The J. Miles Corp. has 26 million shares outstanding with a share price of $18 per share. Miles also has outstanding zero-coupon debt with a 5-year maturity, a face value of $890 million, and a yield to maturity of 10%. 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 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?