Solve for IRR in example

So far, we have considered two methods for evaluating capital investments: payback and net present value. We will now look at a third method called the internal rate of return (IRR). The IRR method determines the discount rate for a capital investment at which the net present value of a given set of cash flows is equal to zero. If the IRR is greater than the organization's MARR, then the capital investment makes sense financially. If the IRR is less than the MARR, the investment does not make sense financially. Example: Using the cash flows developed for the $100,000 medical centre equipment purchase used in the previous example, we can determine the IRR of this investment. Using Equation 5 to determine NPV, IRR is substituted in as the discount rate. By definition, the NPV is set to equal 0 . 0=(1+IRR)0$100,000+(1+IRR)1$30,000+(1+IRR)2$30,000+(1+IRR)3$30,000+(1+IRR)4$30,000+(1+IRR)5$30,000 IRR must now be solved. This is generally done using computer spreadsheet functions (such as Microsoft Excel). It can also be done through solving by trial and error. A guess that the IRR is 10 per cent can be made and the NPV can be calculated using the equation above. The NPV (using 10 per cent) is calculated as +$13,723. This is greater than zero. Since the rate must make the NPV equal to zero, another IRR that will make the NPV smaller is needed; therefore, a larger IRR must be chosen. If the IRR is set at 12 per cent, the NPV is $8,144, and if IRR is set at 16 per cent, the NPV is 1,771. Thus, the IRR is a value somewhere between 12 per cent and 16 per cent. If the medical centre's MARR were 10 per cent, then this IRR indicates that this is a good investment because it exceeds the 10 per cent return used by the hospital for such decisions. The use of the IRR method to evaluate investments does take into account the time value of money, but it can be difficult to calculate exactly without a computer