a.
A Convertible bond, at lowest, trade at the higher of either conversion value or straight value.
First, we have to calculate the price of the bond.
Semi annual payments of $15(1.5% of $1000) for 20 years.Yield is given as 4%
Formula to calculate the price is C*((1-(1+i)^-n)/i), where C=coupon payments, i=yield, n=number of payments.
On substituting, Price = 296.891.
So, Straight value = $296.891
Now calculating Conversion value,
Conversion value=stock price*(par/conversion price)=38*(1000/50)=760.
So, the minimum value if the bond=$760.
b.
Conversion premium for the bond is the difference between current market price of the stock and conversion price
current ratiomarket price is $38 and conversion price is $50. So, the conversion premium of the bond is $12.
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