Bond basics
Pricing a bond
A bond's price is the present value of its coupons and principal at the market's required yield.
Learning objectives
- Price a bond by discounting each coupon and the principal
- Price a semi-annual bond with the per-period yield and number of periods
- Price a bond in one step with the PV function
- Explain why price is above, at or below 100
A bond is a set of promised cash flows, so its value is what any set of cash flows is worth: the sum of their present values. The discount rate is the yield the market requires on bonds of this issuer and maturity. Price a bond at a higher yield and every cash flow is worth less, so the price falls; at a lower yield the price rises.
This is how traders turn a yield quote into a price, how issuers set the coupon on a new bond, and how a portfolio is marked to market every day.
P = Σₜ₌₁ᴺ (C ÷ f) ÷ (1 + y ÷ f)ᵗ + 100 ÷ (1 + y ÷ f)ᴺ In a spreadsheet: P = PV(y ÷ f, N, −C ÷ f, −100)
- C
- annual coupon per 100 of face (coupon rate × 100)
- y
- annual yield, quoted with f compounding periods a year
- f
- coupon payments per year (2 for semi-annual, 1 for annual)
- N
- number of remaining coupon periods = years × f
- t
- the period in which each cash flow is paid
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