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

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1 Question 1 Finance 2 for IBA (30J201) F.Feriozzi Resit exam June 14 th, 2011 Part One: Multiple-Choice Questions (45 points) Assume that financial markets are perfect and that the market value of a levered firm's outstanding securities differs from the market value of an otherwise identical all-equity firm's outstanding securities. According to the logic of the first proposition by Modigliani and Miller, we can conclude that A. investors require "too low" an expected return on some of the levered firm's outstanding securities. B. investors are risk neutral. C. the market value of levered equity is given by capitalizing operating income at a rate equal to the firm's WACC. D. an arbitrage opportunity exists. E. investors are willing to pay a premium price for the shares of the unlevered firm. Question 2 A firm has $8.5 million in permanent debt, $20.5 million in equity, and a tax rate of 30%. Assume that the firm s cost of debt is 5.52%. Then, the firm's present value of the interest tax shields is closest to A. $1 million. B. $2.5 million. C. $3 million. D. $3.5 million. E. $4 million. Question 3 Which of the following statements regarding the use of leverage in the presence of corporate taxation is false? A. No corporate tax benefit arises from incurring interest payments that regularly exceed EBIT. B. The optimal level of leverage from a tax saving perspective is the level such that interest equals EBIT. C. If there is uncertainty regarding EBIT, then with a higher interest expense there is a greater risk that interest will exceed EBIT. D. If there is uncertainty regarding EBIT, then with a lower interest expense there is a lower risk that interest will exceed EBIT. E. To the extent that a firm has other tax shields, its taxable earnings will be increased and it will rely more heavily on the interest tax shield. Question 4 If the clientele effect is an important determinant of firms payout policy, we can conclude that A. investors are indifferent between dividends and capital gains. B. firms should pay out dividends only to those shareholders with a preference for future income over current income. 1

2 C. non-dividend-paying firms should be held by investors seeking capital gains. D. the dividend payout ratio should be set equal to the industry average. E. firms use their payout policy in an attempt to overcome asymmetric information problems with investors. Question 5 Consider the evaluation of a capital budgeting decision with leverage. To calculate the free cash flows that will be discounted using the WACC method, one can calculate the free cash flows that would accrue in the absence of any incremental debt financing (i.e., the unlevered free cash flows), and then A. subtract the incremental corporate taxes. B. add back the incremental tax shields. C. subtract the incremental interest payments. D. subtract the incremental principal and interest payments. E. none of the above. Question 6 Which of the following statements regarding financial options is true? A. The time value of a European call option on a non-dividend-paying stock can never be negative. B. The time value of a European call option on a non-dividend-paying stock can never be positive. C. The time value of a European call option on a dividend-paying stock can never be negative. D. The time value of a European call option on a dividend-paying stock can never be positive. E. The time value of American put and call options on a non-dividend-paying stock is always positive. Question 7 Sometimes managers are awarded stock options, i.e., call options on their company s stock. Managers who receive a great deal of pay in the form of stock options have the incentive not only to increase the price of the stock, but also to A. decrease the size of their business. B. decrease the stock price volatility. C. increase the size of their business. D. increase the stock price volatility. E. acquire firms in unrelated sectors. Question 8 Which of the following statements regarding the option to delay an investment opportunity is false? A. One way to see why it is sometimes optimal to choose not to invest in a positive-npv project is to think about the decision of when to invest as a choice between two mutually exclusive projects: (1) invest today or (2) wait. B. You invest today only when the NPV of investing today exceeds the value of the option of waiting, which from option pricing theory we know to be always nonnegative. C. When you do not have the option to wait, it is optimal to invest in any positive-npv project. 2

3 D. The option to wait is most valuable when there is not a great deal of uncertainty regarding what the value of the investment will be in the future. E. By delaying an investment, we can base our decision on additional information. Question 9 Which of the following statements regarding the value of financial options is true? A. Call options with lower strike prices are more valuable than otherwise identical calls with higher strike prices. Conversely, put options with higher strike prices are more valuable than otherwise identical puts with lower strike prices. B. Call options with higher strike prices are more valuable than otherwise identical calls with lower strike prices. Conversely, put options with lower strike prices are more valuable than otherwise identical puts with higher strike prices. C. Both call and put options increase in value when the price of the underlying stock increases. D. Both call and put options increase in value when the price of the underlying stock decreases. E. Call options increase in value, and put options decrease in value when the price of the underlying stock decreases. Question 10 Consider the following two statements regarding the concept of risk neutral probabilities. I. If all market participants were risk neutral, then the cost of capital of all financial assets (including options) would be the same and would be given by the risk free rate of interest. II. By using risk neutral probabilities we can price any derivative security that is, any security whose payoff depends solely on the prices of other marketed assets. 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 11 Which of the following statements is not true regarding Angel Investors? A. They are typically arranged as limited partnerships. B. For many start-ups, the first round of outside private equity financing is often obtained from them. C. Because their capital investment is often large relative to the amount of capital already in place at the firm, they typically receive a sizeable equity share in the business in return for their funds. D. These investors are frequently friends or acquaintances of the entrepreneur. E. Although in some cases the capital available from angel investors is sufficient, in most cases firms need more capital than what a few angels can provide. Question 12 Milton Industries sold 10 million shares of stock in an SEO. The market price of Milton s stock at the time was $25 per share. Of the 10 million shares sold, 6 million shares were primary shares being sold by the company, and the remaining 4 million shares were being sold by venture capitalists. Milton s underwriters charges 5% of the gross proceeds as an underwriting fee. The amount of money received by the venture capitalists is closest to A. $20 million. 3

