A convertible bond has a 7 percent, semi-annual coupon and a conversion ratio of 20. The bond has a face value of $1,000 and matures in 13.5 years. The current yield to maturity is 7.1 percent. Assume that you buy this bond today and sell it one year from now when the yield to maturity is 7.25 percent and the stock price is $52. What will your holding period return be?

Question

Quizplus · Accepted Answer

First, we need to calculate the price of the bond today:
Coupon payment = $1,000 x 7%/2 = $35
Discount rate = 7.1%/2 = 0.0355 (semi-annual)
Number of periods = 13.5 x 2 = 27
PV of coupon payments = $35 x (1 - 1/(1+0.0355)^27)/0.0355 = $694.86
PV of face value = $1,000/(1+0.0355)^27 = $385.69
Price of bond = $694.86 + $385.69 = $1,080.55

Next, we need to calculate the price of the bond in one year assuming a yield of 7.25% and a stock price of $52:
Coupon payment = $1,000 x 7%/2 = $35
Discount rate = 7.25%/2 = 0.03625 (semi-annual)
Number of periods = 26 (since one semi-annual period has already passed)
PV of coupon payments = $35 x (1 - 1/(1+0.03625)^26)/0.03625 = $690.56
Conversion value = 20 x $52 = $1,040
Price of bond = $690.56 + $1,040/(1+0.03625)^13.5 = $1,404.88

Finally, we can calculate the holding period return as:
($1,404.88 - $1,080.55 + $35)/$1,080.55 x 100% = 4.90%

A Convertible Bond Has a 7 Percent, Semi-Annual Coupon and a Conversion