Pricing a bond

A bond is just a cash flow series: periodic coupon payments plus the face value (principal) returned at maturity. Its price is the present value of all those flows — exactly the NPV machinery, applied to a loan you make to an issuer.

The pricing formula

For a bond with coupon C per period, face value F, yield per period y, over n periods:

Price = C/(1+y)^1 + C/(1+y)^2 + ... + C/(1+y)^n + F/(1+y)^n

The coupons form an annuity; the face value is a single future amount.

Worked example

A bond with face value 1,000, a 5% annual coupon (so C = 50), 3 years to maturity, and a market yield of 6%:

Year 1:   50 / 1.06       = 47.17
Year 2:   50 / 1.06^2     = 44.50
Year 3:   50 / 1.06^3     = 41.98
Year 3: 1000 / 1.06^3     = 839.62

Price = 47.17 + 44.50 + 41.98 + 839.62 = 973.27

The bond trades at 973.27 — below its 1,000 face value (a discount), because its 5% coupon is less attractive than the 6% the market now demands.

The price-yield seesaw

This is the central law of fixed income: price and yield move in opposite directions.

• If the market yield were 4% (below the 5% coupon), the same bond would price above 1,000 — a premium.
• If the yield rose to 8%, the price would fall further below 1,000.

When you own a bond and rates rise, the present value of its fixed future payments drops, so its price falls. How much it falls is what duration measures — the next lesson.