Consider a(n) Ten-year, 12.5 percent annual coupon bond with a face value of $1,000. The bond...

Consider a(n) Ten-year, 12.5 percent annual coupon bond with a face value of $1,000. The bond is trading at a rate of 9.5 percent. a. What is the price of the bond? b. If the rate of interest increases 1 percent, what will be the bond’s new price? c. Using your answers to parts (a) and (b), what is the percentage change in the bond’s price as a result of the 1 percent increase in interest rates? (Negative value should be indicated by a minus sign.) d. Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) *please show via financial calculator if possible*

Solutions

Expert Solution

The formula to calculate the price of the bond:
coupon * PVIFA(market interest rate , years) + Par value * PVIF(market interest rate , years)

a) bond price = (100012.5%) PVIFA(9.5%,10) + $1000 *PVIF(9.5%,10)
bond price = 125 * 6.2788 + 1000 *0.4035 = $1188.35

INCREASE OF 1%:
b) bond price = (100012.5%) PVIFA(10.5%,10) + $1000 *PVIF(10.5%,10)
bond price = 125 * 6.0148 + 1000 *0.3684 = $1120.25


c) The percentage change in the bond's price form a to b:
(1120.25-1188.35)/1188.35 = -5.73%

DECREASE OF 1%:
d) bond price = (100012.5%) PVIFA(8.5%,10) + $1000 *PVIF(8.5%,10)
bond price = 125 * 6.5613 + 1000 *0.4423 = $1262.46


The percentage change in the bond's price form a to d:
(1262.46-1188.35)/1188.35 = 6.24%

jeff jeffy answered 1 year ago

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