What will be the price of the bond in Example 10.7 in yet another year, when only one year remains until maturity? What is the rate of return to an investor who purchases the bond at $982.17 and sells it one year later?

Transcribed Image Text:

To illustrate build-in capital gains or losses, suppose a bond was issued several years ago when the interest rate was 7%. The bond's annual coupon rate was thus set at 7%. (We will suppose for simplicity that the bond pays its coupon annually.) Now, with three years left in the bond's life, the interest rate is 8% per year. The bond's fair market price is the present value of the remaining annual coupons plus payment of par value. That present value is ¹0 $70 x Annuity factor (8%, 3) + $1,000 x PV factor (8%, 3) = $974.23 which is less than par value. In another year, after the next coupon is paid, the bond would sell at $70 X Annuity factor (8%, 2) + $1,000 X PV factor (8%, 2) = $982.17 thereby yielding a capital gain over the year of $7.94. If an investor had purchased the bond at $974.23, the total return over the year would equal the coupon payment plus capital gain, or $70 + $7.94 = $77.94. This represents a rate of return of $77.94/$974.23, or 8%, exactly the current rate of return available elsewhere in the market. EXAMPLE 10.7 Fair Holding-Period Return