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an investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. after the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. assume that interest rates remain unchanged at 8% over the five-year holding period.
-The capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a:
A) loss of 8.45.
B) loss of 3.31.
C) gain of 2.75.

Question

The following information relates to Problems 
an investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. after the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. assume that interest rates remain unchanged at 8% over the five-year holding period.
-The capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a:
A) loss of 8.45.
B) loss of 3.31.
C) gain of 2.75.

Quizplus · Accepted Answer

When interest rates increase, the value of a bond decreases. Since the investor purchased the bond at par value, the initial price was 100. When interest rates increase to 8%, the market value of the bond drops to $92.59 (using the bond pricing formula: PV = C[1 - 1/(1+r)^n]/r + FV/(1+r)^n, where PV is the present value or price of the bond, C is the coupon payment, r is the discount rate, n is the number of periods, and FV is the face value or par value of the bond).

After five years, the bond will have four years until maturity. Using the bond pricing formula, the price of the bond after five years with an 8% discount rate is $94.19. The capital gain/loss per 100 of par value is the difference between the selling price of the bond ($94.19) and the purchase price of the bond ($100), which is a loss of $5.81.

Therefore, the capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a loss of 3.31 ($5.81 / $100) which is option B.

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