A convertible bond has an 8% annual coupon and 15 years to maturity.The face value is $1,000 and the conversion ratio is 40.The stock currently sells for $20.875 per share.Similar nonconvertible bonds are priced to yield 9%.The value of the convertible bond is at least:

Question

Quizplus · Accepted Answer

First, we need to calculate the annual coupon payment, which is $80 (=$1,000 x 8%). 
Then, we need to calculate the conversion value if we were to convert the bond into stock: 
Conversion value = conversion ratio x stock price = 40 x $20.875 = $835. 
Next, we need to compare the bond's annual yield to the yield of the similar nonconvertible bonds. The annual yield of the convertible bond is: 
Annual yield = coupon payment / bond price = $80 / ($1,000 x 100%) = 8%. 
Since the yield of similar nonconvertible bonds is 9%, the convertible bond is selling at a discount. 
To calculate the minimum value of the convertible bond, we need to find the present value of its future cash flows (coupon payments and face value) plus the conversion value: 
Minimum value = PV(coupon payments) + PV(face value) + PV(conversion value) 
Using a financial calculator or Excel, we can find the present value of the coupon payments to be $815.09 and the present value of the face value to be $323.94. 
To calculate the present value of the conversion value, we need to find the present value of the stock if we were to buy it directly: 
PV(stock) = stock price / (1 + yield of similar nonconvertible bonds) ^ remaining years to maturity 
PV(stock) = $20.875 / (1 + 9%) ^ 15 = $4.44 
Therefore, the present value of the conversion value is $177.60. 
Finally, we can calculate the minimum value of the convertible bond: 
Minimum value = $815.09 + $323.94 + $177.60 = $1,316.63 
However, since the question asks for the minimum value that the convertible bond is worth, we need to choose the answer that is closest to this value. Out of the given choices, B is the closest answer.

A Convertible Bond Has an 8% Annual Coupon and 15