1.Using the information in Problem 1, calculate the risk-neutral probabilities. Then use them to price the option.
2.Using the information in Problem 3, calculate the risk-neutral probabilities. Then use them to price the option.
3.Explain the difference between the risk-neutral and actual probabilities. In which states is one higher than the other? Why?
4.Explain why risk-neutral probabilities can be used to price derivative securities in a world where investors are risk averse.
5.Calculate the beta of the January 2010 $9 call option on JetBlue listed in Table 21.1. Assume that the volatility of JetBlue is 65% per year and its beta is 0.85. The short-term risk-free rate of interest is 1% per year. What is the option’s leverage ratio?
6.Consider the March 2010 $5 put option on JetBlue listed in Table 21.1. Assume that the volatility of JetBlue is 65% per year and its beta is 0.85. The short-term risk-free rate of interest is 1% per year.
a. What is the put option’s leverage ratio?
b. What is the beta of the put option?
c. If the expected risk premium of the market is 6%, what is the expected return of the putoption based on the CAPM?
d. Given its expected return, why would an investor buy a put option?
7.Return to Example 20.10, in which Google was contemplating issuing zero-coupon debt due in 18 months with a face value of $96 billion, and using the proceeds to pay a special dividend. Google currently has a market value of $135.1 billion and the risk-free rate is 1%. Using the market data in Figure 20.10, answer the following:
a. If Google’s current equity beta is 1.45, estimate Google’s equity beta after the debt is issued.
b. Estimate the beta of the new debt.
8.You would like to know the unlevered beta of Schwartz Industries (SI). SI’s value of outstanding equity is $400 million, and you have estimated its beta to be 1.2. SI has four-year zero-coupon debt outstanding with a face value of $100 million that currently trades for $75 million. SI pays no dividends and reinvests all of its earnings. The four-year risk-free rate of interest is currently 5.13%. Use the Black-Scholes formula to estimate the unlevered beta of the firm.
9.The J. Miles Corp. has 25 million shares outstanding with a share price of $20 per share. Miles also has outstanding zero-coupon debt with a 5-year maturity, a face value of $900 million, and a yield to maturity of 9%. The risk-free interest rate is 5%.
a. What is the implied volatility of Miles’ assets?
b. What is the minimum profitability index required for equity holders to gain by funding a new investment that does not change the volatility of the Miles’ assets?
c. Suppose Miles is considering investing cash on hand in a new investment that will increase the volatility of its assets by 10%. What is the minimum NPV such that this investment will increase the value of Miles’ shares?