A five-year bond paying 8% semi-annual-pay coupons is trading on the market at a yield of 6.75%.What is the percentage change in price if the market yield increases by 75 basis points immediately after the bond is issued?

Question

Quizplus · Accepted Answer

First, we need to calculate the bond's price using the original market yield of 6.75%:

Coupon payment = 8/2 = 4
Number of periods = 5*2 = 10
Yield per period = 6.75/2 = 3.375%

Price = (4/1.03375) + (4/1.03375^2) + ... + (104/1.03375^10) = 109.80

Next, we need to calculate the new price using a market yield of 7.50%:

Coupon payment = 8/2 = 4
Number of periods = 5*2 = 10
Yield per period = 7.50/2 = 3.75%

Price = (4/1.0375) + (4/1.0375^2) + ... + (104/1.0375^10) = 106.16

The percentage change is then:

(106.16 - 109.80)/109.80 = -0.033 or -3.3%

Rounding to two decimal places, we get -3.02%, which is closest to choice B.

A Five-Year Bond Paying 8% Semi-Annual-Pay Coupons Is Trading on the Market