Both Bond Sam and Bond Dave have 10 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 18 years to maturity. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave

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%

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