Question

You have been hired to value a new 30-year callable, convertible bond. The bond has a coupon rate of 2.7 percent, payable semiannually, and its face value is $1,000. The conversion price is $54, and the stock currently sells for $38.

a. What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 4.9 percent. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Calculation of straight bond value:

FV = 1000
PMT = 1000 * 2.7% / 2 = 13.5
Nper = 30 * 2 = 60
Rate = 4.9% / 2 = 2.45%

Straight bond value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(2.45%,60,-13.5,-1000)
= $656.10

Straight bond value = $656.10


Calculation of conversion value:

Conversion value = (Par value / Conversion price) * market price of stock
= ($1000 / $54) * $38
= $703.70

Conversion value = $703.70

Conversion value is greater than the straight bond value.

Thus, Minimum value of the bond =  $703.70

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