The Internal Rate of Return

There is thus an inverse relationship between NPV and DF the higher the latter, the smaller the value of NPV. The highest value of NPV is the base figure, when the sums are not discounted (DF = 0), and, eventually, for increasing values of DF, NPV becomes negative. 

There is then a single value of the DF for which, uniquely, the NPV is zero. This value of the DF is called the internal rate of return (IRR), or sometimes, the DCF rate of return. The IRR is the other key term in the DCF process 

Because the calculation of the NPVs takes into account the ways in which the relevant sums of money have been invested or recovered, as well as their size, the IRR is characteristic of the project and its cash flows the IRR is the rate of return achieved by investing the total capital employed in the project in the same pattern as in building the project, to produce income in the pattern of the net cash flows of the project. 

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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. 

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...

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. 

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. 

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. 

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. 

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 ... 

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

The most influential and determining factors in decision making are the quantitative financial analyses, which are used to declare the winner as the best use of the firm s assets. The criteria used most often are the net present value, NPV, and the internal rate of return, IRR. A financial plan begins with a time horizon, such as 5 years, and the forecast of a number of parameters of expenditures and incomes for each of the years, on ... 

The Internal Rate of Return (IRR) is the equivalent interest rate at which the Net Present Value of the acquisition would be zero. Given the projected total cost of the system, and the projected total benefits of the system, both projected back (discounted) to today, it is the interest rate that the investment could sustain and still just break even. Since firms, in general, operate at a point where their incremental cost of money is equal to its incremental earning power, any investment that returns an IRR better than the cost of money is a good investment. Traditionally, the IRR is found by calculating the NPV with different interest factors in a trial and error method until the interest factor is found which drives the NPV to approximately zero. 

The annual operating costs are also shown in Table 3. The raw materials costs were estimated from the average purchase cost of crude olive oil in Portugal in 1994. Supplies were empirically calculated from the scale-up study and include water, electric power, fiiel, maintenance, assurances, transports and expedient articles. The labour costs were determined for 4 shifts of 2 persons each, plus supervising personal. With a depreciation time of ten years and an interest rate of 10%, the total annual capital costs was estimated to be 212PTE/kg of oil feed. Several other economical indicators, such as the internal rate of return of the plant, showed a promising economical feasibility for this project. 

The internal rate of return method is a special case of the present worth method. With the IRR, the net present worth of each project first is arbitrarily set equal to zero, with the discount rate kept as an independent variable. Then, each NPW equation is solved (via an iterative procedure) for the unique discount rate/intemal rate of return that yields an NPW of zero. The project with the highest positive IRR would be the one selected. 

Given the data for the inorganic chemicals plant and the textile fibers plant expansion in the problem statement for Example 18.5, use the internal rate of return method to determine which project the firm should fund. 

Take into account how this approach differs from that for NPW analysis. The project lives, rC/s, TACs, depreciation, undiscounted net cash flows, plant lives, and tax rate are the same as those given for Example 18.5, on NPW analysis. However, in this present example, the hurdle (discount) rate is not an input. In Example 18.5, the hurdle rate was an input and, based on this rate, the net present worth was calculated for each project. In this example, by contrast, the net present worth is arbitrarily set to zero and the unique discount rate that produces a NPW of zero is solved for. This discount rate is the internal rate of return (IRR). The project with the higher internal rate of return is selected as the one to be funded. 

Related Calculations. The difference between the two internal rates of returns is so small that, on a purely economic basis, the projects are virtually indistinguishable. By contrast, the difference in the projects net present worths (see Example 18.5) is large enough to make the textile fibers expansion the clear choice for funding. As with the net present worth method, the internal rate of return procedure cannot be used unless the lifetimes of the competing projects are equal. 

Select the most appropriate evaluation method. Note that the control devices have different economic lives. Thus, neither the net present worth nor the internal rate of return method can be used, as both require that all options have the same economic life. However, the equivalent uniform annual revenue method can be used, as this restriction does not apply to it. 

The levelized PV electricity and H2 prices presented in this study are derived from Eq. 6 by choosing the electricity or H2 price level for the revenue component that produces a zero net present value for the net cash flow streams over the invest ment period, which in this case is equivalent to the internal rate of return. The esti mation of levelized PV electricity and H2 prices by the net present value cash flow method insures that all creditors and shareholders receive their expected rates of return. 

