Without sensible number crunching there is no rational investment or spending decision

Why is it needed? It’s because investments in real life rarely come as easy as ‘give me amount X, and will give you back amount Y in Z years’. In a simple situation like that, it’s easy to calculate the rate of return, even on an annualized (that is smoothed out and compounding) basis. The thing gets complicated when there are X1, X2, X3, etc, and also perhaps Y1, Y2, Y3, … and all these occurring along a time line (Z1, Z2, Z3, Z4, etc.), perhaps not even at regular intervals. Simple calculating will not work in a situation like that.

You can find many places on the web where the explanation of the IRR concept is put in more precise and scientific terms, or you can explore and calculate it without Internet as well if you are a savvy user of Excel or similar spreadsheet programs, but if you’re not eager to get those, I think this simple explanation will do for you.

This little calculator here expects you to

The best is probably to illustrate it with an example:

If you pay/invest $500 in Year1, $4,000 in Year 4, and $580 in Year 7, while the withdrawals are: $200 in Year4, $500 in Year 6, and a final $1,250 emptying the account in Year 9, then you enter the following:
Time column: 1, 4, 6, 7, 9; Value column: -500, -3,800, 500, -580, 1,250.
Then when you hit ‘Go’ at the bottom, the calculator gives you the answer: -0.25371283292770386, … meaning -25,4% annualized return.

Let’s see a more optimistic example:
Investments: $20,000 in Yr1, $15,000 in Yr4
Withdrawals: $3,000 in Yr2, $1,500 in Yr4, and $2,000 in Yr6
The value of the account at the end of Yr10 is 18,000
What you’d enter is this: 1, 2, 4, 6, 10 in the left column, and -20,000, 3,000, -13,500, 2,000, 46,400 in the right column. When you hit ‘Go’, the calculator gives the IRR as 0.06032019853591919, meaning 6.03% annualized return on the whole ‘package’. It will not tell you whether it is good or bad, … you consider alternatives and expectations, and decide on your own about that.

The calculation assumes that investments are made at the beginning of the time period, while withdrawals are made at the end. So, using our second example, if you want to indicate that the initial $20,000 investment is made at Jun 30 in the first year, you enter 1.5 first in the left column, … resulting in a higher (6.32%) IRR, since your money worked for a shorter time to achieve the same results as before. If the want to indicate that the final account value of $46,000 is achieved at the middle of Year 10, then you enter 9.5 as the last number in the right column, resulting in an even higher (6.76%) IRR again, for the same reason: your money needed less time to bring about the same return, so the annualized rate is higher.

Don’t get surprised if the calculator responds with the “null” answer. When it happens it’s because it didn’t find any mathematical solution that would satisfy the built-in requirement that the total of the so-called net present values of all periods when the cash flow is positive would balance out the total of net present values of all periods when the cash flow is negative. It may happen most easily when the first and the last period’s numbers are either both positive or both negative. When the second column starts with a positive number and ends with a negative one (or vice versa) then it can never happen.

Just to avoid any potential misunderstanding, here are some rules of thumb. As a general rule, when you invest (when you start the second column with a negative number) then you expect a positive IRR; the higher it is, the better. When you calculate the IRR for a loan - that is when you started with a positive number and ended with a negative one - then the IRR number shows not what you achieve on this stream of cash flow events, but the annualized interest you pay. (It’s rather obvious when you are just paying back a loan, but you may get confused and misled if you enter a series of cash flow items representing investments you made with the borrowed money, e.g. In a situation like this, the lower the IRR number the better it is, … that is -2 is better than -1, and -1 is better than any positive value, e.g. Combining unrelated transactions into a single stream of cash flow series renders the whole calculation rather meaningless, of course, but if the combination makes sense because the items are logically dependent on each other, the calculation can be useful in a borrowing-to-invest scenario. It’s always a good idea though, at least in more complex situations like this would be, not to jump to conclusions as soon as a calculation resulted in some output number, since there might be some strange constellations of numbers involved that produce misleading or easy-to-misunderstand ’spurious’ answers. It’s always useful to try various variants, check out if the outcome responds to changes in input reasonably, etc. No calculator can completely replace thinking and judgment at the end, but it can be a good enhancer.)