# Project #69077 - finance

Read through each question carefully and be sure to show all of your work. If

you 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 âœ©45, write one put option on the stock with a strike price of âœ©55, and you purchase the stock. The options have the same time to expiration. The call is priced at âœ©4, the put is priced at âœ©3, and the stock is priced at âœ©52.

(b) You buy two put options on a stock with a strike price of âœ©20 and you write one put option on the stock with a strike price of âœ©30. The options have the same time to expiration and are priced at âœ©4 and âœ©7 each (not necessarily in that order).

(c) You buy one call option on a stock with a strike price of âœ©40 and write one put option on the stock with a strike price of âœ©50. The options have the same time to expiration. The call is priced at âœ©2 and the put is priced at âœ©5.

2. [26 points] Equity in ABC, Inc., is currently trading for âœ©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 âœ©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 âœ©46-strike put option with three months to expiration. Be sure to draw the binomial tree with all of the relevant nodes filled in.

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 âœ©6,000 to record each album and that it will cost you âœ©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 âœ©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 âœ©18,000; in the third and final year of a musician’s tour, you anticipate that their album and merchandise sales will drop to âœ©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?

. [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 âœ©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 âœ©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 âœ©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 âœ©85 and three years to expiration?

. [8 points] A firm has outstanding convertible bonds with face value of âœ©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 âœ©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?

[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.)

 Subject Business Due By (Pacific Time) 04/30/2015 11:59 pm
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