Question

A convertible bond is selling for $967, matures in 15 years, has a $1,000 face value, pays interest semiannually, and has a coupon rate of 8 percent. Similar non-convertible bonds are priced to yield 4.25 percent per six months. The conversion ratio is 20. The stock currently sells for $47.50 a share. Calculate the convertible bond's option value.

a. $2.92.
b. $7.27.
c. $1.48.
d. $2.03.

Answer 1

D) $8.95

Step-by-step explanation:

Calculation to determine the convertible bond's option value.

First step is to calculate the Straight bond value

Straight bond value = [.08($1,000)/2]PVIFA4.25%, 30 + $1,000/1.042530

Straight bond value = $958.05

Second step is to calculate the Conversion value

Conversion value = 20($47.50)

Conversion value = $950

Now let determine the convertible bond's option value using this formula

Bonds Option value = Bond value – MAX[Straight bond value, Conversion value]

Let plug in the formula

Bond Option value = $967 − MAX[$958.05, 950]

Bond Option value =$967-$958.05

Bond Option value = $8.95

Therefore the convertible bond's option value is $8.95