Present Value of Coupons
Present Value of Coupons
The value today of a bond's coupon stream alone: an ordinary annuity of F × CR / m per period, discounted at the periodic yield y / m over N × m periods. Together with the present value of the face, it makes up the bond price.
When to use: Use to see how much of a bond's price is the income stream versus the return of principal, or to price the coupon strip separately from the principal strip.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| CouponPV | PV of Coupons | Present value of all remaining coupons | $ |
| F | Face Value | Par value paid at maturity | $ |
| CR | Coupon Rate | Annual coupon rate as a decimal (e.g. 0.05 for 5%) | % |
| y | Yield | Annual yield as a decimal; periodic yield is y/m | % |
| N | Years to Maturity | Years remaining until the bond matures | years |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: Coupon Half of a Discount Bond
10-year, 5% coupon, semi-annual, $1,000 face, priced at a 6% yield. What are the coupons worth?
Given
Step-by-Step
The coupons are worth $371.94 and the face $553.68; together, $925.61, the bond's price. About 40% of this bond's value is its income stream.
Example 2: High-Coupon Short Bond
5-year, 8% coupon, semi-annual, $1,000 face at a 5% yield.
Given
Step-by-Step
A high coupon on a short bond: the coupons are worth $350 against $781 for the face, and the bond trades at a premium ($1,131) because the coupon exceeds the yield.
Frequently Asked Questions
Each fixed coupon is discounted less heavily, so the same stream is worth more today. This is the annuity half of bond price risk.
A security made from just the coupon payments of a bond, sold separately from the principal. Its price is exactly this formula.