The Equivalent Rate of Return Defined

Equivalent rate of return is simply how much your investment is growing in a particular financial situation where you know the exact amount of money your investment will yield in the future. In more financial terminology, equivalent rate of return is a financial calculation that helps investors compare investments based on projected future cash flows.

To further define, Equivalent Rate of Return is the rate by which a future flow of cash must be reduced to equal the initial investment hence the term equivalent in addition to rate of return. The reason Equivalent Rate of Return is used instead of simple rate of return is that a standard rate of return does not tell the investor how much money they are making as a percentage in excess of their initial investment.

Equivalent rate of return makes use of two key variables, 1) investment amount and 2) future cash flows. Investors use the equivalent rate of return to make sure they are not overpaying for a future stream of money or investing in the wrong project. The following example illustrates equivalent rate of return further.
Example 1: If your income from an investment is $1,100 per year for 20 years,and your initial investment was $10,000, how much would the annual returns have to be reduced so their total adds up to the same amount as the initial investment. The answer would be your equivalent rate of return.

For additional clarification, the equivalent rate of return is also termed Internal Rate of Return as per definition. (moneychimp.com) That is to say, both Equivalent Rate of Return and Internal Rate of Return calculate the same thing and are considered interchangeable for this particular use of the term.

How to calculate equivalent rate of return

Calculating equivalent rate of return is a matter of entering the future cash flow variables in to 1) a manual equation, 2) a calculator or 3) online or built in software application. The simplest and fastest method is to a let a computer program do it for you. This not only saves time, but also the effort of having to figure out which sequence of small buttons to press on a financial calculator or writing down and calculating present value and rate of return equations on paper. That said, the three methods are described below:

• Method 1: Online Equivalent Rate of Return Software

For this method of calculating Equivalent Rate of Return, simply plug in the future cash flow numbers into the 'input cash flow' boxes at the following link. Remember to use a negative sign before the first number as this is how much money you are investing and is cash flow out not in. The discount rate in the following IRR calculator is somewhat ambiguous as this is better termed an expense rate reduction. The discount is also used to refer to IRR as the return is 'discounted' by the IRR. However, this is not the case in this particular application. Microsoft Excel also has an Internal Rate of Return aka Equivalent Rate of Return calculation function.

http://www.datadynamica.com/IRR.asp

• Method 2: Financial calculator

Depending on which calculator you use the exact method may differ. However, financial calculators have specific IRR function that allows you to calculate equivalent rate of return. One example being the Texas Instruments BA II Plus which makes use of its Cash Flow (CF), Net Present Value (NPV), Internal Rate of Return (IRR) and Compute buttons. Essentially, the same process as in the software method above is used except instead of entering the cash inflows and outflows in the boxes they are done using the CF button, NPV, Interest (I) and then pressing Internal Rate of Return (IRR) then Compute (CPT). These instructions are illustrated in full at the following link.

http://www.fiu.edu/~barberj/calculator.htm

• Method 3: Manual method

Calculating equivalent rate of return manually involves 1) averaging the rate of return on investment of a future series of cash flow, and 2) determining how much that rate of return must be reduced when applied to the cash flows in order for those cash flows to equal the initial investment. The following is a trial and error approach to determining equivalent rate of return. This and other manual calculation methods can be found in the subsequent links.

Step 1: Add up total cash flows and divide by total initial investment
Step 2: Choose a percentage by which the rate of return can be reduced to yield an estimated amount similar to initial investment
Step 3: Adjust discount rate until final net value of cash flows equal initial investment.

http://hadm.sph.sc.edu/Courses/ECON/invest/invest.html
http://invest-faq.com/cbc/analy-int-rate-return.html

In summary, Equivalent rate of return is the rate by which a net amount of money you would receive in a series of future cash flows must be deducted or 'discounted' from the total actual average return on investment. Equivalent Rate of Return can also be calculated as a non-average value if cash flow is consistent. For one additional example, assuming it doesn't matter when you receive a cash award, which would you rather have $1000 now, or $500 with an annual rate of return of 10% over 10 years non-compounded? The answer is it doesn't matter because the rate of return of 10% is equal to the value of the $1000 over 10 years not including inflation risk.

Sources:

1. http://www.moneychimp.com/articles/finworks/fmpresval.htm
2. http://hubpages.com/hub/Internal-Rate-of-Return-for-Dummies
3. http://moneyterms.co.uk/irr/