Present Value of Face Value
Present Value of Face Value
The value today of the principal a bond returns at maturity: the face value discounted at the periodic yield over N × m periods. This is also the price of a zero-coupon bond with the same face and maturity.
When to use: Use to see how much of a bond's price is the return of principal, or to price a principal strip.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| FacePV | PV of Face Value | Present value of the principal repayment | $ |
| F | Face Value | Par value paid at maturity | $ |
| 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: Principal Half of a Discount Bond
$1,000 face due in 10 years, discounted at a 6% semi-annual yield.
Given
Step-by-Step
Ten years of 6% discounting takes the principal to about 55 cents on the dollar. Add the coupons ($371.94) to reach the bond price of $925.61.
Example 2: Five-Year Principal at 5%
$1,000 face due in 5 years at a 5% semi-annual yield.
Given
Step-by-Step
Shorter maturity and a lower yield leave the principal worth 78% of face today.
Frequently Asked Questions
Yes. A zero-coupon bond is nothing but a face value at maturity, so its price is exactly the present value of that face.