# How to Calculate Internal Rate of Return: Definition & Formula

## Internal Rate of Return and Net Present value

There are a number of different methods that a business can use to determine the profitability of a project. One of the more common methods is to determine the internal rate of return. **Internal rate** of return analyzes all of the money that will be earned for a particular project and calculates the rate at which that investment will break even.

In order to determine and understand internal rate of return you will need to understand the concept of net present value. The reason that a company will make an investment is that they will receive some financial benefit at a future date. **Net present value** is the current value of payments that you will receive at a future date. Basically, it answers the question, 'What is the value today of money that I will receive in the future?' This number is important to understand because it is an integral part of understanding internal rate of return.

## Importance of Internal Rate of Return

Internal rate of return is the value of an investment when the net present value equals zero. This means that internal rate of return measures the value of a project that is greater than the current value of a project. This allows a business to compare the value of multiple investments.

Huppy Manufacturing is determining how to spend their money. They can either take their money and invest it in the stock market, or they can purchase a new machine that will increase production. After doing the calculations for both they have determined the following:

Internal Rate of Return for the stock market: 3%

Internal Rate of Return for the new machine: 9%

Using this information they would decide on the machine, since it has a greater internal rate of return than an investment in the stock market.

## The Variables

There are two variables that you will need to determine before you can calculate the internal rate of return.

- The amount of the initial investment. This is how much money a company will spend in order to gain a return on an investment. Huppy Manufacturing purchases a machine for $20,000 and expects that machine to increase production for the next two years. The amount of the initial investment will be $20,000. Note that this will always be a negative number in the formula as it is a cash outlay. We will abbreviate this as
*I*. - The amount of money that the project will pay out for each year. Huppy Manufacturing expects the purchase of the new machine will increase revenue by $15,000 in the first year, $10,000 in the second year and $5,000 in the third year. The payout for year one is $15,000, the payout for year two is $10,000 and the payout for year three is $5,000. We will abbreviate this as
*C*.

## The Calculation

Once you have determined the variables you can now set up the calculation. We will abbreviate internal rate of return as IRR. The formula is as follows:

0 = I + (C1 / (1+IRR)) + (C2 / (1+IRR)^2) +... (Cn / (1+IRR)^n)

In this formula C1 is the cash flow of the investment from the first year and C2 is the cash flow from the second year. The formula will continue with this pattern for every year that a cash flow can be determined.

Let's use our numbers from the Huppy Manufacturing example to see how the formula works:

0 = -$20,000 + ($15,000 / (1+IRR)) + ($10,000 / (1+IRR)^2) + ($5,000 / (1+IRR)^3)

Remember that the initial investment is a cash outlay, so it will always be a negative number.

There is no analytical method to solve this formula, so you will have to use trial and error to determine IRR. These kinds of problems can be solved using a spreadsheet program, but it is important to see the math behind the calculation.

After running a few numbers you will see that the solution is approximately .29 or 29%. This means that the Internal Rate of Return for the purchase of this machine is 29%.

Here is what the math looks like using .29 as the IRR:

0 = -$20,000 + ($15,000 / (1+IRR)) + ($10,000 / (1+IRR)^2) + ($5,000 / (1+IRR)^3)

0 = -$20,000 + ($15,000 / (1+.29)) + ($10,000 / (1+.29)^2) + ($5,000 / (1+.29)^3)

0 = -$20,000 + ($15,000 / 1.29) + ($10,000 / 1.66) + ($5,000 / 2.15)

0 = -$20,000 + $11,627.91 + $6,024.10 + $2,325.28

0 = -$20,000 + $19,977.29 (Note that there will be a slight variance in the solution due to rounding.)

## Lesson Summary

Internal rate of return analyzes all of the money that will be earned for a particular project and calculates the rate at which that investment will break even. It is the value of an investment when the net present value equals zero. In order to calculate internal rate of return you will need to know the initial investment amount and the cash payout for each year of the investment. Once that is determined you will use the following formula to determine the internal rate of return:

0 = I + (C1 / (1+IRR)) + (C2 / (1+IRR)^2) +... (Cn / (1+IRR)^n)

From there you will need to use trial and error to determine the value of internal rate of return.

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Back*How to Calculate Internal Rate of Return: Definition & Formula*

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