# Bond Equivalent Yield: Formula & Examples

Instructor: Morgan Gannarelli
The bond equivalent yield is used to determine the annual yield on a discount bond. In this lesson we will discuss its formula, examples, and making decisions from the results of the bond equivalent yield.

## Bond Equivalent Yield

What type of investment is right for you? Which one will yield the highest return? The bond equivalent yield (BEY) will help you decide, as it is used to determine the annual yield on a discount bond.

It's just as it sounds, you are finding an 'equivalent' yield between two or more investments. Let's remember that a discount bond is a bond that is issued for less than it's par (face) value in the secondary market. This also means it has a lower interest rate than the current market rate, which is how it is sold at a lower price. These are usually paid semiannually.

If you have a long-term bond and want to compare it to a short-term investment, you are going to need to calculate the bond equivalent yield first. Once you calculate the annual yield on the discount bond you can perform an analysis and compare to 'fixed-income' securities that do not make annual payments.

There are spreadsheets with a built-in formula to calculate the bond equivalent yield, but here we will discuss how to do it without a spreadsheet.

## Formula

The bond equivalent yield (BEY) is calculated by first taking the face value or par value (the amount paid at maturity), subtracting the price (the amount originally paid), and then dividing that amount by the price. Next, divide 365 (days) by the days to maturity. Multiply that with the first part of the calculation, then multiply it all by 100 to get a percentage.

Bond Equivalent Yield = ((Par Value - Price) / Price) * (365 / d) * 100

• Where d is days to maturity

## Examples

Let's try out some examples.

Example 1: You want to calculate the bond equivalent yield for a bond with a par value of \$2,000 that was purchased at a discounted price of \$1,900 and has 100 days to maturity.

• ((\$2,000 - \$1,900) / \$1,900) * (365 / 100) * 100
• (\$100 / \$1,900) * 3.65 * 100
• 0.0526 * 3.65 * 100
• = 19.21%

Bond equivalent yield = 19.21%

Ready for the next example? You got this!

Example 2:

Let's calculate the BEY for a bond with a par value of \$1,000 that was purchased at a discounted price of \$980, and has 75 days to maturity.

• ((\$1,000 - \$980) / \$980) * (365 / 75) * 100
• (\$20 /\$980) * 4.87 * 100
• 0.0204 * 4.87 * 100
• = 9.93%

Bond equivalent yield = 9.93%

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