Solve for a bond's yield to maturity from market price, face value, coupon rate, and years remaining, then compare YTM with current yield and coupon rate.
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Bond Analytics
Yield to maturity (YTM) is the total annualised return an investor earns by holding a bond to maturity, assuming all coupon payments are reinvested at the same rate.
YTM is the internal rate of return of a bond's cash flows. Unlike the coupon rate or current yield, YTM captures coupon income, price appreciation or depreciation, and the reinvestment assumption.
For an investor comparing bonds with different coupons, maturities, and prices, YTM provides an apples-to-apples yield comparison.
There is no closed-form solution for YTM. The yield is the discount rate r that equates the present value of all future cash flows to the current market price.
P = Σ [C / (1 + r)^t] + F / (1 + r)^n
Where P = market price, C = periodic coupon, F = face value, r = periodic yield, n = total periods.
At par, all three yields are equal. At a discount, YTM > current yield > coupon rate. At a premium, the reverse.
A 1,000 face value bond, 5% coupon semi-annual, 10 years, priced at 950. The annualised YTM is approximately 5.58%.
Assumes all coupons are reinvested at the YTM rate. Does not model call provisions, credit risk, or tax effects.
Frequently asked questions
The bond pricing equation is a polynomial with no closed-form solution. Newton-Raphson converges in 10–20 iterations.
Only if held to maturity and all coupons reinvested at the YTM rate.
Prices and yields move inversely. Falling prices mean higher YTM.
More frequent payments change the compounding, slightly altering YTM for the same coupon rate and price.
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