Question

Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield...

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?

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Answer #1

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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