What it means
A Treasury bill pays no interest along the way. You buy it below face value and receive the full face value at maturity, and the traditional quote, called the bank discount rate, expresses that gain as a percentage of face value using a 360-day year.
Both of those conventions understate what the investor actually earns. You never invest the face value, because you paid the lower purchase price, and a calendar year has 365 days rather than 360, so the quoted discount rate always comes out below the real return.
The coupon equivalent rate fixes both problems: it divides the gain by the price actually paid and annualises it over 365 days. That puts a bill on the same footing as a coupon-paying bond or a term deposit, which is exactly the comparison a treasurer needs when deciding where to place surplus cash.
Corporate treasury teams meet this every time they weigh a bill against a money market fund or a fixed deposit. Comparing on the quoted discount rate alone systematically makes bills look worse than they are, so the comparison should always be made on a coupon equivalent basis.
One nuance is worth knowing: for bills with more than about six months to maturity, the official calculation uses a longer formula that allows for semi-annual compounding. The simple version below is accurate for the short maturities most corporate treasurers actually hold.
In practice
Real-world examples.
Example
A treasurer has $5,000,000 to place for six months and is choosing between a Treasury bill quoted at a 4.95% discount rate and a bank deposit offering 5.05%. Converting the bill to its coupon equivalent rate of 5.14% reverses the ranking, and the bill is chosen.
Example
A finance director reviewing a cash management report notices that bill yields and deposit rates are listed side by side on different conventions. She asks for every short-term instrument to be shown on a coupon equivalent basis so the comparison is like for like.
Example
An investment committee benchmarks its short-term portfolio against a bill index. Because the index is published on a coupon equivalent basis, the internal reporting is restated from discount rates, removing an apparent underperformance of roughly 20 basis points that was purely a convention difference.
Formula
Calculation
Coupon equivalent rate = ((Face value - Purchase price) / Purchase price) x (365 / days to maturity)
Bank discount rate = ((Face value - Purchase price) / Face value) x (360 / days to maturity)
A treasurer buys a Treasury bill with a face value of $100,000 for $97,500, with 182 days remaining to maturity.
Gain at maturity = 100,000 - 97,500 = $2,500
Return on the amount invested = 2,500 / 97,500 = 0.025641, or 2.5641%
Annualising over 365 days = 0.025641 x (365 / 182) = 0.025641 x 2.005495 = 0.051423
The coupon equivalent rate is therefore 5.14%.
By comparison, the bank discount rate is (2,500 / 100,000) x (360 / 182) = 0.025 x 1.978022 = 0.049451, or 4.95%. The bill genuinely yields about 20 basis points more than its quoted rate suggests, which is enough to change the answer when it is set against a deposit paying 5.05%.Case study
Seen in the real world.
This is an illustrative example featuring a fictional company. Bramfield Logistics held around $40,000,000 of surplus cash and ran a rolling six-month ladder of deposits. Its treasury policy compared instruments on quoted rates, so when Treasury bills were quoted at 4.95% and the company's bank offered 5.05% on a six-month deposit, the deposit won every time.
A new assistant treasurer recalculated a $100,000 bill bought at $97,500 with 182 days to run. The gain of $2,500 on a $97,500 investment, annualised over 365 days, gave a coupon equivalent rate of 5.14%, comfortably ahead of the deposit rather than behind it.
Applied across a $40,000,000 book, the difference between 5.05% and 5.14% is roughly $36,000 over a year, and the bills also offered daily liquidity that the deposit did not. Bramfield rewrote its treasury policy to require every short-term rate to be quoted on a coupon equivalent basis before any placement decision is taken.
Watch out
Common mistakes.
- Comparing a quoted bank discount rate directly with a deposit rate or bond yield, which understates the bill and leads to the wrong decision.
- Dividing the gain by face value rather than by the price actually paid, which is the single biggest source of the understatement.
- Annualising over 360 days out of habit when the coupon equivalent convention requires 365.
Questions
People also ask.
Is the coupon equivalent rate the same as the bond equivalent yield?
Yes. The two names describe the same calculation, and official Treasury tables often label it the investment rate.
Why is the bank discount rate still used at all?
It is a long-standing market quoting convention that makes bills easy to price and trade, not a measure of investor return, which is why the coupon equivalent rate exists alongside it.
Does the coupon equivalent rate account for compounding?
The simple formula does not, which is fine for maturities under about six months; beyond that the official calculation adds a semi-annual compounding adjustment.
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