How to calculate bond price
About this lesson
In this video, I will discuss a corporate bond and its properties. Using a numerical example, I will calculate the maximum price of a bond that a buyer would be willing to pay.
What a bond pays
A typical corporate bond has:
- a face value (par), usually $1,000, repaid at maturity;
- a coupon rate, the yearly interest as a percentage of face value;
- a maturity date, when the face value is repaid.
The bond price formula
A bond is worth the present value of everything it will pay, discounted at the yield investors require (the yield to maturity):
Price = C × [1 − (1 + y)−T] ÷ y + F ÷ (1 + y)T
- C: the yearly coupon payment
- F: face value
- y: the required yield
- T: years to maturity
The first part is the value of the coupons (an annuity); the second is the value of the face value.
Example
A 10-year bond with a $1,000 face value and an 8% annual coupon ($80 a year). Investors require 6%.
- Value of the coupons: 80 × [1 − 1.06−10] ÷ 0.06 = 80 × 7.3601 = $588.81
- Value of the face value: 1,000 ÷ 1.0610 = $558.39
- Price = $1,147.20
This is the most a buyer requiring 6% would pay.
In Excel: =PV(6%,10,80,1000) returns −1,147.20 (negative because it’s money you pay).
Price and yield move in opposite directions
| Required yield | Price | The bond trades at |
|---|---|---|
| 6% (below the coupon) | $1,147.20 | a premium |
| 8% (equal to the coupon) | $1,000.00 | par |
| 10% (above the coupon) | $877.11 | a discount |
When market yields rise, existing bonds with lower coupons become less attractive, so their prices fall.