Yield to Maturity (YTM)
The internal rate of return that equates the present value of a bond's remaining cash flows (coupons + face) to its current market price. Solved iteratively because no closed-form exists for a coupon bond.
When to use: Use as the primary yield measure for any bond held to maturity. YTM is what gets quoted in screens and comparison tables; it folds coupon income and pull-to-par capital gain/loss into a single annualized rate.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| YTM | Yield to Maturity | IRR of the bond if held to maturity, expressed as a nominal annual rate compounded m times per year | % |
| P | Bond Price | Market price of the bond per face value unit | $ |
| F | Face Value | Par value paid at maturity | $ |
| CR | Coupon Rate | Annual coupon rate as a decimal (e.g. 0.05 for 5%) | % |
| N | Years to Maturity | Years remaining until the bond matures | years |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: Discount Bond YTM
10-year, 5% coupon, semi-annual, $1,000 face, trading at $925.61.
Given
Step-by-Step
The bond's YTM is 6%, exceeding both the 5% coupon and the 5.4% current yield. The extra ~60bps over current yield comes from the $74 pull-to-par capital gain over 10 years.
Example 2: Premium Bond YTM
5-year, 6% coupon, semi-annual, $1,000 face, trading at $1,043.76.
Given
Step-by-Step
Premium price ($1,044 > $1,000) implies YTM (5%) below coupon (6%). The $44 pull-to-par capital loss over 5 years drags total return below the coupon income.
Frequently Asked Questions
Because the bond price equation is a high-degree polynomial in y — there is no algebraic solution for the yield given a target price. A bisection or Newton-Raphson search converges quickly to the unique positive yield.
Yes — implicitly. The IRR convention treats every cash flow as discounted at the same rate, which is mathematically equivalent to assuming reinvestment at that rate. Realized return depends on actual reinvestment rates, which usually differ.
On a nominal-annual-rate basis with the bond's natural compounding frequency (typically semi-annual for US bonds). A 6% YTM on a semi-annual bond means 3% per six months, not (1.06)^0.5 − 1.
For callable bonds (use YTC or YTW), for bonds with embedded options, or when reinvestment rates diverge sharply from current yields. It also assumes hold-to-maturity — early sale realizes a different rate of return.