Calculate the value of a $1,000 bond which has 10 years until maturity and pays quarterly interest at an annual coupon rate of 12 percent. The required return on similar-risk bonds is 20 percent.

Question

Quizplus · Accepted Answer

Step 1: Calculate the total number of coupon payments over the life of the bond
= 10 x 4
= 40 coupon payments

Step 2: Calculate the amount of each coupon payment
= Annual coupon payment / Number of coupon payments per year
= (12% x $1,000) / 4
= $30

Step 3: Calculate the present value of the bond's cash flows
= ($30 / (1 + 5%)) + ($30 / (1 + 5%)^2) + ... + ($30 + $1,000 / (1 + 5%)^40)
= $656.82

Since the required return on similar-risk bonds is higher than the bond's coupon rate, the bond will be discounted, resulting in its value being lower than its face value. Therefore, choice A is the correct answer.

Calculate the Value of a $1,000 Bond Which Has 10