Internal rates of return

The IRR column is the internal rate of return of the project at the relevant oil price, and is a measure of what discount rate the project can withstand before the NPV is reduced to 0. This indicator will be discussed in a moment, but is included here as a recommended part of this presentation format. 

At a specific discount rate the net present value (NPV) is reduced to zero. This discount rate is called the internal rate of return (IRR). 

Another useful profitability indicator is the internal rate of return (IRR), already introduced in the last section. This shows what discount rate would be required to reduce the NPV to zero. The higher the IRR, the more robust the project is, i.e. the more risk it can withstand before the IRR is reduced to the screening value of discount rate. Screening values are discussed below. 

Fig. 3. Profitabihty diagram for Venture A. (a) Simple diagram. NRR is net return rate IRR, the internal rate of return, is a given fixed point, (b) Three NRR cutoff lines for Venture A where B, C, and D represent NRR values of 15, 10, and 5%/yr, respectively. For example, at a discount rate of 10% per year, the NRR cutoff for Venture A could be as high as 10.74% per year for marginal acceptance (point X). Acceptable levels are to the left of NRR cutoff...

The best w ay to evaluate free enterprise projects is to use discounted cash flow (DCF) rate of return, sometimes called internal rate of return. 

Now that you have determined the likely savings in terms of annual process and waste-treatment operating costs associated with each option, consider the necessary investment required to implement each option. Investment can be assessed by looking at the payback period for each option that is, the time taken for a project to recover its financial outlay. A more detailed investment analysis may involve an assessment of the internal rate of return (IRR) and net present value (NPV) of the investment based on discounted cash flows. An analysis of investment risk allows you to rank the options identified. 

It is eommon praetice to eompare investment options based on the present-value equation shown above. We may also apply one or all of the following four factors when comparing investment options Paybaek period Internal rate of return Benefit-to-cost ratio and Present value of net benefit. 

Capital investments can also be selected on the basis of other measures of performance such as return on investment, internal rate of return, and benefit-cost ratio (or savings-to-investment ratio). Flowever, care must be taken in the application of these methods, as an incremental analysis is required to ensure consistent comparison of mutually exclusive alternatives. Also, rather than requiring a separate value to be calculated for each alternative, as in the case of the life-cycle cost method, these other methods incorporate the difference between two mutually exclusive alternatives within a single measure. For example, the net benefits measure directly pressures the degree to which one alternative is more economically desirable than another. 

In the above equation, r can indicate the internal rate of return on an investment. Suppose that an investment in an energy-saving technology cost 100 and reduces energy costs by 20 per year indefinitely. The reduction in costs is comparable to net revenues received. The above equation can be modified as follows I equals R/r, where the values of I and R are specified and the value of r is computed. Hence 100 equals 20/r, and r equals 0.20, or 20 percent. The internal rate of return on the 100 investment is 20 percent per year. An investment is generally profitable when its internal rate of return exceeds the (interest rate) cost of obtaining credit. The investment is attractive when its internal rate of return exceeds the investor s hurdle rate, which may vary depending on the riskiness of the investment, and on the rate that can be earned from alternative uses of the investment funds. 

The efficient heat pump reduces energy use by 1,676 kWh per year on average. Is the efficient model heat pump a good investment Suppose the incremental cost of the efficient unit, as compared with the less efficient unit, is 1,000, and electricity cost 10 cents per kWh. With this price of electricity, the efficient heat pump reduces electricity costs by 167.60 per year. Taking a simplified approach for purposes of illustration and assuming that each unit lasts indefinitely and has no repair, maintenance, or replacement costs, and ignoring possible tax effects, the internal rate of return may be calculated as 1,000= 167.60/r, which is 16.76 percent per year. If the household can borrow money at, say, 10 percent per year and earn 16.76 percent, the investment makes economic sense. If we assume a 10 percent discount rate, the present value of the investment is 1,676, which exceeds the initial investment cost. The net present value is 676, which indicates that the investment is feasible. 

In the illustration of the electric heat pump, the simple internal rate of return is 16.76 percent. We observe that some households purchase the efficient... 

