# Effective Annual Yield – Definition, Formula, and Example

Effective annual yield (EAY) or effective annual rate (EAR) considers the compounding effect of return on investment. It provides a realistic annual interest rate of an investment rather than the simple nominal rate.

Investors can use the EAY to calculate the actual return on investment. They can also use the EAR to evaluate whether a security instrument (Bond) is trading at a premium or a discount.

Let us understand the effective annual yield with the help of a working example.

## What is Effective Annual Yield?

The EAY is the rate of return on a bond that reinvests the coupon payments at the same coupon rate of the bond.

The nominal rate of return adjusted for compounding is the EAY for the investor. In other words, it is the effective rate that an investor can earn if all the coupons are reinvested at the same rate for the same period.

Effective yield is derived from the nominal coupon rate that makes payments quarterly, semi-annually, or annually. If the security makes only annual payments, the EAY will equal the nominal coupon rate since there will be no compounding effect for a payment made at maturity.

## How Does Effective Annual Yield Work?

The concept of EAY works with the assumption that the investor can reinvest coupon payments at the same interest rate. Mostly, the concept is associated with the calculation of the rate of return for bonds.

The calculation of EAR uses the same coupon rate that is predefined for the investment. The coupon payment frequency is also known to the investor. Thus, the investor can calculate the compounding effect at the same rate for the given period to find the effective yield.

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A bond can make quarterly, semi-annually, or annually coupon payments. However, the coupon rate and the effective yield are described in annual terms.

The effective yield can be a useful tool to evaluate the actual return on investment. It can also help analysts determine the true cost of debt. The same concept of compounding money can be applied for debt installments over a specific period. The actual cost can be compared against the stated interest rate to analyze the difference.

## Formula

EAY can be calculated with the formula:

Effective annual yield = [1 + (r/n)]n – 1

Where r = interest rate or coupon rate, n = number of compounding periods

## Example

Suppose an investor purchase a bond issued by ABC company. The Bond has a coupon rate of 8%.

### Scenario # 1: The bond makes an annual payment.

Effective annual yield = [1 + (r/n)]n – 1

Effective annual yield = [1+ (8%/1)]1 – 1 = 8%

Since there is no compounding effect for a coupon received after one year, the EAR is the same as the coupon rate.

### Scenario # 2: The bond makes semiannual coupon payments.

Effective annual yield = [1 + (r/n)]n – 1

Effective annual yield = [1+ (8%/2)]2 – 1 = [1+ 0.02]2 – 1 = 1.0816 – 1

Therefore, EAY = 0.0816 or 8.16%

Since the coupon received after six months can be reinvested at 8%, the total effective annual yield increases to 8.16%.

### Scenario # 3: The bond makes monthly payments.

Effective annual yield = [1 + (r/n)]n – 1

Effective annual yield = [1+ (8%/12)]12 – 1 = [1+ 0.00667]12 – 1 = 1.0834 – 1

Therefore, EAY = 0.0834 or 8.34%

Thus, we can see as the compounding frequency increases the effective annual increases. This is because an investment received earlier can be reinvested for a longer period that yields a higher return.

## Effective Annual Yield v Bond Equivalent Yield (BEY)

The bond equivalent yield or the Yield to Maturity (YTM) is the total return on the bond when held till maturity. Investors can compare the YTM and the EAY to analyze return on investment and bond pricing.

If the EAY of the bond is greater than the YTM of the bond, it is selling at a premium. Conversely, if the effective annual yield is less than the YTM of the bond, it is selling at a discount.

Since most investors do not buy bonds at the face value, comparing the YTM and the EAR can be an effective way to analyze the bond. It can help investors analyze the return on investment as well as the bond pricing.

## Importance of Effective Annual Yield

The EAY can help investors calculate actual return on investment. It also lets borrowers consider the true cost of borrowing.

Unlike other rates of return, the effective yield considers the compounding effect. It is closer to the commonly adopted concept of the time value of money.

Effective yield can be a useful tool in analyzing investments that pay monthly payments. Since the frequency of payments will be in shorter intervals, the reinvestment returns will increase due to the compounding effect. Thus, the investor will see the effective yield higher than the nominal interest rate on investment.

## Limitations of Effective Annual Yield

The biggest drawback of the effective yield method is the consideration of reinvestment at the same rate as the nominal interest rate of investment.

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Interest rates of bonds and other fixed-income securities change regularly. In economic recessions, the interest rates continue to fall. Similarly, when economies are recovering, the interest rates tend to increase gradually.

Thus, the comparison with a changing interest rate and the effective yield needs further analysis.

Also, the reinvestment opportunities for coupon payments can be limited for investors. Not all investors would be able to reinvest the coupon payments.

Another limitation of the compounding concept is the frequency of coupon payments. For example, if a bond pays coupon payments annually, the effective yield will equal the nominal interest rate of the bond.

## Final Thoughts

Effective annual yield is a realistic method of analyzing the return on investment. It considers the compounding effect and the time value of money.

The only drawback of the effective yield method is the availability of reinvestment opportunities at the same nominal rate of the security.

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