Bond Equivalent Yield Calculator
Enter the face value, purchase price, and days to maturity of a discount or zero-coupon security to get its Bond Equivalent Yield (BEY). BEY annualizes the holding-period return on a 365-day basis so you can compare T-bills, commercial paper, and bankers acceptances directly against coupon-paying bonds. The calculator also converts a bank discount rate to BEY, shows the effective annual yield (compounded), and walks through every step of the math with your actual numbers.
What is Bond Equivalent Yield (BEY)?
Bond Equivalent Yield (BEY) is an annualized yield measure that puts discount securities - Treasury bills, commercial paper, bankers acceptances, and zero-coupon bonds - on the same footing as coupon-paying bonds. Coupon bonds are quoted on a 365-day year using the purchase price as the base. Discount securities are traditionally quoted using a 360-day year and face value as the base. Without adjusting for both differences, comparing the two is like comparing miles and kilometres without converting. BEY makes the conversion by dividing the profit (face value minus price) by the purchase price, then scaling that ratio by 365 divided by the number of days to maturity: BEY = ((Face Value - Price) / Price) x (365 / Days). The result is always higher than the quoted discount rate because the denominator is the price you paid (smaller than face value) and the year has 365 days rather than 360.
BEY vs. discount rate vs. effective annual yield
Three yield measures are commonly quoted for short-term discount securities, and mixing them up leads to costly comparisons:
- Discount rate (DR): quoted on a 360-day year and on face value as the base. Always understates the true return.
- Bond Equivalent Yield (BEY): uses a 365-day year and purchase price as the base. The standard for apples-to-apples comparison with coupon bonds. Formula: BEY = (365 x DR) / (360 - DR x Days).
- Effective Annual Yield (EAY): compounds the holding-period return to a full year: EAY = (1 + HPR)^(365/Days) - 1. For maturities under a year, EAY is slightly above BEY because it accounts for the reinvestment of the profit at the same rate over the remainder of the year. For a 182-day bill, the difference is small but non-trivial at higher yield levels.
When a broker quotes a Treasury bill at a discount rate of 4.00% for 182 days, the BEY is approximately 4.10% and the EAY is about 4.14% - three different numbers for the same security.
How to use this calculator
Select your input mode from the dropdown at the top:
- Price and face value: enter the face (par) value, the price you paid, and the number of days to maturity. The calculator returns the BEY, the effective annual yield, the holding-period return, and the dollar profit at maturity.
- Discount rate to BEY: enter the bank-quoted discount rate (on a 360-day basis) and the days to maturity. The calculator converts it to BEY using the standard conversion formula.
Results update as you type. The "Show your work" panel beneath the result card traces every arithmetic step with your actual numbers, so you can verify the calculation or walk through it with a client or student.
Real-world applications
BEY comes up in several practical contexts:
- Treasury bill auctions: the U.S. Treasury publishes auction results in both discount rate and BEY terms. When evaluating whether a T-bill yield beats a money-market fund or savings account, always compare BEY to BEY.
- Commercial paper: corporations issue short-term paper at a discount. BEY lets a treasurer compare the cost of commercial paper against other short-term borrowing on a consistent basis.
- Zero-coupon bonds: a multi-year zero-coupon bond has no periodic coupons, so its return is entirely in the difference between price and face value. BEY annualizes that return for comparison against coupon bonds.
- CFA and financial modeling: the BEY convention is tested on the CFA Level 1 exam and is standard in fixed-income models. Knowing when to use BEY versus EAY versus yield to maturity is a core competency in bond analysis.
Yield quality benchmarks for short-term discount securities
| BEY range | Category | Typical environment |
|---|---|---|
| Below 1% | Very low yield | Near-zero rate policy (e.g. 2009-2015, 2020-2021) |
| 1% - 3% | Low yield | Accommodative monetary policy |
| 3% - 5% | Moderate yield | Neutral to mildly restrictive policy |
| 5% - 8% | Attractive yield | Restrictive policy or elevated inflation |
| Above 8% | High yield | Very tight policy or significant credit risk |
Common reference ranges used by analysts to characterize the yield environment for T-bills and similar instruments.
Frequently asked questions
What is the bond equivalent yield formula?
BEY = ((Face Value - Purchase Price) / Purchase Price) x (365 / Days to Maturity). You divide the profit by what you paid, then multiply by 365 divided by the holding period in days. This annualizes the return on a 365-day basis so it is directly comparable to coupon bond yields.
Why does BEY use 365 days instead of 360?
The 360-day year is a banking convention used for discount rates and many commercial loans - it simplifies hand calculations with round numbers. BEY switches to 365 days to match the actual calendar year convention used by coupon-paying bonds. The difference adds roughly 1.4% to the annualized yield (365/360 - 1), which is not trivial on a large portfolio.
Is BEY the same as yield to maturity (YTM)?
No. Yield to maturity accounts for all future cash flows - coupons and the return of principal - and solves for the discount rate that equates the present value of those flows to the current price. BEY only looks at the discount (face value minus price) and annualizes it linearly. For a zero-coupon bond, BEY and YTM are related but not identical because YTM compounds while BEY does not. Use YTM when comparing bonds with coupon payments; use BEY when comparing short-term discount instruments to coupon bonds.
How do I convert a bank discount rate to BEY?
Use the formula: BEY = (365 x DR) / (360 - DR x Days), where DR is the discount rate as a decimal and Days is the number of days to maturity. For example, a 4% discount rate on a 182-day T-bill converts to BEY = (365 x 0.04) / (360 - 0.04 x 182) = 14.6 / 352.72 = approximately 4.14%. The "Discount rate to BEY" mode in this calculator does this automatically.
What is a good BEY for a Treasury bill?
There is no single answer - T-bill yields reflect the federal funds rate target and overall monetary policy, not the quality of any individual bill (all T-bills are backed by the U.S. government). Historically, 3-month T-bill BEYs have ranged from near 0% in crisis and easy-money periods to above 5% during restrictive cycles. A BEY above the current inflation rate is generally considered a positive real yield; below it, you are losing purchasing power in real terms.
When should I use effective annual yield instead of BEY?
Use effective annual yield (EAY) when you want to account for the compounding effect of reinvesting the proceeds at the same rate for the rest of the year. EAY = (1 + HPR)^(365/Days) - 1. For a 91-day bill with a BEY of 5%, the EAY is about 5.12% because 365/91 is slightly above 4. For very short maturities (under 30 days), the gap between BEY and EAY can be more noticeable. For the purpose of comparing a T-bill to a one-year bond, BEY is the conventional choice.
Can BEY be used for coupon-paying bonds?
BEY was originally defined for semi-annual coupon bonds as twice the semi-annual yield - so a bond that pays 2.5% every six months has a BEY of 5%. For discount securities without coupons, the formula above applies. Mixing the two conventions (applying the discount formula to a coupon bond or vice versa) will give incorrect results. This calculator handles only the discount-security version of BEY.