Question

A 9-year maturity convertible bond with a 7% annual coupon on a company with a bond rating of AAA is selling for $1,062. Each bond can be exchanged for 80 shares, and the stock price currently is $13 per share. Other AAA-rated bonds with the same maturity would sell at a yield to maturity of 8%. What is the value of the implicit call option on the bond? (Round your answer to 2 decimal places.) 5 of 6 points
Riskless profit	$
Why is the bond selling for more than the value of the shares it can be converted into? 1 of 6 points
The bond is worth more than the shares it can be converted into because the bond has (Click to select)a shorter life timean upper bounda "floor" value.

Answer 1

A convertion option on bonds act like call option on the stock

First we will calculate straight Value of the bond

Coupon is 7% yield to maturity is 8%

Time to maturity is 9 years

Straight Value of bond is

70(PVIFA 8% 9Y) + 1000/(1.08)^9

= 70( 6.2469) + 500.248

= 937.53

But the bond currently selling for 1062

So value of implicit call option is

1062-937.53 = 124.46

Convertion value of bonds is 80×13 =1040

The bond is selling more than the convertion premium and it is due to further possibility of incerses in share price