Calculating the IRR for a project with an initial outlay and single cash flow is very easy to do. It's also very practical for measuring the returns on investments in collectibles, commodities, nondividend-paying growth stocks, or even funds, where returns are determined by the price at which an investment is sold rather than a series of cash flows over time.

A simple example
Suppose you have the opportunity to invest in a project that will require a \$100 investment today and pay out a single cash flow of \$250 in year five. Though this project sounds appetizing with no math at all -- and it is -- you'll need to calculate an IRR to know exactly the return you'll receive on your investment.

Because this project has a single outlay and cash flow, we can use the compound annual growth rate formula to solve for the internal rate of return. Thus, the formula is as follows:

IRR = (Expected Cash Flow ÷ Initial Outlay)^(1 ÷ Number of Periods)-1

Thus, to calculate the IRR on the example investment, we'd input all the variables so that the formula looks like this:

IRR = (\$250 ÷ \$100)^(1 ÷ 5)-1

The remaining steps are to simplify and solve:

IRR = (2.5)^(0.2)-1
IRR = 1.2011 -1
IRR = 0.2011

The answer is expressed in percentages, thus the IRR for this investment is 20.11%.

Another way to think of an IRR is to think of it as an average annual return earned on your investment over time. If we take the beginning investment of \$100 and compound it at a rate of 20.11%, it will have grown to exactly \$250.00 by year five.

Time 0: \$100.00
Time 1: \$120.11
Time 2: \$144.27
Time 3: \$173.29
Time 4: \$208.14
Time 5: \$250.00

Working backwards is a good way to check to make sure that your IRR calculations are correct.

That's the short and sweet method for calculating an internal rate of return for a simple problem with a single outlay and cash flow. More difficult problems will likely necessitate a hot date with a finance calculator or spreadsheet, however.

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