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%.

How to think about IRRs
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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