Question details

What is the value of the straight bond component of the convertible bond?
$ 15.00

Specifically, you are considering the issuance of a convertible bond with a face value of $100M, a maturity of 10 years, and an annual coupon rate of 6 percent. The conversion option is European and can only be exercised on the day before maturity. The conversion ratio is 2M shares. Based on your firm’s credit rating and regular bonds that have been issued by your firm in the past, you determine the expected return on straight debt to be 5 percent. Given that the convertible bond is issued, assume that the stock price can take on only one of three values on the day before maturity: $30 (State B), $60 (State M), or $90 (State G). The respective riskneutral probabilities are 40 percent, 40 percent, and 20 percent. Because we are given risk-neutral probabilities, the proper discount rate for the expected payoff from the conversion option is the riskfree rate, which we will assume is 4 percent. 

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

b) What is the payoff of the conversion option in each of the three states of the world on the day before maturity? The option payoff is given by max{Stock price × 2M − final bond payment, 0}. c) What is the value of the conversion option today? This is calculated as the present value of the expected payoff from the conversion option. 

d) Based on your numbers in (a) and (c), what is the value of the convertible bond?

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