Finance 2 for IBA (30J201) F.Feriozzi Final exam December 14 th, Part One: Multiple-Choice Questions (45 points)

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1 Finance 2 for IBA (30J201) F.Feriozzi Final exam December 14 th, 2011 Question 1 Part One: Multiple-Choice Questions (45 points) d'anconia Copper is an all-equity firm with 60 million shares outstanding, which are currently trading at $20 per share. Last month, d'anconia announced that it will change its capital structure by issuing $400 million in debt. The $400 million raised by this issue will be used to repurchase existing shares of stock. Assume that capital markets are perfect. Suppose you are a shareholder in d'anconia Copper holding 300 shares, and you disagree with the decision to lever the firm. You can undo the effect of this decision by A. borrowing $2,000 and buying 100 shares of stock. B. selling 60 shares of stock and lending $1,200. C. selling 100 shares of stock and lending $2,000. D. borrowing $1,200 and buying 60 shares of stock. E. selling 75 shares of stock and lending $1,500. Question 2 Nielson Motors is currently an all-equity firm. It expects to generate EBIT of $20 million next year. Currently Nielson has 8 million shares outstanding and its stock is trading at $20 per share. Nielson is considering changing its capital structure by borrowing $50 million at an interest rate of 8% and using the proceeds to repurchase shares. Assume perfect capital markets. Nielson's expected EPS for next year if they change their capital structure is closest to A B C D E Question 3 Assume that corporate taxation is the only imperfection in capital markets. Which of the following statements regarding interest tax shields is false? A. With respect to equity, the use of debt financing has an important tax advantage due to the future interest tax shields it produces. B. The total value of the levered firm exceeds the value of the firm without leverage by an amount equivalent to the present value of the future tax savings from debt. C. By increasing the amount paid to debt holders through interest payments, the amount of the pre-tax cash flows that must be paid as taxes increases. D. When a firm uses debt, the interest tax shield provides a corporate tax benefit each year. E. Given a forecast of future interest payments, we can determine the corresponding interest tax shield and compute its present value by discounting it at the rate which is appropriate to its risk. 1

2 Question 4 Assume that the only imperfections in capital markets are corporate and personal taxation. Consider the following top federal tax rates in the United States: Personal Tax Rates Interest Year Corporate Tax Rates Income Dividends Capital Gains % 40% 40% 20% % 35% 15% 15% In 2000, assuming an average dividend payout ratio of 50%, the effective tax advantage for debt was closest to A. 40%. B. 24%. C. 30%. D. 18%. E. 10%. Question 5 Which of the following statements regarding financial distress and default is false? A. Real estate firms are likely to have low costs of financial distress, as much of their value derives from physical assets. B. For low levels of debt, the risk of default remains low and the main effect of an increase in leverage is an increase in the interest tax shield. C. Firms whose value and cash flows are very volatile (for example, semiconductor firms) must have much higher levels of debt to avoid a significant risk of default. D. The probability of financial distress depends on the likelihood that a firm will be unable to meet its debt commitments and therefore default. E. Firms with steady, reliable cash flows, such as utility companies, are able to use high levels of debt and still have a very low probability of default. Question 6 The cost of is highest for firms that can easily increase the risk of their investments. A. asset substitution. B. debt overhang. C. debt seniority. D. debt maturity. E. sovereign debt. Question 7 Taggart Transcontinental has announced a $2 dividend. If Taggart's last price cum-dividend is $45, then, assuming perfect capital markets, what should its first ex-dividend price be? A. $0. B. $2. C. $43. D. $45. 2

