1. Abilene Corporation stock sells at a price of $80 a share and the riskless rate is 7%. Calculate the price of a 9-month call option on Abilene stock with an exercise price of $70.
2. Beaumont Co common stock has market price $75 per share and its sigma is 0.3. Find the value of a European call option, with an exercise price of $80 and expiring after 73 days, on the Beaumont stock.
3. Corpus Christie Inc has $10 million face value zero-coupon bonds due in 6 years, and its σ is 0.4. The total market value of Corpus Christie is $25 million and the riskless rate is 4%. The company has 3 million shares outstanding. Find its price per share.
4. Dallas Company has a total value of $65 million. Its debt is in the form of zero-coupon bonds, which will mature in 9 years. The face value of bonds is $15 million. The riskless rate is 3.5% at present. The σ of Dallas is 0.35. Find the debt/assets ratio of Dallas.
5. Sisters Amy and Beth jointly own El Paso Corporation. Amy's share is 70%. The value of the corporation is $500,000 and its risk in terms of σ is 0.6. Amy would like to buy Beth out and offers her $150,000 cash or a note for $300,000 payable by El Paso Corporation after 5 years. The riskless rate is 8%. Should Beth take the cash or the note? Value of note is $145,472.61.
6. Thomas and Gerard bought Galveston Corporation by investing $500,000 each. Thomas was a stockholder, and thus the owner of the company. The corporation agreed to pay Gerard $1.5 million after ten years for his share of the business. However, by mutual agreement, they sold the business after 5 years for $6 million and divided the money according to the option pricing theory. The riskless rate at the time was 4%, and the σ of Galveston Corporation was 0.5. Find the amount of money that went to Thomas and to Gerard.
7. Sam Houston has bought 100 oz of gold at $1150 an oz. He has sold call options on 30 oz of gold, with exercise price $1200, for $25 each; and options on 40 oz of gold, exercise price $1175, for $50 each. All options will expire after 6 months and then Houston will liquidate his position. Houston expects the price of gold after six months to be $1187.50 an oz. He uses 12%, continuously compounded, as the discount rate. Calculate the NPV of this hedge.
8. Irving Company has total value $325 million, and it has $100 million (face value) of zero-coupon bonds maturing after 10 years. The σ of Irving is .45 and the risk-free interest rate is 5%. Using Black-Scholes model, estimate the debt/assets ratio for the company.