Question

Consider three bonds with 5.20% coupon rates, all making annual coupon payments and all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has a maturity of 8 years, and the long-term bond has a maturity of 30 years.
a. What will be the price of the 4-year bond if its yield increases to 6.20%?
b. What will be the price of the 8-year bond if its yield increases to 6.20%?
c. What will be the price of the 30-year bond if its yield increases to 6.20%?
d. What will be the price of the 4-year bond if its yield decreases to 4.20%?
e. What will be the price of the 8-year bond if its yield decreases to 4.20%?
f. What will be the price of the 30-year bond if its yield decreases to 4.20%?

Answer 1

Face Value = $1,000

Annual Coupon Rate = 5.20%
Annual Coupon = 5.20% * $1,000
Annual Coupon = $52

Answer a.

Time to Maturity = 4 years
Annual YTM = 6.20%

Current Price = $52 * PVIFA(6.20%, 4) + $1,000 * PVIF(6.20%, 4)
Current Price = $52 * (1 - (1/1.062)^4) / 0.062 + $1,000 / 1.062^4
Current Price = $965.51

Answer b.

Time to Maturity = 8 years
Annual YTM = 6.20%

Current Price = $52 * PVIFA(6.20%, 8) + $1,000 * PVIF(6.20%, 8)
Current Price = $52 * (1 - (1/1.062)^8) / 0.062 + $1,000 / 1.062^8
Current Price = $938.39

Answer c.

Time to Maturity = 30 years
Annual YTM = 6.20%

Current Price = $52 * PVIFA(6.20%, 30) + $1,000 * PVIF(6.20%, 30)
Current Price = $52 * (1 - (1/1.062)^30) / 0.062 + $1,000 / 1.062^30
Current Price = $865.25

Answer d.

Time to Maturity = 4 years
Annual YTM = 4.20%

Current Price = $52 * PVIFA(4.20%, 4) + $1,000 * PVIF(4.20%, 4)
Current Price = $52 * (1 - (1/1.042)^4) / 0.042 + $1,000 / 1.042^4
Current Price = $1,036.13

Answer e.

Time to Maturity = 8 years
Annual YTM = 4.20%

Current Price = $52 * PVIFA(4.20%, 8) + $1,000 * PVIF(4.20%, 8)
Current Price = $52 * (1 - (1/1.042)^8) / 0.042 + $1,000 / 1.042^8
Current Price = $1,066.77

Answer f.

Time to Maturity = 30 years
Annual YTM = 4.20%

Current Price = $52 * PVIFA(4.20%, 30) + $1,000 * PVIF(4.20%, 30)
Current Price = $52 * (1 - (1/1.042)^30) / 0.042 + $1,000 / 1.042^30
Current Price = $1,168.80