Bond Equivalent Yield Calculator

1. What is the Bond Equivalent Yield Calculator?

Definition: This calculator computes the bond equivalent yield ($ BEY $) and discount ($ D $), representing the annualized yield of a discount bond based on its price, face value, and time to maturity.

Purpose: Helps investors compare the yield of short-term bonds or Treasury bills with other investments by annualizing the return on a 365-day basis.

2. How Does the Calculator Work?

The calculator follows a four-step process to compute the results:

Formulas:

$ D = FV - BP $

$ BEY = \frac{D}{BP} \times \frac{365}{DTM} \times 100 $

Where:

$ BEY $: Bond Equivalent Yield (%)
$ D $: Discount (dollars)
$ FV $: Face Value (dollars)
$ BP $: Bond Price (dollars)
$ DTM $: Days to Maturity

Steps:

Step 1: Determine bond price. Use the market price of the bond ($ BP $).
Step 2: Determine face value. Use the bond’s principal amount at maturity ($ FV $).
Step 3: Determine days to maturity. Use the number of days until the bond matures ($ DTM $).
Step 4: Compute discount and BEY. Calculate $ D = FV - BP $ and apply $ BEY = \frac{D}{BP} \times \frac{365}{DTM} \times 100 $.

3. Importance of Bond Equivalent Yield

Calculating the BEY and discount is crucial for:

Yield Comparison: $ BEY $ standardizes yields for bonds with maturities less than a year, enabling comparison with other investments.
Investment Decisions: $ D $ shows the potential gain at maturity, aiding in assessing bond profitability.
Short-Term Bonds: Useful for evaluating Treasury bills or zero-coupon bonds with short maturities.

4. Using the Calculator

Example (Bond A): $ BP = \$980 $, $ FV = \$1,000 $, $ DTM = 300 $:

Step 1: $ BP = \$980 $.
Step 2: $ FV = \$1,000 $.
Step 3: $ DTM = 300 $.
Step 4:
- $ D = 1,000 - 980 = \$20 $.
- $ BEY = \frac{20}{980} \times \frac{365}{300} \times 100 = 2.48\% $.
Results: $ D = \$20 $, $ BEY = 2.48\% $.

A BEY of 2.48% indicates the annualized return for a bond maturing in 300 days, purchased at a discount.

Example 2: $ BP = \$950 $, $ FV = \$1,000 $, $ DTM = 180 $:

Step 1: $ BP = \$950 $.
Step 2: $ FV = \$1,000 $.
Step 3: $ DTM = 180 $.
Step 4:
- $ D = 1,000 - 950 = \$50 $.
- $ BEY = \frac{50}{950} \times \frac{365}{180} \times 100 = 10.67\% $.
Results: $ D = \$50 $, $ BEY = 10.67\% $.

A higher BEY of 10.67% reflects a larger discount and shorter maturity period.

Example 3: $ BP = \$990 $, $ FV = \$1,000 $, $ DTM = 360 $:

Step 1: $ BP = \$990 $.
Step 2: $ FV = \$1,000 $.
Step 3: $ DTM = 360 $.
Step 4:
- $ D = 1,000 - 990 = \$10 $.
- $ BEY = \frac{10}{990} \times \frac{365}{360} \times 100 = 1.02\% $.
Results: $ D = \$10 $, $ BEY = 1.02\% $.

A low BEY of 1.02% indicates a small discount and near-full-year maturity.

5. Frequently Asked Questions (FAQ)

Q: Why is BEY useful for short-term bonds?
A: BEY annualizes the yield of bonds with maturities less than a year, allowing comparison with other investments on a 365-day basis

Q: What does the discount represent?
A: $ D $ is the difference between face value and bond price, reflecting the investor’s potential gain at maturity if held to term.

Q: Can BEY be negative?
A: No, since $ FV \geq BP $ and $ DTM > 0 $, BEY is typically positive. Negative BEY would imply invalid inputs (e.g., $ BP > FV $).