Question

Suppose you purchase a ten-year bond with 6 percent annual coupons. You
hold the bond for four years, and sell it immediately after receiving the fourth
coupon. If the bond's yield to maturity was 4.5% when you purchased and 7%
when you sold the bond. What is your annual rate of return on the bond in
each of the following situations:
a) All coupons were immediately spent when received.
b) All coupons were reinvested in a bank account, which pays 2 percent
interest until the bond is sold.

Answer 1

The annual rate of return is the gain or loss in terms of percentages that an investor expects from the investment in bonds.

Given information:

Annual coupon payment is 6%

Maturity period is 10 years

Holding period is 4 years

Yield to maturity when the bond is purchased is 4.50%

Yield to maturity when it was sold is 7%

Face value (assumed) is $1000

Formula used:

Calculations for an annual rate of return:

(a)

Firstly, calculate the purchase price by using the present value formula in excel sheet which is as shown below:

Likewise, the computation of the sales price can be done. As per given data, the bond is sold after holding it for four years. The selling price of the bond is computed as follows:

(b)

If the coupons were reinvested at 2% of interest at the end of the 4^th year, then the annual rate is computed by using the following formula:

(a)

The annual return is -3.95%

(b)

The annual return is 1.76% if the coupons are reinvested at 2% interest in the 4^th year.