Question

How is IRR calculated with unequal net cash inflows?

Short answer

The after-tax cash flow for each period at time t is divided by some rate, r. The initial investment is then subtracted from the total of these discounted cash flows, yielding the present NPV. It is important to "reverse engineer" the value of r needed to make the NPV equal zero in order to determine the IRR.

Step-by-step solution

Example

years	Net PV Present Cash factor value Inflow (i=16%)	Net PV Present Cash factor value Inflow (i=18%)
PV of each year’s inflow: 1 (n=1) 2 (n=2) 3 (n=3) 4 (n=4) 5 (n=5) Total PV of cash inflows 0 Initial investment NPV	$500,000 0.862 $431,000 350,000 0.743 260,000 300,000 0.641 192,300 250,000 0.552 138,000 40,000 0.476 19,000 (1,040,390) 1,000,000) $40,390	$500,000 0.847 $431,000 350,000 0.718 251,300 300,000 0.609 182,700 250,000 0.516 129,000 40,000 0.437 17,000 (1,003,980) (1,000,000) $3,980

In this example for 1,000,000 initial investment in a project and these irregular cashflows we can conclude that IRR for this project is 18%.

IRR advantage over NAV

NPV will be negative when IRR <cost of capital. Benefits: Since this strategy is expressed in percentage form, it is simple for financial managers to compare it to the necessary cost of capital.