A convertible bond has an 7% coupon and 10 years to maturity. The face value is $1000 and the conversion ratio is 35. The stock currently sells for $27 3/8 per share. Similar nonconvertible bonds are priced to yield 9%. The value of the convertible bond is at least:

Question

Quizplus · Accepted Answer

We can use the following formula to calculate the minimum price of the convertible bond:

Minimum price = Straight bond value + Conversion value

Straight bond value = (Coupon payment / Yield) x [1 - 1 / (1 + Yield)^n] + Face value / (1 + Yield)^n
= (70 / 0.09) x [1 - 1 / (1 + 0.09)^10] + 1000 / (1 + 0.09)^10
= 613.22

Conversion value = Conversion ratio x Stock price
= 35 x 27.375
= 959.063

Therefore, the minimum price of the convertible bond is:
Minimum price = Straight bond value + Conversion value
= 613.22 + 959.063
= $958.125

A Convertible Bond Has an 7% Coupon and 10 Years