3 E. $47. Question 8 Rockwood Industries has 100 million shares outstanding, a current share price of $25, and no debt. Rockwood's management believes that the shares are under-priced, and that the true value is $30 per share. Rockwood plans to pay $250 million in cash to its shareholders by repurchasing shares. Management expects that very soon new information will come out that will cause investors to revise their opinion of the firm and agree with Rockwood's assessment of the firm's true value. Assume that Rockwood is able to repurchase shares prior to the market becoming aware of the new information regarding Rockwood's true value at a price of $25 per share. After the repurchase, and following the release of the new information regarding the true value of Rockwood, the firm's share price is closest to: A. $ B. $ C. $ D. $ E. $ Question 9 Consider an American put option and an American call option, both written on Rearden Metal stock with the same strike price of $60 and the same time to expiration of one year. Assume that Rearden pays no dividends, its stock is currently trading at $15 per share, and the one year interest rate is 5%. Also assume that it is optimal to exercise the put option immediately. Given the information provided, it is possible to conclude that the maximum value of the call option is closest to: A. $0. B. $1.84. C. $2.48. D. $2.86. E. $3.24. Question 10 Which of the following statements regarding financial options and their valuation with the Black-Scholes Option Pricing Model is false? A. Only one parameter input for the Black-Scholes formula, the volatility of the stock price, is not observable directly. B. Because a stock's volatility is much easier to measure (and forecast) than its expected return, the Black-Scholes formula can be very precise. C. We do not need to know the expected return on the stock to calculate the option price in the Black-Scholes Option Pricing Model. D. Because a leveraged position in a stock is riskier than the stock itself, this implies that call options on a positive beta stock are more risky than the underlying stock and therefore have higher returns and higher betas. E. The option delta,, in the Black-Scholes replicating portfolio of a call option has a natural interpretation: It is the change in the price of the stock given a $1 change in the price of the option. 3

4 Question 11 A firm is evaluating the opportunity to invest in a new project that can either be started immediately or at some future date. Consider the following two statements regarding the real option to wait before starting. I It is optimal to invest today only when the NPV of investing today exceeds the value of the option to wait, which from option pricing theory we know to be always non negative. II If there is a lot of uncertainty on the future profitability of the project, the benefit of waiting is diminished. A. Statement I is correct, statement II is false. B. Statement I is false, statement II is correct. C. Statement I is false, statement II is false. D. Statement I is correct, statement II is correct. Question 12 You founded your own firm three years ago. You initially contributed $200,000 of your own money and in return you received 2 million shares of stock. Since then, you have sold an additional 1 million shares of stock to angel investors. You are now considering raising capital from a venture capital firm. This venture capital firm would invest $5 million and would receive 2 million newly issued shares in return. The post-money valuation of the firm is closest to: A. $12.5 million. B. $5.2 million. C. $10 million. D. $5 million. E. $0.5 million. Question 13 Which of the following statements regarding call provisions of corporate bonds is false? A. A call provision gives the issuer of a bond the right (but not the obligation) to retire the bond on (or after) a specific future date for a specific price. B. When yields have risen, the issuer will not choose to exercise the call on the callable bond. C. The issuer will exercise the call option only when the prevailing market rate exceeds the coupon rate of the bond. D. A callable bond is relatively less attractive to the bondholder than the identical non-callable bond. E. The holder of a callable bond faces reinvestment risk precisely when it hurts: when market rates are lower than the coupon rate she is currently receiving. Question 14 If a lease contract is classified as a true tax lease for tax purposes, then A. both the lessor and the lessee receive the depreciation deductions associated with the ownership of the leased asset. B. the lessor receives the depreciation deductions associated with the ownership of the leased asset. 4

5 C. the lessee receives the depreciation deductions associated with the ownership of the leased asset. D. the lessor and the lessee can privately negotiate who receives the depreciation deductions associated with the ownership of the leased asset. E. nobody receives the depreciation deductions associated with the ownership of the leased asset. Question 15 In a(n) merger, the target and the acquirer operate in the same industry A. conglomerate. B. vertical. C. horizontal. D. diagonal. E. arbitrage. Question 1 Part Two: Open Questions (55 points) Your firm currently has $250 million in debt outstanding with an 8% interest rate. The terms of the loan require the firm to repay $50 million of the balance each year until the debt is extinguished. Suppose that the marginal corporate tax rate is 35% and that the interest tax shields have the same risk as the loan. What is the present value of the interest tax shields from this debt? (10 points) Question 2 Nielson Motors (NM) is a private firm with 25 million shares outstanding. You are doing a valuation analysis of Nielson and you estimate its free cash flow in the coming year to be $40 million. You expect the firm's free cash flows to grow by 4% per year in subsequent years. Because the firm is private, you do not have an accurate assessment of Nielson's equity beta. However, you do have the following data for a comparable firm in the same industry: Equity Beta Debt Beta Debt-Equity Ratio Nielson has a much lower debt-equity ratio of 0.5, which is expected to remain stable, and Nielson's debt is risk free. Nielson's corporate tax rate is 40%, the risk-free rate is 5%, and the expected return on the market portfolio is 10%. a) Compute an estimate of Nielson equity beta based on the data for the comparable firm you have available, and use the CAPM to obtain an estimate of Nielson equity cost of capital. (7 points) b) What is a reasonable estimate for the value of Nielson shares? (8 points) 5

