Question

6. Consider a 10 year bond with face value $1,000 that pays a 6.8% coupon semi-annually and has a yield-to-maturity of 8.4%. What is the approximate percentage change in the price of bond if interest rates in the economy are expected to decrease by 0.60% per year? Submit your answer as a percentage and round to two decimal places. (Hint: What is the expected price of the bond before and after the change in interest rates?)

Answer 1

Face Value = $1,000

Annual Coupon Rate = 6.80%
Semiannual Coupon Rate = 3.40%
Semiannual Coupon = 3.40% * $1,000
Semiannual Coupon = $34

Time to Maturity = 10 years
Semiannual Period to Maturity = 20

If Annual YTM is 8.40%:

Annual YTM = 8.40%
Semiannual YTM = 4.20%

Price of Bond = $34 * PVIFA(4.20%, 20) + $1,000 * PVIF(4.20%, 20)
Price of Bond = $34 * (1 - (1/1.042)^20) / 0.042 + $1,000 / 1.042^20
Price of Bond = $893.18

If Annual YTM decreases to 7.80%:

Annual YTM = 7.80%
Semiannual YTM = 3.90%

Price of Bond = $34 * PVIFA(3.90%, 20) + $1,000 * PVIF(3.90%, 20)
Price of Bond = $34 * (1 - (1/1.039)^20) / 0.039 + $1,000 / 1.039^20
Price of Bond = $931.44

Percentage Change in Price = ($931.44 - $893.18) / $893.18
Percentage Change in Price = 4.28%