Question

Consider a(n) Six-year, 16 percent annual coupon bond with a face value of $1,000. The bond is trading at a rate of 13 percent.

a. What is the price of the bond?
b. If the rate of interest increases 1 percent, what will be the bond’s new price?
c. Using your answers to parts (a) and (b), what is the percentage change in the bond’s price as a result of the 1 percent increase in interest rates? (Negative value should be indicated by a minus sign.)
d. Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates.
  
(For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16))

Answer 1

a)

Coupon = 0.16 * 1000 = 160

Current price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Current price = 160 * [1 - 1 / (1 + 0.13)⁶] / 0.13 + 1000 / (1 + 0.13)⁶

Current price = 160 * 3.99755 + 480.318527

Current price = $1,119.93

b)

Rate = 13% + 1% = 14%

New price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New price = 160 * [1 - 1 / (1 + 0.14)⁶] / 0.14 + 1000 / (1 + 0.14)⁶

New price = 160 * 3.888668 + 455.586548

New price = $1,077.77

c)

Percentage change = [(1,077.77 - 1,119.93) / 1,119.93] * 100

Percentage change = -3.76%

d)

Rate = 13% 1 1% = 12%

New price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

New price = 160 * [1 - 1 / (1 + 0.12)⁶] / 0.12 + 1000 / (1 + 0.12)⁶

New price = 160 * 4.111407 + 506.631121

New price = $1,164.46

Percentage change = [(1,164.46 - 1,119.93) / 1,119.93] * 100

Percentage change = 3.98%