Answer:
The percentage change in the price of Bond Sam is -4.917%
and
The percentage change in the price of Bond Dave is -14.621%
Explanation:
As both bonds are priced at par, hence the existing interest rate is equal to the coupon rate of 10%
Now increase the interest rate by 2%
Interest rate = 10% + 2% = 12%
Now use 12% to calculate the prices of both bonds by using the following formula
P = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]
Bond Sam
F = Face value = $1,000
C = Periodic coupon payment = $1,000 x 10% x 6/12 = $50
r = Periodic interest rate = 12% x 6/12 = 6%
n = Numbers of periods = 3 years x 12/6 = 6 periods
Placing values in the formula
P = [ $50 x ( 1 - ( 1 + 6% )^-6 ) / 6% ] + [ $1,000 / ( 1 + 6% )^6 ]
P = $245.87 + $704.96
P = $950.83
Bond Dave
F = Face value = $1,000
C = Periodic coupon payment = $1,000 x 10% x 6/12 = $50
r = Periodic interest rate = 12% x 6/12 = 6%
n = Numbers of periods = 18 years x 12/6 = 36 periods
Placing values in the formula
P = [ $50 x ( 1 - ( 1 + 6% )^-36 ) / 6% ] + [ $1,000 / ( 1 + 6% )^36 ]
P = $731.05 + $122.74
P = $853.79
Now calculate the percentage change
Bond Sam
Percentage Change = [ ( $950.83 - $1,000 ) / $1,000 ] x 100 = -4.917%
Bond Dave
Percentage Change = [ ( $853.79 - $1,000 ) / $1,000 ] x 100 = -14.621%
