1. Trump Company common stock has market price $130 per share and its σ is 0.38. Find the value of a European call option and put option on Trump Company, with an exercise price of $120 and expiring after 73 days. The stock is not paying any dividends. The riskless rate is 6%.
2. Sanders Corporation stock sells at a price of $73 a share and the riskless rate is 4%. Calculate the price of a European call option and a put option on the stock, which will expire after 247 days, with an exercise price of $75. The σ of Sanders Corporation is 0.352 and it pays no dividends. Answer not given
3. Cruz Incorporated has $30 million face value zero-coupon bonds due in 8 years, and its σ is 0.35. The total market value of Cruz is $60 million and the riskless rate is 7%. The company has 4.5 million shares outstanding. Find the price per share of Cruz.
4. Kasich Corporation has zero coupon bonds maturing after 10 years. The overall value of the firm is 2.5 times the face value of the bonds. The company has σ of .55 and the riskless rate is 6%. Using the option pricing theory, find the market value of a $1000 bond.
5. Bush Corporation is valued at $60 million, and is owned equally by two brothers George and Jeb. George would like to sell his share of business to Jeb. Jeb accepts that, and offers to pay him $30 million in cash. Or, George can take a note guaranteed by the corporation, payable after 4 years, with a face value of $45 million. The riskless rate of interest is 5%, and the σ of the company is .4. Using Black-Scholes theory, what is your suggestion for George?
6. Chris Christie has bought 100 oz of gold at $1200 an oz. He has sold call options on 40 oz of gold, exercise price $1200, for $90 each; and call options on 30 oz of gold, exercise price $1250, for $50 each. The cost of capital for Christie is 8%, with continuous compounding. All options will expire after 4 months and then Christie will liquidate his position. Calculate the NPV of this hedge if Christie expects the price of gold after 4 months to be $1250 an oz. Hint: Find the initial investment, including the options sold, I0. Find the final payoff, including the options exercised, F. Find the NPV as NPV = - I0 + Fe-rT.
7. Hillary & Bill Clinton is a company formed by two partners. Hillary owns the entire stock of the company, but Bill has lent some money to the company with the understanding that the company will pay him $150,000 after 5 years. The σ of the company is 0.45, and the riskless rate is 5%. Hillary and Bill are interested in selling the company to a buyer for $300,000. Based on the option pricing theory, what is an equitable distribution of the proceeds of the sale between Hillary and Bill?
8. Rubio Corporation has total value of $90 million. It has $60 million (face amount) of zero-coupon bonds outstanding in 2016, which will mature in 2025. The riskless rate is 7% at present. The risk of Rubio measured in terms of its σ is .45. Using option-pricing theory, find the debt/assets ratio of Rubio.