Bond Yield to Maturity Calculator – Price, Yield, Duration and Calls
Yield to maturity (YTM) answers one question: if I buy this bond at this price and hold it until it matures, what annual return do I earn? This calculator solves for that yield from a price, or for the price that delivers a yield you want. Around that number it shows the current yield, accrued interest, yield to call, duration, convexity and how much of the return depends on reinvesting coupons.
The YTM equation
Price = Σ C ÷ (1 + y/f)^k + Redemption ÷ (1 + y/f)^n
Take a 10-year bond with a 1,000 face value and a 5% coupon paid twice a year: twenty coupons of 25 and 1,000 at the end. At a price of 950 the one rate that makes the discounted payments add up to 950 is 5.662%. The cash-flow chart shows it: the present value of the coupons (377.82) plus the present value of the face value (572.18) is exactly 950.00. Their PV-weighted balance point, the Macaulay duration, is 7.93 years.
The price–yield seesaw and convexity
When yields rise, prices fall. The modified duration of 7.71 says a 1% rise costs about 7.71% of the price, or 73.24 on this bond. The actual fall is only 69.91, while a 1% drop in yield adds 76.80 rather than 73.24. The curve bends away from the straight duration line, and that bend is convexity. It works in the holder's favour in both directions.
Premium, discount and par
A bond priced below its redemption value trades at a discount, and its yields line up as coupon rate < current yield < YTM (5.000% < 5.263% < 5.662% above). A premium bond reverses the order, because the price falls back to par by maturity. At par, all three are equal.
The reinvestment assumption
YTM quietly assumes every coupon is reinvested at the YTM itself. In the example, 160.32 of the 710.32 total return, or 22.6%, is interest on interest. Reinvest at 3% instead and that falls to 78.09, and the realized yield drops to 5.140%. Zero-coupon bonds have no coupons to reinvest, so their YTM is locked in.
Clean price, dirty price and accrued interest
Between coupon dates the seller has earned part of the next coupon. Bonds are quoted clean, and the buyer pays the clean price plus accrued interest. In Excel's YIELD help example (settlement 15 February 2008, maturity 15 November 2016, 5.75%, 30/360), 90 of 180 days have accrued, so the accrued interest is 1.4375 per 100 and the dirty price is 96.48037. The yield is 6.500%, and the dates mode reproduces spreadsheet YIELD, PRICE, DURATION and COUPDAYBS across the five day-count bases.
Callable bonds and yield to worst
An issuer can redeem a callable bond early, usually when rates have fallen. Each yield to call treats a call date as maturity and the call price as redemption. A 7% 10-year bond at 1,080 yields 5.928% to maturity, but only 4.736% if it is called in three years at 102. The yield to worst is the lowest of these.
Bond-equivalent yield, effective yield and XIRR
YTM is quoted as a bond-equivalent yield: the periodic rate times the number of coupons a year. Compounding it gives the effective annual yield, 5.742% for the example. An XIRR on the same dated flows compounds annually, so it lands near the effective yield, not the quoted YTM. For present values at a rate you already know, use the Present Value Calculator; for any irregular cash-flow series, use the IRR Calculator.