Question

Problem 24-11 Calculating Values for Convertibles [LO6]

You have been hired to value a new 20-year callable, convertible bond. The bond has a coupon rate of 2.8 percent, payable semiannually, and its face value is $1,000. The conversion price is $59, and the stock currently sells for $46.

a.	What is the minimum value of the bond? Comparable nonconvertible bonds are priced to yield 3 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.)

   

a.	Minimum value of the bond
b.	Conversion premium		%

Answer 1

a). The minimum bond price is the greater of the straight bond value or the conversion value. The straight bond value is:

INPUT	20*2=40	3/2=1.5		(2.8%/2)*1,000=14	1,000
TVM	N	I/Y	PV	PMT	FV
OUTPUT			-970.08

Hence, Straight Bond Value = $970.08

Conversion Ratio = Par Value / Conversion Price = $1,000 / $59 = 16.95

Conversion Value = Conversion Ratio x Stock Price = 16.95 x $46 = $779.66

The minimum value for this bond is the straight bond value of $970.08.

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

= [$59 - $46] / $46 = 28.26%