6 Question 3 Froode Inc., is a worldwide industrial company which does not pay dividends. Suppose that its current stock price is $50 per share. In each of the next two years, the stock price will either increase by 10% or decrease by 10%. The one-year risk-free rate of interest is 2% and will remain constant. Consider a European put option on the stock that expires in 2 years and is currently at the money. a) Draw the binomial tree for the stock price, together with the final payoffs of the European put option. (5 points) b) Use risk neutral probabilities to compute the current value of the European put option. (5 points) Consider now an American put option on Froode stock with the same expiration date and the same strike price as the European put option described above. The owner of the American put can decide to wait until the expiration date to possibly exercise the option, but can also decide to exercise it after one year, or even immediately. c) Verify that it is not optimal to exercise the American put immediately. Also, verify that it is optimal to exercise the American put option after one year if Froode s stock price drops, while it is better to wait until the expiration date if in one year Froode s stock price increases. (5 points) d) Compute the current value of the American put option. (5 points) Question 4 Rearden Metal is considering the purchase of a new blast furnace costing a total of $5 million. This furnace will qualify for accelerated depreciation: 20% can be expensed immediately, followed by 32%, 19.2%, 11.52%, 11.52% and 5.76% over the next five years. However, because of Rearden's substantial tax loss carry forwards, Rearden estimates its marginal tax rate to be only 10% over the next five years. Since Rearden will get very little tax benefit from the depreciation expense, they consider leasing the furnace instead. Suppose that Rearden and a potential lessor face the same 8% borrowing rate, but the lessor has a 40% marginal tax rate. Assume that the furnace is worthless after five years, the lease term is five years, and the lease contract would qualify as a true-tax lease. Currently, Rearden has been offered by the lessor a lease contract involving annual up-front lease payments of $1.2 million for 5 years. Given the conditions offered by the lessor, compute the amount of the lease-equivalent loan and use it to evaluate the leasing decision. (10 points) SOLUTIONS Part 1: Multiple-Choice Questions 1 C Before the recapitalization d Aconia had no leverage and your portfolio consisted of 300 shares $20 = $6000 in stock. After the recapitalization the share price and therefore the value of your portfolio do not change, but d Aconia Debt-to- Value ratio becomes 400/1200 = 1/3. To undo the effects of this leveraged recapitalization on your portfolio of shares, you have to sell 1/3 of the shares you own and lend the proceeds out. So you need to sell $6,000/3= $2000 / $20 per 6

7 share = 100 shares of stock and then lend this money out. 2 D Nielson can repurchase $50 million / $20 share = 2.5 million shares. This leaves 8 million million = 5.5 million shares outstanding. Earnings = EBIT - Interest expense = $20 million - $50 million 8% = $16 million available to shareholders. EPS =Earnings/shares outstanding = $16 million/5.5 million = $ C 4 B The average personal tax rate on equity income is (40% + 20%) / 2 = 30%. The effective tax advantage for debt is therefore ( τi) ( τc)( τe) ( τ ) ( ) ( )( ) ( ) τ* = = = i 5 C 6 A 7 C In perfect capital markets the share price drops exactly by the amount of the dividend on the ex-dividend date. In this case it therefore drops to 45 2 = $43. 8 D $250 Million Cash Number of shares repurchased = = 10 million shares. So, total $25 per share shares outstanding after repurchase = 100 million initial - 10 million repurchased = 90 million remaining. True value of the firm before repurchase = $ million shares = 3,000 million. True value after repurchase = $3,000 million - $250 million in cash spent on $2,750M repurchase = $2,750 million. Hence, price per share = = $ M share 9 D We know that the value of a European put can be decomposed as follows: P = K - S + C - dis(k). Hence, it is optimal to exercise early its American counterpart whenever the time value component [C - dis(k)], is non-positive. It follows that the maximum value of the call which is consistent with a non positive time value of the put option is such that [C - dis(k)] = 0. Therefore C = dis(k) = K -PV(K) = $60 - $60/1.05 = $ E 11 A 12 A Total shares outstanding = 2M (yours) + 1M (angels) + 2M (Venture) = 5 million $5 million shares. The venture capitalist would be paying = $2.50 per 2 million shares share. Therefore, post-money valuation = $ million shares = $12.5 million. 13 C 14 B 15 C 7

