The logic behind IRR

Question

I can't still completely understand the logic behind the calculation of IRR.

It's all clear with NPV. Let's use simple example:

NPV = CashFlow / DiscountRate
100 = 110 / 1,1

But with the IRR..., the definition of IRR says:

"To find the IRR, you would need to "reverse engineer" what discount rate is required so that the NPV equals zero."

In this case: 0 = 110 / x => x = 110 / 0

So, how can such a discount rate exist at all, if the solution requires the division by zero?

Chris Degnen · Accepted Answer · 2020-12-26 10:57:03Z

1

The sum of the discounted cash flows (NPVs) should equal zero.

For example, you deposit £100 today (NPV) and expect to receive £110 next year. Discount £110 to NPV and sum the cash flows.

100 - 110/(1 + x) = 0

∴ x = 10 %

answered Dec 26, 2020 at 10:49

Chris Degnen

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I don't understand, the IRR definition says that NPV should be zero. In this case 0 (NPV) = 110 (CashFlow) / x (DiscountRate). And x = 110 / 0
– Jane Mänd
Dec 26, 2020 at 12:33
The sum of the NPVs of all the cash flows is the overall NPV, and should be zero, as shown here: IRR Calculation
– Chris Degnen
Dec 26, 2020 at 13:03
Ok, now I understand :). Thanx!
– Jane Mänd
Dec 26, 2020 at 13:18
Note that IRR has a unique solution if the sign of the cash flows changes only once: you pay (negative cash flow) and then you only receive (positive cash flows). But more general cash flows, e.g., pay, then receive, then pay some more, then receive again.. might have multiple distinct solutions, all of which make NPV = 0.
– Dimitri Vulis
Dec 26, 2020 at 22:02

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