How to Calculate Yield to Maturity Step by Step
Yield to maturity (YTM) is the discount rate that makes a conventional bond’s promised future cash flows equal its current dirty price, under specified settlement and compounding conventions. It is not necessarily the return an investor will realise, because reinvestment, default, taxes and early sale prices introduce uncertainty.
Understand the cash flows
A plain fixed-rate bond typically promises coupon payments at stated intervals and principal at maturity. Its price is the present value of these payments discounted using a rate consistent with payment frequency and day-count conventions. Bond pricing often distinguishes a quoted clean price from the dirty or full price, which includes accrued interest. Using a clean price in a formula intended for total settlement cash can give an inaccurate result.
The basic pricing equation
For N equal annual coupon periods, price P = C/(1+y) + C/(1+y)^2 + … + (C+F)/(1+y)^N, where C is annual coupon cash, F is principal, and y is an annual effective yield for the example. Real securities may pay semiannual coupons or use other conventions. When N exceeds one and the coupon differs from yield, the equation generally must be solved numerically; there is no universally exact shortcut formula.
Worked one-year example
Consider a fictional one-year bond with £100 principal, a £5 coupon at maturity and a current full price of £98. Its promised maturity payment is £105. Therefore 98 = 105/(1+y), so y = 105/98 − 1 = approximately 7.14%. The coupon rate is 5% of par, while the yield is higher because the purchase price is below £100. The example assumes no default or fees and a one-year interval.
Worked two-year example
Suppose a £100 par bond pays £4 in one year and £104 in two years and trades at a dirty price of £96. The yield satisfies 96 = 4/(1+y) + 104/(1+y)^2. By trying 6%, the price is about £96.33; the exact yield is slightly higher, approximately 6.19%. Solver results depend on the stated cash-flow timing and compounding assumptions. An approximate yield is useful for orientation but should not be mistaken for an exact market settlement calculation.
Why price and yield move oppositely
Holding fixed cash flows constant, a higher discount rate lowers their present value, and a lower rate increases it. This inverse relationship is especially significant for long-duration bonds. If market yields rise, an existing lower-coupon bond may trade below par. Conversely, a bond offering coupons above the market discount rate may trade at a premium. Changes in credit risk and liquidity can alter the relevant required yield as well.
YTM versus current yield
Current yield is annual coupon amount divided by the bond’s market price; it usually ignores the principal gain or loss on maturity. For the one-year example, £5/£98 ≈ 5.10% current yield versus approximately 7.14% YTM. Yield-to-call and yield-to-worst calculations may be more relevant where an issuer can repay before maturity. Comparing bonds without recognising embedded options can be misleading.
Why realised return can differ
An investor selling before maturity receives a market price that may change with rates, credit conditions and liquidity. Coupons received during the holding period may be reinvested at different yields, and default may change contractual cash flows. Transaction costs, withholding tax, inflation and exchange-rate conversion can further affect results. A mathematically correct YTM is a quotation of promised cash-flow discounting, not a guarantee of realised profit.
A calculation checklist
Identify settlement date, principal, coupon frequency, cash-flow dates, day-count basis, clean price, accrued interest and any call features. Convert quoted price to the full cash amount relevant for settlement. Use a numerical solver consistent with contract conventions and compare the output with independent market data. State assumptions clearly when using simplified educational formulas.
Bond yield calculations: one-year versus two-year examples
Hypothetical fixed-rate cash flows; yields assume the exact annual payment dates shown.
| Input | One-year bond | Two-year bond |
|---|---|---|
| Full purchase price | £98 | £96 |
| Principal redeemed | £100 | £100 |
| Coupon cash flow | £5 at year 1 | £4 at year 1; £4 at year 2 |
| Redemption cash | £105 at year 1 | £104 at year 2 (coupon plus principal) |
| Pricing equation | 98 = 105 ÷ (1+y) | 96 = 4 ÷ (1+y) + 104 ÷ (1+y)² |
| Approximate annual YTM | 7.14% | 6.19% |
The yields shown are effective annual discount rates for deliberately simplified cash-flow schedules. For an actual gilt or Treasury, do not use a made-up one-year day-count approximation: settlement date, accrued interest, coupon frequency and the exchange or market convention all affect an accurate result. A callable bond also requires analysis of possible early redemption dates. The two-year example generally needs a numerical root solver, because its cash flows occur on two different dates.
Frequently asked questions
Is YTM the same as coupon rate?
No. Coupon rate refers to contractual coupon as a percentage of face value, while YTM reflects price and remaining cash flows.
Does a bond trading at a discount have a higher yield?
For otherwise identical conventional fixed cash flows, discount prices imply yields above the coupon rate.
Is YTM a guaranteed return?
No. Credit, reinvestment and holding-period risks can affect realised results.
Sources and further reading
Continue learning with Bond Prices and Yields Explained in the Traders MBA Education library.