How to Calculate Bond Equivalent Yield (BEY): A Guide to Comparing Discounted Bonds and Maximizing Returns

What is Bond Equivalent Yield (BEY)?

Bond Equivalent Yield (BEY) is a financial metric used to analyze bond investments, particularly those sold at a discount. It measures the annualized yield on a bond, taking into account the return on investment from the purchase price to the face value at maturity. BEY is especially useful for zero-coupon bonds or any bond sold at a discount because it provides a standardized way to compare these investments.

It’s important to note that BEY does not equal yield to maturity, as it only considers the principal return and does not account for any periodic interest payments. This distinction makes BEY a valuable tool for comparing bonds with different maturities and purchase prices.

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Formula for Calculating Bond Equivalent Yield

To calculate the Bond Equivalent Yield, you can use the following formula:

[ \text{BEY} = \left( \frac{\text{Face Value} – \text{Purchase Price}}{\text{Purchase Price}} \right) \times \left( \frac{365}{\text{Days to Maturity}} \right) \times 100 ]

Let’s break down the components of this formula:

• Face Value: The amount paid at maturity.

• Purchase Price: The amount originally paid for the bond.

• Days to Maturity: The number of days until the bond matures.

Here’s how you can step through the calculation:

1. Calculate the difference between the face value and the purchase price.

2. Divide this difference by the purchase price.

3. Multiply this result by the ratio of 365 days to the number of days to maturity.

4. Finally, multiply by 100 to convert it into a percentage.

Example Calculations

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Let’s go through some examples to make this clearer:

Example 1:

• Face Value: $2,000

• Purchase Price: $1,900

• Days to Maturity: 100 days

Using the formula:

[ \text{BEY} = \left( \frac{2000 – 1900}{1900} \right) \times \left( \frac{365}{100} \right) \times 100 ]

[ \text{BEY} = \left( \frac{100}{1900} \right) \times 3.65 \times 100 = 0.0526 \times 3.65 = 19.19\% ]

Example 2:

• Face Value: $1,000

• Purchase Price: $980

• Days to Maturity: 75 days

Using the formula:

[ \text{BEY} = \left( \frac{1000 – 980}{980} \right) \times \left( \frac{365}{75} \right) \times 100 ]

[ \text{BEY} = \left( \frac{20}{980} \right) \times 4.867 \times 100 = 0.0204 \times 4.867 = 9.93\% ]

Example 3: Comparing Two Bonds

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Consider Mr. Yamsi who has two bond options:

• Bond A: Face Value $1,500, Purchase Price $1,400, Maturity in 90 days.

• Bond B: Face Value $1,200, Purchase Price $1,100, Maturity in 60 days.

Calculate BEY for each and compare them to decide which bond offers a better return.

Interpretation and Use of BEY

Once you have calculated the BEY, it’s important to understand how to interpret these results. Here are a few key points:

• Combining with Coupon Rate: If the bond also pays a coupon rate, you can combine this with the BEY to find the total yield on your investment.

• Comparing Bonds: BEY allows you to compare bonds with different maturities and purchase prices on an equal footing.

• Informed Decisions: By using BEY, investors can make more informed decisions about their bond portfolios by evaluating which bonds offer higher returns relative to their risk.

Practical Applications and Comparisons

BEY is particularly useful in several scenarios:

• Short-term vs Long-term Investments: When comparing short-term and long-term bonds, BEY helps you understand which investment offers a better annualized return.

• Evaluating Profitability: It allows you to evaluate the profitability of different bond options by considering factors like time to maturity and return on investment.

For instance, if you’re deciding between a short-term bond maturing in 60 days and a long-term bond maturing in 180 days but offering different returns at purchase price and face value, calculating BEY will help you determine which one is more lucrative.

Additional Resources

For further assistance or to simplify your calculations, you might find online Bond Equivalent Yield calculators useful. These tools can help streamline your analysis process when evaluating multiple bond options.

By mastering the concept of BEY and applying it effectively in your investment strategy, you’ll be better equipped to navigate the complex world of bond investments with confidence.

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