Q27RQ - Horngren'S Financial And Managerial Accounting

Question

How is IRR calculated with unequal net cash inflows?

Step-by-Step Solution

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 1: 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%.

Step 2: 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.