Bond coupon and yield: the same payment at different prices
Compare coupon rate, current yield and the yield of one promised payment exactly one year away.
A coupon describes a cash payment under a bond’s terms. Yield also depends on purchase price and payment timing. Rather than hide a multi-year calculation behind an approximation, use one hypothetical payment exactly one year from valuation.
Define the hypothetical bond
Face value is 1000 and the fixed final coupon is 60. Under the example’s terms, coupon 60 and redemption 1000 both arrive after one year: total cash flow 1060. There are no interim coupons. Amounts use one fictional currency; the purchase price is all-in and accrued interest is zero at the valuation boundary.
Assume no default, early redemption, taxes or fees. These are model conditions, not facts about a real issuer. Coupon rate 60/1000=6% uses face value and does not change when we choose a different purchase price.
Two denominators answer different questions
At price 980, current yield is 60/980=3/49≈6.122449%. It compares annual coupon cash with price but excludes the difference between purchase price and redemption value. For one promised payment after a year, solve 980=1060/(1+y): y=4/49≈8.163265%.
At price 1020, current yield is 60/1020=1/17≈5.882353%, while the whole-payment yield is 1060/1020−1=2/51≈3.921569%. The coupon is unchanged; buying above par reduces the redemption result. These are hypothetical calculations, not current market offers.
Our own teaching example; all figures are hypothetical.
60/1000 = 6%; 60/980 = 3/49; 1060/980 − 1 = 4/49; 60/1020 = 1/17; 1060/1020 − 1 = 2/51
| Measure | Ratio | Percentage |
|---|---|---|
| Coupon rate | 60/1000 | 6% |
| Current yield at 980 | 60/980 | 3/49 ≈ 6.122449% |
| Whole payment at 980 | 80/980 | 4/49 ≈ 8.163265% |
| Current yield at 1020 | 60/1020 | 1/17 ≈ 5.882353% |
| Whole payment at 1020 | 40/1020 | 2/51 ≈ 3.921569% |
Know when the shortcut stops applying
With several coupons or several years to maturity, each cash flow and its date must be included. The single-payment expression is not a general multi-year yield-to-maturity, or YTM, formula. Reinvesting interim coupons can change the realized outcome.
Record full price, coupon schedule, maturity and assumptions in an external table. Promised cash flows do not guarantee actual payment; taxes and costs are excluded here. Elliott neither calculates bond yields nor promises bond quotes or bond screening.
At an all-in price of 1000 and the same 1060 payment after exactly one year, do current yield and whole-payment yield coincide?
Yes, both are 6%: 60/1000 and 1060/1000−1. Equality follows from buying at par and this single-payment setup, not from a rule applying to every bond.
Sources
Sources checked: 2026-10-21
This material and its translations were prepared with AI assistance. Educational calculations were checked programmatically. Sources explain concepts; examples and files were created for this article.
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