Question

Consider three bonds with 6.6% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.

a. What will be the price of each bond if their yields increase to 7.6% in 4 Years, 8 Years, 30 Years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

What will be the price of each bond if their yields decrease to 5.6% in 4 Years, 8 Years, 30 Years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Bond with 4 years to Maturity:

Face Value = $1,000

Annual Coupon Rate = 6.60%
Annual Coupon = 6.60% * $1,000
Annual Coupon = $66

Time to Maturity = 4 years

If interest rate increases to 7.60%:

Annual Interest Rate = 7.60%

Price of Bond = $66 * PVIFA(7.60%, 4) + $1,000 * PVIF(7.60%, 4)
Price of Bond = $66 * (1 - (1/1.076)^4) / 0.076 + $1,000 / 1.076^4
Price of Bond = $966.58

If interest rate decreases to 5.60%:

Annual Interest Rate = 5.60%

Price of Bond = $66 * PVIFA(5.60%, 4) + $1,000 * PVIF(5.60%, 4)
Price of Bond = $66 * (1 - (1/1.056)^4) / 0.056 + $1,000 / 1.056^4
Price of Bond = $1,034.97

Bond with 8 years to Maturity:

Face Value = $1,000

Annual Coupon Rate = 6.60%
Annual Coupon = 6.60% * $1,000
Annual Coupon = $66

Time to Maturity = 8 years

If interest rate increases to 7.60%:

Annual Interest Rate = 7.60%

Price of Bond = $66 * PVIFA(7.60%, 8) + $1,000 * PVIF(7.60%, 8)
Price of Bond = $66 * (1 - (1/1.076)^8) / 0.076 + $1,000 / 1.076^8
Price of Bond = $941.65

If interest rate decreases to 5.60%:

Annual Interest Rate = 5.60%

Price of Bond = $66 * PVIFA(5.60%, 8) + $1,000 * PVIF(5.60%, 8)
Price of Bond = $66 * (1 - (1/1.056)^8) / 0.056 + $1,000 / 1.056^8
Price of Bond = $1,063.09

Bond with 30 years to Maturity:

Face Value = $1,000

Annual Coupon Rate = 6.60%
Annual Coupon = 6.60% * $1,000
Annual Coupon = $66

Time to Maturity = 30 years

If interest rate increases to 7.60%:

Annual Interest Rate = 7.60%

Price of Bond = $66 * PVIFA(7.60%, 30) + $1,000 * PVIF(7.60%, 30)
Price of Bond = $66 * (1 - (1/1.076)^30) / 0.076 + $1,000 / 1.076^30
Price of Bond = $883.04

If interest rate decreases to 5.60%:

Annual Interest Rate = 5.60%

Price of Bond = $66 * PVIFA(5.60%, 30) + $1,000 * PVIF(5.60%, 30)
Price of Bond = $66 * (1 - (1/1.056)^30) / 0.056 + $1,000 / 1.056^30
Price of Bond = $1,143.75