8 Part 2: Open Questions Question 1 Each year the firm must pay interests on the outstanding balance of the loan, and such interests represent tax deductible expenses. To obtain the present value of the corresponding tax shields we can use the following table. Year Outstanding Balance Interest Expense Tax Shield PV of Tax Shield Total = Notice that Interest expense = outstanding balance.08 Tax shield = interest expense.35 PV of tax shield in year n = (tax shield in year n) /(1.08)n Question 2 The unlevered beta is given by E D β u = β E + β D. D + E D + E Using the comparable firm we obtain β u = ( 1.8) + = (a) ( ) Nielson has a debt beta equal to zero, because its debt is riskless, and a debt-to-equity ratio equal to 0.5. Using this information we can obtain an estimate of Nielson equity beta as follows: βu = 0.96 = ( βe ) + ( 0) => βe = = The equity cost of capital can be obtained using the CAPM as follows (b) To obtain an estimate of Nielson shares value, we need to estimate the value of equity. This can be readily done using the WACC method. First we compute the WACC E D 1.5 rwacc = re + rd ( 1 τ c ) = (.122) + (.05)( 1.40) = % D + E D + E Now we can compute the total (estimated) value of Nielson with the WACC method: 8

9 CF $40 Total Value = rwacc g = = Of this amount or is equity, that is Equity = /3 = $ million Finally, the value of Nielson shares is $ million / 25 = $20.78 per share. Question 3 (a) Stock Put (b) The risk-neutral probability, ρ, that the stock price increases satisfies the following conditions 2% = 10% ρ 10% (1 ρ), which can be solved to obtain ρ = 0.6. The risk neutral probability of a stock price increase is the same in year one and in year two. The current value of the put is therefore given by (c) The current intrinsic value of the American put is zero and is therefore better to wait rather than exercising it. On the other hand, if the price increases to $55 in year one the American put becomes out of the money and it is surely optimal to wait until expiration in this case. If however the price drops to $45 in year one the American put is in the money and an immediate exercise would produce a cash flow of $5. To verify that it is indeed optimal to exercise the put in this case we can use the risk-neutral probabilities to compute the value of waiting until expiration. We obtain 9

10 !" # which is indeed smaller than what results from an immediate exercise. (d) To compute the current value of the American put notice that it will be exercised in year one if the stock price drops. The risk-neutral probability of this happening is 0.4 and in this case the put produces a cash flow of $5 dollar in year one. If instead the stock price rises after one year, the American put will be maintained until expiration and will finally produce a cash flow of $0.5 if the stock price drops between year 1 and year 2 and zero otherwise. Hence, the risk-neutral probability of the year-two cash flow $0.5 is Finally, the value of the American put is $ %& ' Question 4 Loan Balance = PV(Future FCF Lease - Buy) at r D (1 τ C ) = 8%(1-0.10) = 7.2% 1, 240, 000 1,176, 000 1,137, 600 1,137, , Loan Balance = ( ) ( ) ( ) ( ) ( ) = $3,985,238. The loan balance exceeds the savings in year zero from leasing of $3,820,000, and so leasing the furnace is unattractive at these conditions. In fact with respect to the lease contract, if the firm buys the furnace and borrows using the lease equivalent loan, it can save $3,985,238 $3,820,000 = $165,238 at year 0, while assuming equivalent obligations in years 1 to 5. 10