## These factors come from a Present Value of an Annuity table

Exhibit 7.2 Example of a Net Present Value Calculation

$22,000 for the next 8 years, the IRR that will be earned on this investment can be calculated as follows:

The formula for calculating present value is:

PV = cash flow X PV factor (from table) In our example, 80,000 = 22,000 X PV factor; or PV factor = 80,000/22,000 = 3.6364

By referring to a "Present Value of An Annuity" table, the corresponding discount rate can be found. In this example the discount rate represented by the cash flows in the example is about 21.8 percent. This is consistent with the NPV calculation above, where NPV at 16 percent equaled a positive $15,559. Obviously, this means that the IRR would be substantially in excess of 16 percent.

Determining IRR with uneven cash flows is more complicated than with level cash flows. It involves a trial-and-error process; and since the cash flows are not the same every year, the present value must be calculated on a year by year basis (rather than on an annuity basis). The first step is to determine a discount rate that may be close to the actual IRR and use this discount rate to calculate the PV of the cash flows for the project. If the PV of the cash inflows exceeds the PV of the investment, the discount rate selected was too low; while if the discounted cash flow is negative, the discount rate selected was too high. Recalculate the PV using a discount rate that is appropriately higher or lower. An attempt should be made to find two discount rates between which the actual rate lies, and then find the actual rate by interpolation. To see how this works, look at the example in Exhibit 7.3.

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