Question 1. Introduction to Options (2 pts.)

Option traders often refer to "straddles" and "butterflies". Here is an example of each:

• Straddle: Buy call with exercise price of $100 and simultaneously buy put with exercise price of $100.
• Butterfly: Simultaneously buy one call with exercise price of $100, sell two calls with exercise price of $110, and buy one call with exercise price of $120.

Draw position diagrams for the straddle and butterfly, showing the payoffs from the investor's net position. Each strategy is a bet on variability. Explain briefly the nature of each bet.

Question 2. Valuing Options (2 pts.)

An investor is said to take a position in a "collar" if she buys the asset, buys an out-of-the-money put option on the asset, and sells an out-of-the-money call option on the asset. The two options should have the same time to expiration. Suppose Marie wishes to purchase a collar on Hollywood, Inc., a non-dividend-paying common stock, with six months until expiration. She would like the put to have a strike price of $55 and the call to have a strike price of $95. The current price of Hollywood's stock is $70 per share. Marie can borrow and lend at the continuously compounded risk-free rate of 7 percent per annum, and the annual standard deviation of the stock's return is 50 percent. Use the Black-Scholes model to calculate the total cost of the collar that Marie is interested in buying.

Question 3. Cost of Capital (2 pts.)

A company has the following financing outstanding. What is the WACC for the company?

Debt: 240,000 coupon bonds outstanding with 7.5% coupon rate, 20 years to maturity, selling for 94% of par, the bond have a $1,000 par value each and make semiannual payments.

Common stock: 9,000,000 shares outstanding, selling for $71 per share, the beta is 1.2

Preferred stock: 400,000 shares of 5.5 percent preferred stock with a par value of $100, selling for $81 per share.

Market: market risk premium is 8%, risk-free rate is 5%, and tax rate is 35%

Question 4. Capital Structure (2 pts.)

Levered, Inc., and Unlevered Inc., are identical in every way except their capital structure. Each company expects to earn $23 million before interest per year in perpetuity, with each company distributing all its earnings as dividends. Levered's perpetuity debt has a market value of $73 million and costs 8 per cent per year. Levered has 2.1 million shares outstanding, currently worth $105 per share. Unlevered has no debt and 4.5 million shares outstanding, currently worth $78 per share. Neither firm pay taxes. Is Levered's stock a better buy than Unlevered's stock?

Question 5. Derivatives and Hedging Risk (2 pts.)

Suppose there were call options and forward contracts available on coal, but no put options. Show how a financial engineer could synthesize a put option using the available contracts. What does your answer tell you about the general relationship between puts, calls, and forwards?