of sign in the sequence of cash flows.) INTERNAL RATE OF RETURN (IRR) In the IRR study the aim is to find the discount rate which leads to an NPV of zero, that is; NPV of outgoing cash flows just balances NPV of incoming cash flows. The procedure to find IRR is iterative: guess values for IRR; calculate and plot values of NPV; find the value that gives a zero NPV by interpolation. These calculations can be done with computers (e.g. Excel). IRR for a project can be compared with the corporate discount rate i: if IRR is less than i, the project is not profitable; the more IRR exceeds i, the more profitable the project. Example This example shows a trial-and-error method which also uses interpolation. Understanding Changing Telecommunications - Building a Successful Telecom Business The table below shows a series of cash flows corresponding to an initial investment of $1 million, which results in yearly income of $263 800 per annum over a five-year period. End of Actual cash Discount factor Discounted Discount factor Discounted flow ($M) @ 5 % pa cash flow @ 15 % pa cash flow ($M) (1000) (1000) (1000) 263.80 0.952 251.10 0.867 228.70 263.80 0.907 239.30 0.756 199.40 263.80 0.864 227.90 0.658 173.60 263.80 0.823 217.10 0.572 150.90 263.80 0.784 206.80 0.497 131.10 142.20 (116.30) Deduce the IRR by calculating the NPV of the cash flows for two discount rates, one hopefully larger than the IRR, and the other hopefully smaller. Then interpolate to derive the discount rate for which the NPV is zero: this is the IRR. (Note: The usual condition for the existence of an IRR is that there must be at least one change of sign in the sequence of cash flows.) As desired, one NPV is positive and the other negative, SO we then know that the IRR lies between the two discount rates 5 % and 15 %. A straight-line interpolation will give a satisfactory result (the actual curve is not quite straight). The point where the straight line crosses the discount rate axis gives the IRR, since this rate would give a zero NPV. It is not easy to i