The discounted cash flow rate of return (DCFRR) or internal rate of return (IRR) is the percentage interest i at which the NPV becomes equal to zero. Fig. 5.2-4 illustrates the relationship between NPV and DCFRR (IRR), the intersection of the NPV curve with the axis of percentage interest i corresponds to the DCFRR (IRR) for NPV = 0. The investment is considered advantageous if DCFRR > 15 - 20 % (depending on the risk). 

Other names for DCFRR are interest rate of return and internal rate of return. 

In general, one or more of three methods are used to justify major expenditures. The first, payback, is a measure of the time it will take for cumulative benefits to equal cumulative costs (time to break even). This, by itself, may not be sufficient to compare alternative investments and projects competing for the same limited resources so one of two other methods may be used. These methods, Net Present Value and Internal Rate of Return, consider the earning power of money in making comparisons. Because investments earn compound interest, a dollar to be gained in the future has less present value than one gained today. The NPV is computed by estimating the yearly... 

Heikkila et al. (1996) have expanded the work of Hurme and Jarvelainen (1995) with environmental and safety aspects (Fig. 11). The alternatives are simulated to determine the material and heat balances and to estimate the physical properties. Then the alternatives are assessed in economic terms for which the internal rate of return is used. The environmental effects are estimated by equivalent amount of pollutant that takes into consideration the harmfullness of the different effluent substances. With environmental risks are also considered aspects of occupational health to choose inherently healthier process. Even though most health related rules are considered later in the work instructions, health effects should also be a part of the decision procedure. The inherent safety is estimated in terms of the inherent safety index as described later. 

IRR is the rate of return (interest rate, discount rate) at which the future cash flows (positive plus negative) would equal the initial cash outlay (a negative cash flow). The value of the IRR relative to the company standards for internal rate of return indicates the desirability of an investment ... 

The basis for the calculations will be L = 100m. Because the insulation comes in 1-cm increments, let us calculate the net present value of insulating the pipe as a function of the independent variable jc vary x for a series of 1-, 2-, 3-cm (etc.) thick increments to get the respective internal rates of return, the payback period, and the return on investment. The latter two calculations are straightforward because of the assumption of five even values for the fuel saved. The net present value and internal rates of return can be compared for various thicknesses of insulation. The cost of the insulation is an initial negative cash flow, and a sum of five positive values represent the value of the heat saved. For example, for 1 cm insulation the net present value is (r = 0.291 from Table 3.1)... 

Insulation thickness x (cm) Insulation cost ( > Value of fuel saved ( /year) Payback period (years) Return on investment (% per year) Net present value ( > Internal rate of return (%)... 

One member of your staff suggests that if your department spends just 10,000 to improve a process, it will yield cost savings of 3000, 5000, and 4000 over the next 3 years, respectively, for a total of 12,000. Your company policy is to have an internal rate of return of at least 15% on process improvements. What is the NPV of this proposed improvement ... 

In Chemical Engineering (Jan. 1994, p. 103) the following explanation of internal rate of return appeared ... 

Refer to Problem 3.5. The same staff member asks if the internal rate of return on the proposed project is close to 15%. Calculate the IRR. 

Internal rate of return (IRR) the interest or discount rate for which the future net cash flows equal the initial cash outlay. 

Suppose project C has a 20-year life and a yearly after-tax cash flow of 48,000 for an initial investment of 300,000. Project D has a 5-year life, with a yearly cash flow of 110,000 for an initial investment of 300,000. Compare the internal rate of return and net present value (for i = 0.08) for each option. 

Solution. Because the annual cash flows are uniform for projects C and D, we can apply Equation (3.4a). The internal rates of return are ic = 0.15 for project C and iD = 0.25 for project D. The advantage of project D is a more concentrated period of early cash, generation at a high level. For a value of i = 0.08, the NPV of each project is as follows ... 

Inflation can be a significant factor in analysis of profitability. High inflation rates frequently occur in many countries. In computing the rate of return or net present value, you need to obtain a measure of profitability that is independent of the inflation rate. If you inflate projections of future annual income, the computed rate of return may largely result from the effects of inflation. Most companies strive for an internal rate of return (after taxes) of 10-20 percent in the absence of inflation ... 

What criterion should you use to make the evaluation You can calculate the internal rate of return for case (a) from... 

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