y 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 interpolate on Figure A2.7, but the line crosses the horizontal axis at the IRR = 10.2 %. Using the IRR function of Microsoft Excel, the internal rate of return is calculated instantly as 10.27 %. If this rate of return exceeds the weighted average cost of capital for the company, then the investment is assessed as favourable. Otherwise, the investment is not regarded as economic. Graphical method for IRR Discount rate Figure A2.7 Interpolation of internal rate of return, IRR Appendix 2: Financial Calculations BUSINESS PERFORMANCE MEASURES In this chapter some financial measurements are accounted for. Note that there are other important performance measures that are non-financial, e.g. customer satisfaction mea- surements, people satisfaction measurements, efficiency, quality and time measurements, innovation measures etc. Return on Investment (ROI) The relationship between profit and money invested in a project or company, usually expressed as a percentage, ROI, is also called the accounting rate of return (ARR). ROI is normally used when evaluating a company or organization and ARR is used when evaluating an investment or a project. Differences can occur: e.g. in some calculations the net profit is the numerator and the total assets are the denominators. Result (profit) * 100 ROI = Invested capital Return on Capital Employed (ROCE) Profit shown as a percentage of the capital in a business. Capital employed = C