in a world where only one of the Modigliani-Miller assumptions does not hold: there is asymmetric information. Several banks in the economy look exactly like BankWest, but half of them are good, and really worth £105 billion and half of them are bad, and only worth £95 billion. The market cannot tell them apart and assigns to all of them a value of £100 billion. Currently only the CEOs of each bank know whether their bank is a good or a bad bank but in one year the true value of each bank will become public knowledge. Banks can issue at most £5 billion of debt or equity per year. Assume that the value of debt is unaffected by the total bank value.

c) Suppose that investors are naïve and do not infer anything from the financial policy of banks. The CEOs of both types of banks own '/4 of the shares and plan to take advantage of this situation. Calculate the total wealth of the CEOs of good banks and bad banks after a year if they do nothing. Calculate what happens if they take advantage of naïve investors (i.e. by issuing debt to buy back other shareholder's equity or vice versa).

d) Suppose now that investors are not naïve. BankWest happens to be a good bank. Carefully explain what would investors infer if BankWest decides to issue equity.

e) Suppose now that all banks are forced by law to issue more equity and buy back some debt. Compare this situation with the situations in questions c) and d). In light of your answer, explain whether you think it is a good idea to let banks voluntarily issue capital during a crisis or it is better to force all of them to do so.

Section B-

Question 4: Bond Valuation

At the end of Year 0, you observe the following prices for zero-coupon U.S. Treasury securities with a face value of $1,000 maturing at the end of Year 1, Year 2, Year 3, and Year 4, respectively:

Maturity	Price
Year 1	980.39
Year 2	951.81
Year 3	915.14
Year 4	871.44

a) Compute the yields to maturity of these four bonds (using annual compounding)?

b) Give two plausible reasons for the shape of the yield curve?

c) What is the one-year forward interest rate between Year 1 and Year 2?

d) At the end of Year 0, AMR (parent company of American Airlines) just promised you payments of $1,000 in one year, $2,000 in two years, $3,000 in three years, and $4,000 in four years. Currently, the spread between the yields of debt securities from the U.S. Federal government and AMR is 5% at all maturities. What is the present value of these promised payments at the end of Year 0?

e. What is the Macaulay duration of AMR's payments?

f. Using all four bonds, can you fully immunize your exposure to interest rate risk in part (d) and how? If only Year 1 and Year 4 bonds are available, how would you manage your interest rate risk (be specific)? In this case, can you fully immunize your interest rate risk exposure?

Question 5: Equity and Option

Yippie is a recent startup and is currently not paying any dividends. The earnings in 2011 are expected to be $4 a share and analysts predict that Yippie's earnings will grow at an annual rate of 30% for the next three years (until 2014).

The return of new investments of Yippie is expected to be 10% indefinitely starting in 2015. Yippie is expected to start paying annual dividends in 2014 and these dividends will be equal to 60% of the earnings. Assume that all earnings accrue at the end of the year and that the dividends are also paid once at the end of the year. Yippie has a beta of 1.5, the market return is 7%, and the risk-free rate is 2%.

a) What is the intrinsic value of Yippie's stock in April 2011 using the dividend discount model?

b) Suppose you are a fund manager. Your assistant claimed that he found the optimal risky portfolio (tangency portfolio) in a universe of N stocks and one risk-free asset. The risk-free rate is 5%. ABX and CBD are two of the N stocks in the tangency portfolio with equal weights. The risk-return profiles of these two stocks are:

Stock	Standard Deviation	Covariance with Tangency Portfolio	Expected Excess Return
ABX	15%	0.03	20%
CBD	20%	0.01	15%

Do you agree with your assistant? What changes would you make if you disagree with him? [5 marks]

c) What are the assumptions behind the CAPM. In equilibrium, according to CAPM what risky portfolio(s) do people hold and why?

d) Explain how the CAPM equation is derived.

e) You noticed the following prices: Stock= $55, Call(X=55) = $5.5, Put(X=66) = $5, Riskfree rate-10%, where X denotes strike price. Both call and the put options are European and the maturity of both options is one year. Stock does not pay any dividends. Given the information, is the call clearly mispriced? Is the put clearly mispriced? Show how to construct an arbitrage with the mispriced derivative, the underlying stock and the risk-free bond.

Question 6: Equity and Option

a) You expect that GE stock will not be doing well over the next year. Specifically, you think the price will fall from 37 to around 30 per share but unlikely to fall below 25. Currently there are call and put options traded on GE with strike prices at 25 and 35, respectively. To take advantage of this expectation, you create a bear spread. Describe two ways to create such a bear spread. Comment on the advantage of a bear spread over a put.

b) On December 13, 2009 the spot price of live cattle is 85.60 cents per pound. The December 2010 futures contract trades at 90.60 cents. The corresponding interest rate is 4% per year. Is there an arbitrage opportunity here? If yes, explain the arbitrage transactions and the resulting profits in more detail. If no, explain why an arbitrage is not possible. What incentives do these prices give to farmers who are considering whether they should raise live cattle.

Parts c-e. A stock price is currently $50. It is known that at the end of six months it will be either $60 or $42. The annualized risk-free rate of interest is 2%.

c) Calculate the value of a six-month European put option on the stock with an exercise price of $48. If such a put option is not available, please show how to replicate the payoff of this put option using a portfolio of the stock and the riskfree bonds.

d) Calculate the value of a six-month European call option on the stock with an exercise price of $48.

e) The stock has a beta of 1.5 and the market portfolio has an expected return of 7%. What is the expected rate of return of the put option in part c? [Hint: Part c. shows that a put is a portfolio of the stock and the risk-free bond. The beta of a put is equal to the beta of such a portfolio.]