How this instrument works
Yield to maturity condenses everything a bond promises — its coupon, today's price, and a payoff years away — into one blended annual rate, on the assumption that each coupon gets put back to work at that identical rate until the bond retires. Because two bonds can share a coupon yet trade at different prices, this single number is what actually lets a $950 bond and a $1,050 bond be lined up against one another on equal footing.
The people who lean on this shortcut hardest are corporate treasury teams parking a company's idle cash in short-dated bonds rather than a checking account: an analyst juggling several broker quotes in one sitting needs a number fast enough to answer yes or no before the quote expires, not a model that hunts for an exact discount rate. Leveling the difference between price and face into equal yearly installments, rather than letting it compound, is the trick that keeps this arithmetic within reach of a phone call.
What comes out is a straight-line average, not a compounded rate — weighing it directly against a bank's compounded annual percentage yield mixes two different kinds of arithmetic even when the two numbers land close together. The shortcut also holds up best near face value: paper trading within a few cents of $1,000 tracks the exact, solved yield closely, while a bond priced far under face — the kind common among troubled issuers — can pull noticeably away from the true rate.
- Start with Annual coupon payment, $ — the flat dollar sum the issuer sends every year, unrelated to the percentage printed on the bond.
- Add Face value, $ — the redemption amount due at payoff, $1,000 for most corporate issues.
- Add Current bond price, $ — what the secondary market is actually charging for the bond right now.
- Fill in Years to maturity — the count of years still owed before payoff arrives.
- The sheet returns Approximate yield to maturity, % — the blended rate those four numbers combine into.
Worked example — a bond bought below face value
A treasury analyst gets a quote on a bond carrying a $1,000 face value and a $50 annual coupon, priced at $950 with 10 years left to run. Because the price sits under face value, the coupon by itself undersells what the bond will actually hand back. Leveling the $50 shortfall over the 10 remaining years adds $5 to each year's return, for a combined $55 annual figure. Weighing that against the midpoint between price and face — $950 and $1,000 average out to $975 — and converting to a percentage yields 5.64%, exactly what this sheet returns for that quote.
The 5.64% clears the bond's 5% coupon rate because the discount is contributing return on top of the coupon: $950 buys $1,000 worth of face value, and that $50 gap gets credited back by payoff. Reprice the identical bond at $1,050 instead and the approximate yield drops to roughly 4.39%, under the coupon rate — the price actually paid moves the outcome as much as the coupon itself does.
Questions
Does this yield already account for compounding?
No. It levels the difference between price and face into equal yearly slices, the way simple interest works, rather than compounding it the way a bank quotes an annual percentage yield. Weighing this figure directly against a CD's compounded APY lines up two different kinds of return — close in size for short, near-par bonds, but not the same math underneath.
Why do two bonds with the same coupon rate show different yields?
Because yield to maturity turns on the price paid, not the rate printed on the certificate. Two bonds can carry an identical 5% coupon, yet one bought at $950 returns roughly 5.64% while one bought at $1,050 returns roughly 4.39% — the discount or premium to face value carries as much weight in the formula as the coupon itself.
Why isn't this the exact yield a bond-pricing terminal would show?
Because this is a shortcut, not a solver. The exact yield is whichever single discount rate makes a bond's remaining cash flows — every coupon plus the face repayment — worth exactly today's price once each is discounted back; pricing software finds that rate by trial and error. This formula skips the trial and error by leveling the price gap across the remaining years instead of compounding it, tracking the exact rate closely near face value and drifting further away the farther a bond sits from par.
How far below face value does the approximation stop being reliable?
There is no fixed cutoff, but the gap widens with distance from par and with years remaining. Investment-grade bonds trading within a few cents of $1,000 face typically land within a few hundredths of a percentage point of the exact, solved yield. A bond trading at 60 or 70 cents on the dollar, common among troubled issuers, can show a noticeably wider gap, because leveling a large discount in a straight line departs further from compounding it.
Does the math change if the bond gets called before maturity?
Yes, and this sheet will not catch that on its own. When an issuer calls a bond early, the coupon checks end and the face amount lands on the call date, not the printed maturity date, so plugging in the original maturity stretches the price gap over too many years and skews the result. Swap in years to the call date whenever an issuer looks likely to redeem the bond ahead of schedule.
What does this figure leave out that a realized return would include?
Trading costs, accrued interest owed to the seller at purchase, taxes on coupon income, and the assumption that each coupon goes back to work at this identical rate the moment it lands. Real accounts rarely reinvest at a constant rate, so what an investor actually realizes over the holding period commonly differs from the figure this formula produces on day one.
References
- SEC Investor.gov — Bonds or fixed income products
- Federal Reserve — Selected Interest Rates (H.15 release)
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.