Bond
How is bond price calculated?
Bond price is the theoretical present value of future coupons and principal at the investor's required yield.
Definition
Bond price is the theoretical present value of future coupons and principal at the investor's required yield.
Intuition
Coupon rate determines scheduled payments; required yield determines what they are worth today. Holding cash flows fixed, a higher yield lowers price.
Formula
Price equals the present value of each coupon and final face value discounted at the required yield per period; N is remaining payment periods.
Formula variables
Face is principal repaid at maturity; Coupon Rate is the nominal annual coupon rate; YTM is the nominal annual required yield; m is payments per year; Years is time remaining; N = Years × m is the number of payments. Coupon per period = Face × Coupon Rate ÷ m; discount rate per period = YTM ÷ m.
How coupon rate and YTM affect price
All else equal, a higher coupon rate raises each payment and price; a higher required yield discounts the same payments more and lowers price. When the two rates match, a standard fixed-coupon bond prices at par.
Discount, par, and premium bonds
A discount bond trades below face when required yield generally exceeds coupon rate; a par bond trades at face when the rates match; a premium bond trades above face when required yield is generally lower.
Example
- Enter 1,000 face value, a 5% coupon rate, 6% required yield, five years remaining, and semiannual coupons.
- Each coupon is 1,000 × 5% ÷ 2 = 25 for 10 periods. Discount each coupon and the final principal at 3% per period.
- Coupon PV is about 213.26 and principal PV about 744.09, totaling about 957.35. Below 1,000 face value, it is a discount bond.
Common mistakes
Do not confuse coupon rate with required yield or treat this theoretical price as a market dirty price including accrued interest.
Frequently asked questions
Why does a higher required yield lower price?
The same scheduled payments are discounted at a higher rate, reducing their present value.
Can I price a zero-coupon bond?
Yes. Set coupon rate to 0%; price then equals the discounted face value at maturity.
Does this include accrued interest?
No. It assumes valuation on a coupon date and prices full future coupons; it excludes accrued interest, taxes, default, and early redemption.
How do I infer yield from a market price?
Use the YTM calculator and enter the known market price.