Question

A convertible bond has a coupon of 7 percent, paid semiannually, and will mature in 20 years. If the bond were not convertible, it would be priced to yield 6 percent. The conversion ratio on the bond is 15 and the stock is currently selling for $54 per share. What is the minimum value of this bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Minimum value

Answer 1

a. Straight Bond Value  
Face value =   1000
Yield rate is 6% or    0.06
semiannual rate = 6%/2=   0.030
Bond coupon rate is 7% or   0.07
semiay coupon rate is 7%/2= 3.5% or    0.035
Coupon amount = Par value*SemiAnnual coupon rate  
1000*0.035=   35
No of Semiannual periods =20*2=   40

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n  
(35*(1-(1/(1+0.03)^40))/0.03) + (1000/(1+0.03)^40)  
1115.57386  
So, straight bond value is   $1,115.57

conversion value = conversion ratio * Market price per share  
15*54  
=810  
Conversion value of Bond is   $810.00

Bond will not be converted, if straight value is more than conversion value. so  
minimum Market value of bond is straight value of Bond that is    $1,115.57