Answer the questions below
1. A 10-year annuity paying $x at the beginning of every year (i.e. the first of ten payments is made today) is worth the same (today) as an annuity of $300 payable every 6 months for 10 years (20 payments), the first payment of which is due 66 months from now. If the annual interest rate (compounded annually) is 3%, find x. a. $232.73 d. $508.11 b. $502.48 e. $521.42 C. $506.23 2. A machine costing $3,000 must be replaced at the end of 8 years. The resale value of the machine at the time of replacement is $600. At what annual discount rate (compounded annually) would it be equally economical to use a similar machine costing $4,000 with a life of 8 years and a resale value of $1,900? (Assume that there is no taxes.) a. 2.4% d. 3.3% b. 2.7% e. 3.6% C. 3.0% 3. What is the present value of 15 payments of $100 each received every 18 months (the first one occuring in 18 months from now), if the annual discount rate (compounded annually) is 9%? a. $620.43 d. $951.28 b. $875.56 e. $1,209.10 c. $930.61 4. Corporate managers can maximize shareholder wealth by choosing positive NPV projects because: a. all investors have the same preferences. b. the unhappy shareholders can sell off their shares. c. given the existence of financial markets, investors will be satisfied with the same real investment decisions regardless of personal preferences. d. managers are wiser than shareholders regarding investments. e. none of the above.. (5 points) Suppose that the price of the stock is $,, and its annual volatility is G. Suppose also that the annual riskfree rate is r. According to Black-Scholes, what is the price of a European put option with a strike price of X maturing in T years? NOTE: In the answers below, we use log X/(1+r/ ]] I = +=ovT. GVT X a. 1 - N(x - GVT) - 50 1 - N(2) X b. So N(x) - (Itrat N(x - GVT) X C. So N(x - GVT) - X d. So 1 - N(x) - (1 + ry)7 1 - N(x - avT) e. 50 1 - N(x - GVT)] X (1 + re)7 1 - N(2) 2. (5 points) Which of the following statements are true? I. In a perfect capital market, it is advantageous for the firm to issue debt (vs. equity) to finance a project, because the cost of debt (r ) is always smaller than the cost of equity (r). II. The reason that Modigliani and Miller's Proposition I does not hold in the presence of corporate taxes is because levered firms pay less taxes than identical unlevered firms. III. Equity financing is always better than debt financing when the personal tax rate on equity income (t ) is smaller than the personal tax rate on interest income (). a. I and II d. I, II and III b. I and III e. fewer than two statements are true. C. II and III3. (5 points) If a firm borrows $50 million for one year (i.e., the firm is levered for one year only) at an interest rate of 9%, what is the present value of the interest tax shield? Assume that there are no per- sonal taxes, and that the corporate tax rate is 35%. a. $50.000 million d. $1.575 million b. $17.500 million e. $1.445 million c. $4.128 million (5 points) Suppose that you would like to take a position that will give you the following payoff at time T, as a function of the stock price S, at that time: Payoff 20 Which of the following strategies will give you this position (assume that all the call and put options are European options maturing at T, and are written on the given stock)? I. Buy 1 put with a strike price of 60, buy I call with a strike price of 40, and buy I call with a strike price of 20. II. Buy 1 call with a strike price of 40, buy 1 put with a strike price of 20, and lend (at the riskfree rate) the present value of $40 deliverable at time T. Ill. Buy 1 put with a strike price of 40, buy I put with a strike price of 20, and buy 1 share of the stock. a. I and II d. I, II and III b. I and III e. fewer than two positions will give you the desired payoff. c. II and III 5. (5 points) The Hifalutin Corporation has no debt in its capital structure, and the expected rate of return on its equity is 15%. There are 300,000 shares outstanding. The company has expected annual pre-tax earnings of $3 million in perpetuity. The corporate tax rate is 40%. If Hifalutin announces that it will issue $3.75 million worth of perpetual debt and use the entire proceeds to buy back some stocks, what will be its new share price? (Ignore personal taxes.) a. 40.00 d. 50.00 b. 45.00 e. 52.50 C. 48.50