A convenient basis for comparison consists in determining the minimum profitable selling prices by setting a value of the POT (five years for example) or of the internal rate of return. In the latter case, an approximate method for linear depreciation of the fadlities over ten years and an internal rate of return of 15 per cent, consists in applying the following expression ... 

This study concluded that processing of MPW with VR at a capacity of 200 000 ton/yr (80000 ton/yr MPW and 120000 ton/yr VR), is economically feasible for Saudi Arabian conditions. This capacity is adequate in view of the amount of MPW generated in Saudi Arabia. The internal rate of return (IRR) is about 14.6% with a payback period of 6.4 years and break-even capacity of 47.6%. Although profitability is not very attractive, the project is recommended to solve the waste disposal problem of both MPW and VR. Some assistance should be provided to operate these plants through environmental protection agencies. 

Baker SL. Perils of the internal rate of return. (Internet at http //hadm.sph.sc.edu/Courses/Econ/ invest/in vest.html.)... 

Investment decisions are often based upon several criteria, such as annual return on investment (ROI), payback period (PBP), net present value (NPV), the average rate of return (ARR), present value ratio (PVR), or the internal rate of return (IRR). Discounted cash flow rate on return (DCFRR) is another popular means of evaluating the economic viability of a proposed project. Horwitz [1] recommended the DCFRR as the best means to determine the return on investment, because it accounts for the time value of money. The internal rate of return as an investment criterion gives the possibility that given cash flows may result in more than one internal rate of return. Cannaday et al. [2] developed a method for determining the relevance of an internal rate of return. They inferred that an internal rate of return is relevant, if its derivative with respect to each of the cash flows is positive. 

The internal rate of return (IRR) is that value of i that makes NPV equal to 0. Therefore, if NPV is set to 0, the IRR that makes the future cash flows equal to the investment (the break-even point) can be estimated. Equation 9-12 then becomes ... 

The discounted cash flow rate of return is known by other terms, for example, the profitability index, the true rate of return, the investor s rate of return, and the internal rate of return. It is defined as the discount rate, i, which makes the NPV of a project equal to zero. This can be expressed mathematically by... 

A widely used method of analysis Is that based upon the Internal rate of return. Also known as the Discounted Cash Flow method, this approach Is based on the criterion that the sum of the present value of all cash flow returns associated with a given project be equal to the Initial Investment outlay namely,... 

Figure 2 shows the relationship between internal rate of return and gross payback for a specific set of tax regulations (10% investment tax credit, 50% tax rate), 6% per year increase in power, fuel, and O M costs, and sum-of-digits depreciation for both 10-year life (for recuperators and heat exchangers) and 20-year life (for power generation equipment and boilers). We see that life has little effect on the internal rate of return for gross payback periods less than about 3 years. 

At the company level, the return on investment is defined by the internal rate of return (RR), the interest rate at which the net present value of all cashflows into and out of the firm equals zero. If the IRR across all companies in an industry is greater than the industry s cost of capital, then the industry returned more to its investors than was necessary to bring forth the investment dollars, and one would suspect that barriers to entry or other forms of monopoly power (perhaps obtained through patent protection) might exist in the industry (86). On the other hand, a low IRR relative to the cost of capital would, if companies... 

The return on investment method is defined as the net profit after taxes divided by the total capital investment. Many variations on this measure have been used in the past. It does not include the time value of money but is simple enough that it can be used for simple screening purposes. The payout period is defined as the fixed capital investment divided by the after-tax cash flow. It indicates how long it will take to recover the fixed capital investment from the after-tax cash flow. Again, this is used for screening purposes. The payout period with interest takes into account the time value of money (Couper and Rader, 1986) but is a tedious calculation, and the results are not as informative as the net present value or the internal rate of return methods. 

The internal rate of return (IRR) method is similar to the NPV method in principle, hi the NPV method, the interest rate is stated, and the NPV is calculated. In the IRR method, an interest rate is sought by trial and error such that the NPVs sum to zero. That interest rate is the return that the venture will earn. There has been much discussion in the literature about which method is preferred (Couper et al., 2000). 

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