4 B. $45 million. C. $75 million. D. $95 million. E. $125 million. Question 13 Callable bonds allow the issuing entity the opportunity to retire the issue prior to maturity. When is a bond most likely to be called? A. When the issuing entity has lower working capital. B. When market interest rates have decreased. C. When the issuing entity has excess cash. D. When the issuing entity has an excess of Treasury stock on the books that can be used to replace the callable bonds. E. When the issuing entity's bondholders are unhappy with the firm after interest rate increases. Question 14 A rights offering that gives existing target shareholders the right to buy shares in the target at a deeply discounted price if certain conditions are met is called a A. golden parachute. B. poison pill. C. proxy fight. D. white knight. E. sleeping beauty. Question 15 St. Martin's Hospital was offered the possibility to obtain a $2.5 million dollar CT scanner through a true tax lease involving up-front annual lease payments of $600,000 for five years. However, St. Martin decided to buy the CT scanner and to (partially) finance its acquisition with the lease equivalent loan. The CT scanner could be depreciated on a straight-line basis over five years, and was worthless thereafter. St. Martin s cost of debt is 8% and its tax rate is 35%. The amount that St. Martin could save at the time of the acquisition of the CT scanner by purchasing instead of leasing at the above conditions is closest to A. $20,000. B. $25,000. C. $30,000. D. $35,000. E. $40,000. Question 1 Part Two: Open Questions (55 points) Assume that capital markets are perfect. You are an entrepreneur starting a new biotechnology firm. If your research is successful, the technology can be sold for $45 million. If your research is unsuccessful, it will only be worth $5 million. To fund your research, you need to raise $6 million. Investors are willing to provide you with $6 million in initial capital in exchange for 25% of the unlevered equity in the firm. 4

5 (a) Compute the total market value of the firm without leverage, and the value of your share in the firm s equity. (5 points) (b) Assume you borrow $4 million. According to MM, what fraction of the firm s equity will you need to sell to raise the additional $2 million you need? Compute also in this case the total market value of the firm, and the value of your share in the firm s equity. (5 points) Question 2 Clark Industries has 150 million shares outstanding, a current share price of $45, and no debt. Clark s management believes that some of their long term assets are under-valued by the market and, as a result, the shares are under-priced. In particular, Clark s management believes that the true value of their long term assets would induce a share price of $50. Clark plans to pay $900 million in cash to its shareholders by repurchasing shares at the current market price of $45 per share. Suppose that soon after the transaction is completed, new information comes out that causes investors to revise their opinion of the firm and agree with management s assessment of Clark s value. (a) Compute the market capitalization, the number of outstanding shares, and the share price of Clark Industries before and after the share repurchase, as well as after the new information comes out. (5 points) (b) Assume now that Clark waited until after the new information come out to repurchase the shares, so that the repurchase could only be realized at the price of $50 per share. Compute the market capitalization, the number of outstanding shares, and the share price, before and after the share repurchase. (5 points) Question 3 Consider the following information about Lintner Industries: Lintner Industries' Market Value Balance Sheet ($ Millions) and Cost of Capital Cost of Assets Liabilities Capital Cash 0 Debt 300 Debt 5.50% Other Assets 700 Equity 400 Equity 11.50% c 30% Lintner Industries has available a new project whose free cash flows are as follows: Lintner Industries New Project Free Cash Flows Year Free Cash Flows ($120) $70 $60 $30 Free cash flows are zero beyond year 3. Assume that this new project is of average risk for Lintner, and that the firm wants to hold constant its debt-to-equity ratio. (a) Calculate the interest tax shield provided by Lintner s new project in year 1, 2, and 3. (10 points) (b) Calculate the present value of the interest tax shields obtained in point a). (5 points) 5

6 Question 4 Consider a firm which does not pay dividends. Suppose that its current stock price is $21 per share. In each of the next two years, the stock price will either increase by $4 or decrease by $5. The 2.50% one-year risk-free rate of interest will remain constant. Consider a two-year European call option on the stock with a strike price of $21. (a) Draw the binomial tree for the stock price, together with the final payoffs of the European call option. (5 points) (b) Use the Binomial Option Pricing Model to compute the current value of the European call option. (5 points) (c) Calculate the risk-neutral probabilities and use them to price the European call option. (5 points) (d) Would your answer to points b) and c) change if the option were an American call instead of a European Call? Provide a brief explanation motivating your answer. (5 points). SOLUTIONS Part 1: Multiple-Choice Questions 1 D 2 B PV(Interest tax shields) = τ c D =.30($8.5m) = $2,550m 3 E 4 C 5 E 6 A 7 D 8 D 9 A 10 D 11 A 12 D 4 million shares $25 per share = $100 million gross proceeds Underwriter receives $100 5% = $5 million so, net proceeds = $100 million - $5 million = $95 million. 13 B 14 B 15 A The FCFs from leasing are the annual lease payments (1 - c) since these payments are deductible for tax purposes. The FCFs from buying represent the original cost of the purchase in year 0, and the depreciation tax shield of ($2M / 5 years).35 thereafter. The free cash flows are as follows - - 6

