Finance-AW-Q380

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Read through each question carefully and be sure to show all of your work. Ifyou show no work on a question, you will receive no credit, regardless of whether the answer is correct.
 
1) For each of the following strategies, create the payoff and profit tables and graph the payoff and profit as a function of the terminal stock price. Be sure to label your axes, mark all relevant points, and to denote the slope of the payoff/profit functions at every relevant interval. For each strategy, at what prices do you break even and what must the terminal stock price be for you to earn a profit?
 
(a) You write one call option on a stock with a strike price of ✩45, write one put option on the stock with a strike price of ✩55, and you purchase the stock. The options have the same time to expiration. The call is priced at ✩4, the put is priced at ✩3, and the stock is priced at ✩52.
 
(b) You buy two put options on a stock with a strike price of ✩20 and you write one put option on the stock with a strike price of ✩30. The options have the same time to expiration and are priced at ✩4 and ✩7 each (not necessarily in that order).
 
(c) You buy one call option on a stock with a strike price of ✩40 and write one put option on the stock with a strike price of ✩50. The options have the same time to expiration. The call is priced at ✩2 and the put is priced at ✩5.
 
2. [26 points] Equity in ABC, Inc., is currently trading for ✩50 a share. Each month, the price can either go up or down by 15 percent. Riskless bonds earn 6 percent per month.
 
(a) Using the replicating portfolio approach, find the price of a ✩46-strike call option with three months to expiration. Be sure to draw the binomial tree with all of the relevant nodes filled in.
 
(b) Using the risk-neutral probability approach, find the price of a ✩46-strike put option with three months to expiration. Be sure to draw the binomial tree with all of the relevant nodes filled in.
 
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3. [16 points] You are planning on starting your own music label based in East Lansing and will begin by signing contracts with eight local musicians. For each musician you sign to your label, you will provide the funds necessary for them to record a studio album in the first year of their contract and then pay for them to tour the Midwest for three additional years. You estimate that it will cost you about ✩6,000 to record each album and that it will cost you ✩10,000 a year to send a musician on tour. In the first year of a musician’s tour, you anticipate revenues from album and merchandise sales to be about ✩8,500 (per musician); in the second year, once a musician has become more established and starts to build a following, you anticipate that the revenues they will generate from album and merchandise sales will amount to ✩18,000; in the third and final year of a musician’s tour, you anticipate that their album and merchandise sales will drop to ✩12,000, since the album will have been out for a while by this time. Riskless bonds earn an annualized return of 8 percent, but based on the riskiness of this venture, you use a discount rate of 20 percent per year.
 
(a) What is the NPV of this venture?
 
(b) You figure that there is a chance that one out of the eight musicians you sign will be a superstar. In the event that this turns out to be true, you retain the right to sign a new contract with this musician at the end of their first album tour. Under this new contract, you will spend ✩12,000 to fund the recording of their second album, which will take a year to complete, and then you will finance the musician for yet another three-year tour, this time across the entire United States. You estimate that it will cost you about ✩30,000 each year to send the musician on tour. In the first year of the tour, you anticipate revenues from album and merchandise sales to be about ✩70,000; in the second year, you anticipate that revenues will be about ✩50,000; finally, in the third year, you anticipate that revenues will be about ✩40,000. Obviously, there is uncertainty about whether or not one of your eight musicians will turn out to be a superstar. You assess the volatility of this event to be roughly 50 percent. Taking into account this option, what is the new NPV of this venture?
 
(c) Discuss your findings.
 
4. [16 points] XYZ Company is a levered firm with 4,000 shares outstanding. Analysts anticipate that its earnings before interest and taxes will be about ✩56,000 per year in perpetuity. XYZ is in the 35 percent corporate tax bracket and it can borrow from the debt markets at a rate of 6 percent per year (before taxes). Additionally, the firm has a cost of equity capital of 10 percent per year. Furthermore, the firm’s debt-equity ratio is 0.40 and the present value of the firm’s annual tax shield amounts to ✩42,000. The firm is planning on issuing warrants as a means of raising capital. A financial team at XYZ has proposed a plan to the board of directors to issue 2,000 warrants each with an exercise price of ✩85 and three years to expiration. The firm’s equity has an annualized volatility of about 45 percent and Treasury bills earn an annualized return of 5 percent.
 
(a) What is the market value of the firm before the warrant issuance?
(b) What is the market value of the firm after the warrant issuance?
 
(c) What is the price of a put option on XYZ’s stock with an exercise price of ✩85 and three years to expiration?
5. [8 points] A firm has outstanding convertible bonds with face value of ✩1,000, an annual coupon rate of 12 percent with coupons paid quarterly, and four years to maturity. The yield-to-maturity on similarly rated bonds is 10 percent. The firm has 3,500 shares outstanding and the market value of its equity is ✩57,400. The bonds have a conversion ratio of 40.50. Currently, the convertible bonds are trading at 108 percent of face value. What is the implied value of the option to wait?
 
6.[16 points] Consider a strategy where you purchase one call option with exercise price of X1, write two call options with exercise price of X2, and purchase one call option with exercise price of X3. The strike prices are chosen such that X1 < X2 < X3 and so that they are evenly spaced out (i.e., X2 − X1 = X3 − X2). All of these calls have the same expiration date, T.   (a) Create the payoff table for this strategy. (b) Draw the payoff diagram for this strategy.   (c) Let C0(X1), C0(X2), and C0(X3) be the price of the three call options at the given strike prices. Based on your observations, there is an important relationship that you can deduce about these three prices. Express this relationship with a single inequality. (Hint: What does the absence of arbitrage imply?)   (d) Can you explain the relevance of the inequality you found above? (Hint: I’ve alluded to this in class.)   Product Code-Finance-AW-Q380
 

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