Problem 2411 Calculating Values for Convertibles [LO6]
You have been hired to value a new 20year 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). 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%
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