Question

You have been hired to value a new 20-year callable, convertible bond. The bond has a coupon rate of 8.4 percent, payable semiannually, and its face value is $1,000. The conversion price is $67, and the stock currently sells for $54.

a.	What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 9 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the conversion premium for this bond? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

   

Answer 1

á). Conversion Ratio = Par Value / Conversion Price = $1,000 / $67 = 14.93

Conversion Value = Stock Price x Conversion Ratio = $54 x 14.93 = $805.97

Straight Bond Value = $42[PVIFA_4.5%,40] + $1,000/1.045⁴⁰ = $772.87 + $171.93 = $944.80

The minimum bond price is the greater of the straight bond value or the conversion value, which is conversion value of $805.97

b). Conversion Premium = [Current Stock Price - Conversion Price] / Current Stock Price

= [$54 - $67] / $54 = -$13 / $54 = -0.24.07, or 24.07%