A convertible bond has a face value of $1,000 and a conversion price of $20. The bond has a 7 percent coupon and pays interest semi-annually. The bond matures in 8 years. Similar bonds are yielding 7.5 percent. The current price of the stock is $19.74. What is the straight bond value?
A) $969.18
B) $970.32
C) $970.71
D) $971.47
E) $971.53

Question

Quizplus · Accepted Answer

The straight bond value can be calculated using the present value of the bond's future cash flows, which include the semi-annual interest payments and the principal repayment at maturity. Given a 7 percent annual coupon on a $1,000 face value bond, the semi-annual coupon payment is $35 ($1,000 * 7% / 2). The bond matures in 8 years, so there are 16 semi-annual periods. The market yield of similar bonds is 7.5 percent annually, or 3.75 percent semi-annually. The present value of the bond's cash flows can be calculated using the formula for the present value of an annuity for the coupon payments, plus the present value of a lump sum for the face value repayment at maturity. The calculation is as follows:$$ \text{Present Value of Coupons} = C \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) $$$$ \text{Present Value of Face Value} = F / (1 + r)^n $$Where:- $C$ is the semi-annual coupon payment ($35),- $r$ is the semi-annual market yield (3.75% or 0.0375),- $n$ is the total number of semi-annual periods (16),- $F$ is the face value of the bond ($1,000).$$ \text{Present Value of Coupons} = 35 \times \left( \frac{1 - (1 + 0.0375)^{-16}}{0.0375} \right) $$$$ \text{Present Value of Face Value} = 1000 / (1 + 0.0375)^{16} $$$$ \text{Present Value of Coupons} \approx 439.62 $$$$ \text{Present Value of Face Value} \approx 530.70 $$Adding these two components gives the straight bond value:$$ \text{Straight Bond Value} \approx 439.62 + 530.70 = 970.32 $$Therefore, the correct answer is $970.32.

A Convertible Bond Has a Face Value of $1,000 and a Conversion