Question

a $1,000 face value coupon bond will pay 5 percent interest annually for 12 years. What is the percentage change in the price of this bond if the market yield rises to 6 percent from the current level of 5.5 percent?

Answer 1

Given Details :

Bond Face value - $1,000

Coupon rate - 5% p.a. i.e,$50

Period - 12 years

Current market yield - 5.5%

Price of Bond concept :

The price of a bond is the present value of all the probable cash flows discounted at market yield. The formula is given below

$\sum_{i=1}^{n} \frac{C}{(1+r)^{n}} + \frac{F}{(1+r)^{n}}$

Where , C = Coupon payment

F = Face value

r = yield to maturity

n = No. of periods

Current price of the bond = $50*PVAF(5.5%,12) + $1000*PVID(5.5%,12)

= 50*8.6185 + 1000*.526

= 430.93 + 526

= 956.93

Price of the bond if market yield increases to 6% = 50*PVAF(6%,12) + 1000*PVIF(6%,12)

= 50*8.3838 + 1000*.497

= 419.19 + 497

= 916.19

Decrease in price due to increased market yield = 956.93 - 916.19 = $40.74