Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?
Bond price = PV of CFs from it.
Let X be the coupon amount.
| Year | CF | PVF @6% | Disc CF |
| 1 | X | 0.9434 | 0.9434X |
| 2 | X | 0.8900 | 0.890X |
| 3 | X | 0.8396 | 0.8396X |
| 4 | X | 0.7921 | 0.7921X |
| 5 | X | 0.7473 | 0.7473X |
| 5 | $ 1,000.00 | 0.7473 | $ 747.26 |
| Bond value | 4.2124X + 747.26 | ||
Thus 4.2124X + 747.26 = 900
.4.2124X = 900 - 747.26
= 152.74
X = 152.74 / 4.2124
= 36.26
Coupon Rate = Coupon amount / Face Value
= 36.26 / 1000
= 3.63%
Pls comment, if any further assistance is required.
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