You buy an 8 percent coupon, 10-year maturity bond when its
yield to maturity is 9 percent. One year later, the yield to
maturity is 10 percent. Assume the face value of the bond is
$1,000.
(a) What is the price of the bond today?
(b) What is the price of the bond one year later?
(c) What is your rate of return over the one-year holding
period?
Value of the bond is Present value of future cash inflows. So, the value of the bond is calculated by discounting the future cash inflows.
(a) Price of the bond today:
| Year | Nature | Amount | PVF@9% | Present value |
| 1-10 | Coupon | $ 80 | PVAF(9%,10)=6.4176 | $513.408 |
| 10 | Redemption | $1000 | PVF(9%,10) =0.4224 | $422.4 |
| Value of the Bond today | $935.808 |
(b) Price of the bond 1 year later:
| Year | Nature | Amount | PVF@10% | Present value |
| 1-9 | Coupon | $ 80 | PVAF(10%,9)=5.7590 | $460.72 |
| 9 | Redemption | $1000 | PVF(10%,9) =0.4241 | $424.1 |
| Value of the Bond after 1 yr | $884.82 |
(c) Rate of return over 1 yr holding period:
Rate of return = coupon received + (Sale price - purchase price) / Bond purchase price
= ($80 + ($884.82 - $935.808)) /$935.808
= ($80 - $50.98) / $935.808
= $29.02 / $935.808
=0.03101 (or) 3.101%
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