Question

A company issues a ten-year $1,000 face value bond at par with a coupon rate of 6.7% paid semiannually. The YTM at the beginning of the third year of the bond (8 years left to maturity) is 8.1%. What was the percentage change in the price of the bond over the past two years

Answer 1

-8.13%

Step-by-step explanation:

The computation of the percentage change in the price of the bond is shown below;

Given that

Face Value = $1,000

Annual Coupon Rate = 6.7%

Semi-annual Coupon Rate = 3.35%

Semi-annual Coupon = 3.35% × $1,000 = $33.50

Now

After 2 years:

Annual YTM = 8.1%

Semi-annual YTM = 4.05%

Price of Bond = $33.50 × PVIFA(4.05%, 16) + $1,000 ×PVIF(4.05%, 16)

= $33.50 × (1 -(1 ÷ 1.0405)^16) ÷ 0.0405 + $1,000 ÷ 1.0405^16

= $918.73

Now

Change in Price = ($918.73 - $1,000) ÷ $1,000

= -8.13%