Your electric car company, Electron, sells a single convertible bond on December 31st, 2008 for $102M. The convertible bond prospectus states that the convertible bond has a face value of $100M, an annual coupon rate of 4 percent, and a maturity of 6 years. The bond can only be converted into 250K shares on December 31st, 2011. To gauge the level of optimism that investors have for the company, you would like to know the value of the option component of the convertible bond. Assume a risk-free rate of 3 percent, a market risk premium of 5 percent, and that the company’s beta of straight debt is 0.22. The company has no other debt.

a) What is the value of the straight bond component of the convertible bond? 

b) What is the value of the convertible option component of the convertible bond? 

c) What percentage of the firm will the convertible bondholder own if she converts on December 31st, 2011? Assume that the firm currently has 1M shares outstanding. (4 points)

Assume for the remainder of this question that it is December 31st, 2011. The owner of the convertible bond is trying to figure out if she should convert the bond right now or not convert the bond and receive the next three coupon payments and the final face value payment.

d) What is the minimum market value of the firm such that the bondholder will convert? 

e) Suppose instead that the convertible bond can be converted at any time. Would the convertible bondholder convert the bond on December 31st, 2011 if the market value of the firm was currently $800M? Assume that there is a highly-liquid market where this type of convertible bond can easily sold to other investors at a fair price.