Bond Equivalent Yield Calculator
Yield Comparison
What Is a Bond Equivalent Yield Calculator?
A Bond Equivalent Yield Calculator converts the return on a short-term discount security into an annual percentage based on its purchase price and a 365-day year. This makes the return easier to compare with yields quoted for traditional interest-bearing bonds.
The calculator is useful for securities that are purchased below face value and pay their full face value at maturity. Common examples include Treasury bills and other discount notes. Instead of receiving regular coupon payments, the investor earns the difference between the purchase price and the amount received at maturity.
This tool also calculates the investment banker’s discount yield. That measure uses the security’s face value as its return basis and assumes a 360-day year. Showing both results helps users understand why two yield quotations for the same investment may differ.
The results are annualized estimates. They help with comparison, but they do not show the exact dollar return after taxes, transaction costs, market price changes, or other investment expenses.
How the Bond Equivalent Yield Formula Works
The calculator first finds the investment discount by subtracting the purchase price from the face value. It then divides that discount by the actual amount invested and annualizes the result over a 365-day year.
In this formula:
- BEY is the bond equivalent yield as an annual percentage.
- F is the face value, also called par value.
- P is the price paid for the investment.
- D is the number of days remaining until maturity.
The calculator also displays the investment banker’s discount yield using this formula:
Worked Example
Assume a short-term note has a $10,000 face value, costs $9,800, and matures in 180 days.
- Find the discount: $10,000 − $9,800 = $200.
- Divide the discount by the purchase price: $200 ÷ $9,800 = 0.020408.
- Annualize the return: 0.020408 × 365 ÷ 180 × 100 = 4.138%.
- For discount yield, calculate $200 ÷ $10,000 × 360 ÷ 180 × 100 = 4.000%.
The calculator therefore displays a bond equivalent yield of 4.138% and an investment banker’s discount yield of 4.000%. Both percentages are formatted to three decimal places.
The formulas use simple annualization rather than compounding. The calculator also assumes that the face value, price, and maturity period are entered correctly. It does not require the purchase price to be below face value. A price above face value produces a negative yield, while an equal price and face value produce a zero yield.
How to Use the Bond Equivalent Yield Calculator: Step by Step
- Enter the investment’s Face Value (Par Value) in U.S. dollars. This is the amount the security is expected to pay at maturity.
- Enter the Purchase Price in U.S. dollars. Use the amount paid for the security, not its face value.
- Enter the number of Days to Maturity. This is the time from the purchase or measurement date until the security matures.
- Select Calculate to display the yield comparison. All three entries must be greater than zero for results to appear.
- Review the bond equivalent yield, investment banker’s discount yield, and plain-English summary.
- Select Reset to clear the input fields and hide the previous results.
The main result is the Bond Equivalent Yield. It expresses the discount return as an annual percentage based on the money actually invested and a 365-day year. The second result uses face value and a 360-day year. For a typical security purchased below face value, the BEY will usually be higher than the discount yield.
How to Read Your Yield Comparison
Bond equivalent yield and discount yield describe the same investment from different calculation bases. Neither result changes the cash amount earned. The difference comes from how the return is measured and annualized.
| Feature | Bond Equivalent Yield | Investment Banker’s Discount Yield |
|---|---|---|
| Return basis | Actual purchase price | Face value |
| Annualization period | 365 days | 360 days |
| Main purpose | Comparison with interest-bearing bonds | Traditional quotation for discount securities |
| Displayed format | Annual percentage | Annual percentage |
Comparing Short-Term Securities
BEY can help compare two discount securities with different prices or maturity periods. It can also make a Treasury bill quotation easier to compare with a bond yield that uses the amount invested as its base. The comparison is most useful when the securities have similar risk, liquidity, and tax treatment.
Understanding the Limitations
The calculator does not include compounding, coupon payments, reinvestment income, brokerage charges, bid-ask spreads, taxes, inflation, or changes in market value. It also does not assess credit risk or determine whether an investment is suitable for you.
Results are estimates based only on the three values entered. Actual returns may vary because of transaction timing, fees, taxes, settlement rules, market conditions, and the security’s payment terms. Use the result as a comparison tool, not as financial, tax, or investment advice.
Frequently Asked Questions
What is bond equivalent yield?
Bond equivalent yield is an annualized measure of a short-term discount investment’s return. It divides the discount earned by the purchase price and scales the result to a 365-day year. This approach makes the yield easier to compare with returns quoted for traditional interest-bearing bonds.
How do I calculate bond equivalent yield?
Subtract the purchase price from the face value. Divide that difference by the purchase price. Then multiply by 365 divided by the days to maturity and convert the result to a percentage. This calculator performs those steps automatically using the values you enter.
What is the difference between BEY and discount yield?
BEY divides the investment gain by the purchase price and uses a 365-day year. Discount yield divides the gain by face value and uses a 360-day year. Because the formulas use different bases, they can produce different annual percentages for the same security.
Why is bond equivalent yield usually higher than discount yield?
For a security purchased below face value, BEY usually has a smaller denominator because it uses the purchase price instead of face value. It also uses 365 days rather than 360. Both differences tend to make BEY higher, although unusual inputs can produce different results.
Can bond equivalent yield be negative?
Yes. The calculator produces a negative yield when the purchase price is greater than the face value. In that case, the formula treats the difference as a loss rather than a discount. The tool does not block this input or require the purchase price to be below par.
Does bond equivalent yield include compounding?
No. This calculator uses simple annualization. It scales the return according to the number of days to maturity but does not assume that earnings are reinvested during the year. It therefore should not be treated as an effective annual yield or compounded annual return.
How accurate is the Bond Equivalent Yield Calculator?
The calculator accurately applies the formulas shown on this page to the values entered. Its usefulness depends on correct face value, purchase price, and maturity information. It does not account for fees, taxes, settlement timing, compounding, market changes, or other factors that can affect realized returns.