Interest rates have fallen over the seven years since a $1,000 par, 10-year bond was issued with a coupon of 7%. What is the present value of this bond if the required rate of return is currently four and one-half percent? (For simplicity, assume annual payments.)
Each of the remaining cash flows on the bond is discounted at the annual rate of 4.5%.
Period |
Payment |
Discount |
PV |
1 |
$1,000 × 7% = $70 |
(1.045)1 |
$ 66.99 |
2 |
$1,000 × 7% = $70 |
(1.045)2 |
$ 64.10 |
3 |
$1,000 × 7% = $70 |
(1.045)3 |
$ 61.34 |
3 |
$1,000 principal |
(1.045)3 |
$ 876.30 |
Total Present Value of Cash Flows |
$1,068.73 |
The present value can also be determined with a financial calculator. N = 3, I = 4.5%, PMT = $1,000 × 7%, FV = $1,000. Solve for PV = $1,068.724.
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