Question

CraMerica has 8% coupon bond issue with 8 years to maturity. Each of these bonds make semi-annual interest payments. These bonds have a yield to maturity of 10%. Suddenly, the yield to maturity on these bonds fall to 8%. What is the percentage change in the price of these bonds. Assume a par value of $1,000. Enter your answer to two decimal plances with no percentage sign. That is, like this: 13.61

Answer 1

Answer:

Face Value = $1,000

Annual Coupon Rate = 8%
Semiannual Coupon Rate = 4%
Semiannual Coupon = 4% * $1,000
Semiannual Coupon = $40

Time to Maturity = 8 years
Semiannual Period = 16

If interest rate is 10%:

Annual Interest Rate = 10%
Semiannual Interest Rate = 5%

Price of Bond = $40 * PVIFA(5%, 16) + $1,000 * PVIF(5%, 16)
Price of Bond = $40 * (1 - (1/1.05)^16) / 0.05 + $1,000 / 1.05^16
Price of Bond = $891.62

If interest rate is 8%:

Annual Interest Rate = 8%
Semiannual Interest Rate = 4%

Price of Bond = $40 * PVIFA(4%, 16) + $1,000 * PVIF(4%, 16)
Price of Bond = $40 * (1 - (1/1.04)^16) / 0.04 + $1,000 / 1.04^16
Price of Bond = $1,000.00

Percentage Change in Price = ($1,000.00 - $891.62) / $891.62
Percentage Change in Price = 0.1216 or 12.16