You are given the following information concerning a noncallable, sinking fund debenture: Principal: $1,000 Coupon rate of interest: 7 percent Term to maturity: 15 years Sinking fund: 4 percent of outstanding bonds retired annually; the balance at maturity If you buy the bond today at its face amount and interest rates rise to 13 percent after two years have passed, what is your capital gain or loss

Capital loss of $257.38

Explanation:

Use the following formula to calculate the capital gain or (loss).

Capital Gains / (Loss) = Current Price - Purchase price

As two year have been passed and we need to calculate the current price of the debenture using the following formula

Use the following formula to calculate the price of the bond

Price of the bond = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Where

F = Face value = $1,000

C = Periodic coupon payment = 7% x $1,000 = $70

r = Periodic interest rate = 13%

n = Numbers of periods = 15 years - 2years = 13 years

Placing values in the formula

Price of the bond = [ $70 x ( 1 - ( 1 + 13% )^-13 ) / 13% ] + [ $1,000 / ( 1 + 13% )^13 ]

Price of the bond = $538.46 + $204.16 = $742.62

Purchase price = $1,000

Placing values in the capital gain or (loss) formula

Capital Gain / ( Loss ) = $742.62 - $1,000

Capital Gain / ( Loss ) = ($257.38)

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