How to Calculate Yield to Maturity (YTM)
Yield to maturity is the annual return on a bond bought at its current price and held to maturity, counting every coupon and the face value.
The Yield to Maturity formula
Calculator
Enter face value, coupon rate, years left and the price to get the yield a buyer earns holding the bond to maturity.
What the issuer repays at maturity, also called par value.
Fixed when the bond is issued. It never moves with the market price.
Whole years until the face value is repaid.
What the bond trades for now. Below face value is a discount, above it is a premium.
Discounting every coupon and the face value back to $920.15 gives an annual return of 8% for a buyer who holds to maturity.
- Approximate YTM
- 7.91%
- Approximation error
- 0.09%
- Current yield
- 6.52%
- Annual coupon payment
- $60
- Price against face value
- Discount, YTM above the coupon rate
The hand formula, coupon plus the yearly share of the discount over the average of price and face value, gives 7.91%.
The gap between the hand formula and the exact yield. Averaging price and face value instead of discounting each payment by how long you wait is what opens it.
Coupon over price alone is 6.52%, which misses the gain or loss collected at maturity.
Coupon rate times face value pays $60 a year no matter what the bond trades for.
A price below face value has to deliver a yield above the coupon rate, since the buyer also collects the difference at maturity.
How to calculate Yield to Maturity, step by step
- 1Write down the four inputs. Face value F, the annual coupon payment C, years to maturity n, and the current market price P.
- 2Find the annual coupon payment. C = coupon rate × face value. The coupon rate is fixed at issue and never moves with the market price.
- 3Spread the price gain or loss over the years left. (F − P) ÷ n is the yearly share of the discount you collect at maturity, and it turns negative for a premium bond.
- 4Divide by the average of price and face value. Approximate YTM = [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2], which uses the average amount of money tied up in the bond.
- 5Check the answer against the coupon rate. A bond priced below face value must have a YTM above its coupon rate, and a premium bond must have a YTM below it.
Worked example: Yield to Maturity
A bond has a face value of $1,000, a 6% coupon rate, 5 years to maturity, and a current price of $920.15. The annual coupon = 0.06 × 1,000 = $60, so the current yield = 60 ÷ 920.15 = 6.52%. The approximation gives [60 + (1,000 − 920.15) ÷ 5] ÷ [(1,000 + 920.15) ÷ 2] = 75.97 ÷ 960.075 = 7.91%. Discounting each payment exactly gives 8%, about 0.09 points higher. Both sit above the 6% coupon rate, which is what a discount price requires.
Yield to Maturity questions
Why do bond prices and yields move in opposite directions?
The coupons and the face value are fixed once the bond is issued, so paying less for that same stream of payments raises the return you earn, and paying more lowers it.
What is the difference between current yield and yield to maturity?
Current yield is only the coupon divided by the price. Yield to maturity also counts the gain or loss between the price paid and the face value repaid at maturity, so it is the fuller measure of the return.
Why is the approximation formula not exact?
It averages the price and face value instead of discounting each payment by how long you wait for it. In the example above it lands about 0.09 percentage points below the exact yield.
What does it mean when YTM equals the coupon rate?
The bond is trading at par, so its price equals face value. There is no gain or loss waiting at maturity, which leaves the coupon as the whole return.
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