EXAMPLE 10.9 Fair Holding-Period Return To illustrate built-in capital gains or

Question

EXAMPLE 10.9 Fair Holding-Period Return To illustrate built-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 is9 $70 × Annuity factor(8%, 3) + $1,000 × PV factor(896, 3) = $974.23 which is less than par value. In another year, after the next coupon is paid and remaining maturity falls to two years, the bond would sell at $70 × Annuity factor(8%, 2) + $1,000 × 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.

Explanation / Answer

a)

Let bond price be x

so X * (1+8.8%) = 1000

1.088x = 1000

x = 1000/1.088

= $ 919.12

b-1

=919.12/1.088^1

= 844.78

B-2)

8.8%

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