Pricing a Bond with Coupons That Begin After a Delay

Summary

The document explains how to value a bond that pays no coupons during an initial period, then pays regular coupons until maturity. The stated example has a face value, annual coupons beginning after six years, and a constant discount rate. Applying an ordinary coupon-bond formula with the full coupon-paying period but without accounting for its delayed start overstates the price.

The corrected approach first values the coupon stream and principal as of the date the coupons begin. It uses the number of coupon periods remaining from that date to maturity, then discounts the resulting value back to today across the initial zero-coupon interval. This separates the bond’s initial waiting period from its coupon-paying life. The answer supplies a formula but no derivation or comparison across discounting conventions; it assumes the stated annual schedule and a constant yield.

Key ideas

• A bond’s coupon-paying period can begin after issuance, so its cash flows are delayed.
• Value the remaining coupons and principal at the start of the coupon period.
• Discount that intermediate value back to the valuation date across the initial delay.
• Use the number of payments after coupons begin when valuing the coupon stream.

Tags

# Calculating value of bond


# Calculating value of bond












The bond has a facevalue of 40 and maturity of 20 years. It produces 0 coupon payments during the first 6 years but pays coupons of 2 annually during the last 14 years. The discount rate is 7%.

The formula looks like this;

$$ P=\frac{CPN}{y}[1-\frac{1}{(1+y)^{N_1}}]+\frac{FV}{(1+y)^{N_2}} $$

Since the coupon only pays during the last 14 years, I tried $N_1=14, N_2=20, CPN=2,y=0.07, FV=40$ in the formula above. But that gave me an answer of $P=27.83$, but the answer should be $P=21.99$.

## Answer by RandyF (score 2, accepted)

https://quant.stackexchange.com/a/43561

You question is saying that you have 14 payments coming starting in 6 years. This implies that the formula is as you have it, but replace both $N_1$ and $N_2$ with $N_2-N_1$ and discount that whole cashflow from T=6 to today. Accordingly, this is the equation you're looking for.

$$P=(1+y)^{-{N_1}} * [\frac{CPN}{y}(1-\frac{1}{(1+y)^{N_2-N_1}})+\frac{FV}{(1+y)^{N_2-N_1}}]$$

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.