Bond Pricing & Yield

A bond's price is the present value of its promised cash — and it seesaws against the yield.

The idea

A bond is a promise of fixed cash. It pays a coupon $C$ at the end of each year for $n$ years and returns its face value $F$ at maturity; once the bond is issued, none of those numbers changes.

Pricing a bond is a present-value computation: discount every promised payment back to today at the market yield $y$ and add. The coupons are $n$ equal payments — an annuity — and the face value is a single lump sum at the end, so

$P = C\,\frac{1-(1+y)^{-n}}{y} + \frac{F}{(1+y)^{n}}.$

The yield $y$ is the rate the market currently charges for waiting, and it is the only quantity in the equation free to move; $C$, $F$ and $n$ are written into the contract. A bond's price therefore changes over its life without any of its promises changing — the market revalues future dollars.

Traders usually work the equation the other way: observe the price and solve for $y$, the single rate at which the promised cash flows are worth exactly what the bond costs. That rate is the bond's yield to maturity, the number compared across bonds.

Ways to work on it

• Walkthrough. Price a bond by discounting its promised payments.
• Practice. Price zero-coupon and coupon bonds, and compare each price to par.
• Hardest. Recover a bond's yield from its price and quantify its interest-rate risk.

Not sure where to start? Take the ten-question placement test.