7 The lease equivalent loan (LEL) is equal to the present value of the difference in FCFs from years 1 to 5 discounted at the after tax borrowing rate (.08)(1 -.35) =.052 or 5.2%. LEL= $ 2,130,009. Hence, at the time of the acquisition St. Martin s outflow were $2,500,000 - $2,130,009= $369,991. On the other hand, with the lease contract the initial net outflow would have been $390,000 and the savings therefore amounted to $390,000 $369,991= $20,009. Question 1 Part 2: Open Questions (a) Investors are willing to pay $6 million for an equity stake of 25%, which implies that the value of unlevered equity is $6m 4 = $24 million. You can keep an equity stake of 75% which is worth.75 $24m = $18 million. (b) As capital markets are perfect, MM ensure that the values of the firm is not affected by leverage so that the total value is still $24 million. The value of levered equity is therefore $24m - $4m = $20 million. To raise the additional $2 million needed to finance the project you must therefore sell an equity stake of 10% and are left with an equity stake of 90% which is worth $18 million. Hence, the use of leverage does not affect your wealth in any ways. Question 2 (a) Clark initial market capitalization is $45/share 150 million shares = $6,750 million, of which $900 million in cash. Hence, assets other than cash, including long term assets, are valued by the market at $6,750m $900m = $5,850 million. The true value would instead induce a total market capitalization of $50/share 150 million shares = $7,500 million, so that assets other than cash should be worth $7,500m $900m = $6,600 million. The following table summarizes what happens before and after the repurchase, and after the new information becomes available. Notice that at a price of $45 per share, it is possible to buy back 900/45 = 20 million shares. Before Repurchase After repurchase After New Information Cash Other Assets Total Market value Shares (millions) Share price ($) (b) In this case assets other than cash are correctly valued at $6,600 million before the share repurchase is realized. The following table summarizes what happens before and after the 7

8 share repurchase. Notice that at a price of $50 per share, it is possible to buy back 900/50 = 18 million shares.. Question 3 Before Repurchase After repurchase Cash Other Assets Total Market value Shares (millions) Share price ($) (a) E rwacc = r E + D E + rwacc = D r E + D D (1 - c ), where D = net debt = Debt - Cash or 8.22% Year L D0 = d V 0, hence D0 = (139.58) = Interest tax shield year 1 = 59.82(.055)(.30) = or 0.99 Year D1 = d, hence D1 = (81.06) = Interest tax shield year 2 = (.055)(.30) = or 0.57 Year D2 = d, hence D1 = (27.72) = Interest tax shield year 2 = (.055)(.30) = or 0.20 E runlevered = r E + D E + runlevered = PV of tax shield = (b) D r E + D D, where D = net debt = Debt - Cash = or 8.93%

9 Alternatively, V 0 U = 70/(1.0893) /(1.0893) /(1.0893) 3 = PV of tax shield = V 0 L V 0 U = = Question 4 (a) Stock Call At t = 1, if the stock price is 25 we have (b) = (8 0)/(29 20) = 0.89 B = ( )/1.025 = Hence if the stock price is 25 after one year the European call is worth = At t = 1, if the stock price is 16 the call is worthless and we clearly have = 0 and B = 0. At t = 0 we have = ( )/(25 16) = B = ( )/1.025 = Finally, the value of the European call at t = 0 is = rounded to $2.92 At t = 0 the risk neutral probability that the stock price will increase in one period by $4 is given by (c) 9

10 ! " " "# Similarly, if at t = 1 the stock price jumps to $25, the risk-neutral probability that it will jump to $29 at t = 2 is given by! $ " % Finally, if at t = 1 the stock price drops to $26, the risk-neutral probability that it will jump to $20 at t = 2 is given by "! $ " At expiration, the call produces a positive cash flow of $8 only if the price increases both in year one and two, which happens with a risk-neutral probability of = In all other cases the cash flow of the call is zero at expiration. The value at t = 0 of the call can therefore be computed as & '(!' % (d) A call option on a non-dividend paying stock always has a positive time value, which means that it is never optimal to exercise it before expiration, if this is possible. For this reason an American call option on a non-dividend-paying stock should never be exercised before maturity and is therefore essentially equivalent to a European call option on the same stock with identical maturity and strike price. This means that the answers provided to points b) and c) would remain the same also in the case of an American call. 10

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