Question

Bond prices and maturity dates. Les Company is about to issue a bond with semiannual coupon payments, an annual coupon rate of 11​%, and a par value of ​$5,000. The yield to maturity for this bond is 10​%.

a. What is the price of the bond if it matures in 5​, 10​, 15​, or 20​years?

b. What do you notice about the price of the bond in relationship to the maturity of the​ bond?

a. What is the price of the bond if it matures in 5 ​years?

​$__________​ (Round to the nearest​ cent.)

b. What is the price of the bond if it matures in 10 ​years?

​$___________​ (Round to the nearest​ cent.)

c. What is the price of the bond if it matures in 15 ​years?

​$___________​ (Round to the nearest​ cent.)

d. What is the price of the bond if it matures in 20 years?

​$____________ ​(Round to the nearest​ cent.)

b. What do you notice about the price of the bond in relationship to the maturity of the​ bond? ​(Select the best​ response.)

A. As the time to maturity​ increases, the price of the bond increases first and then decreases.

B. As the time to maturity​ increases, the price of the bond decreases first and then increases.

C. As the time to maturity​ increases, the price of the bond decreases.

D. As the time to maturity​ increases, the price of the bond increases.

Answer 1

a)

Coupon = (0.11 * 5000) / 2 = 275

Rate = 10% / 2 = 5%

Number of periods = 5 * 2 = 10

price of bond after 5 years = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

price of bond after 5 years = 275 * [1 - 1 / (1 + 0.05)¹⁰] / 0.05 + 5000 / (1 + 0.05)¹⁰

price of bond after 5 years = 275 * 7.72173 + 3,069.56627

price of bond after 5 years = $5,193.04

b)

Coupon = (0.11 * 5000) / 2 = 275

Rate = 10% / 2 = 5%

Number of periods = 10 * 2 = 20

price of bond after 10 years = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

price of bond after 10 years = 275 * [1 - 1 / (1 + 0.05)²⁰] / 0.05 + 5000 / (1 + 0.05)²⁰

price of bond after 10 years = 275 * 12.46221 + 1,884.44741

price of bond after 10 years = $5,311.56

c)

Coupon = (0.11 * 5000) / 2 = 275

Rate = 10% / 2 = 5%

Number of periods = 15 * 2 = 30

price of bond after 15 years = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

price of bond after 15 years = 275 * [1 - 1 / (1 + 0.05)³⁰] / 0.05 + 5000 / (1 + 0.05)³⁰

price of bond after 15 years = 275 * 15.372451 + 1,156.88724

price of bond after 15 years = $5,384.31

d)

Coupon = (0.11 * 5000) / 2 = 275

Rate = 10% / 2 = 5%

Number of periods = 20 * 2 = 40

price of bond after 20 years = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

price of bond after 20 years = 275 * [1 - 1 / (1 + 0.05)⁴⁰] / 0.05 + 5000 / (1 + 0.05)⁴⁰

price of bond after 20 years = 275 * 17.159086 + 710.22841

price of bond after 20 years = $5,428.98

b)

D. As the time to maturity​ increases, the price of the bond increases.