What is yield to maturity?
YTM is the discount rate that makes the present value of a bond's future cash flows (coupons plus face value) equal to its current price. It's essentially the bond's internal rate of return and is the standard way to compare bonds with different prices, coupons and maturities.
Approximate formula
YTM ≈ [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]
- C = annual coupon
- F = face value
- P = current price
- n = years to maturity
The exact YTM is solved by iteration, usually with a financial calculator or spreadsheet (RATE or YIELD functions).
Example
A bond with a $1,000 face value, a 5% coupon ($50 a year) and 5 years to maturity trades at $950.
YTM ≈ [50 + (1,000 − 950) ÷ 5] ÷ [(1,000 + 950) ÷ 2] = 60 ÷ 975 ≈ 6.15%
Because the bond trades below face value (at a discount), YTM is above the coupon rate.
Premium, par and discount
- Price above face value (premium): YTM < coupon rate
- Price equal to face value (par): YTM = coupon rate
- Price below face value (discount): YTM > coupon rate
Assumptions and limits
YTM assumes all payments are made on time and coupons are reinvested at the same rate. It doesn't account for default risk or bonds being called early.