Discounted cash flow return

Finding the DCF for a project is a matter of trial and error calculation. When carrying out manual calculations a value of i (the discount rate) is selected and the project NPV calculated. If this is positive the value of i chosen is lower than the project DCF, so a higher lue of i is selected and a new NPV calculated. If a negative value of NPV is then obtained then the higher value of i is above the DCF for the project. Graphical interpolation between NPV values will enable the DCF value to be estimated. From the figures in Table 

The DCF method is not suitable for projects where a net negative cash flow takes place late in the project taking the cumulative cash flow back below the zero line. In most cases such a large cash outflow is a result of additional capital investment in a planned expansion of capacity. It is unlikely that a decision to commit funds to the expansion will be made at the same time as the decision on the original project so the two can be treated separately and individual cash flows evaluated. 

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The other indices to be described, net present value and discounted cash flow return, are more comprehensive because they take account of the changing pattern of project net cash flow with time. They also take account of the time value of money. 

Internal return rate. The internal return rate (IRR), also known as the discounted cash flow return rate, is the iteratively calculated discounting rate that would make the sum of the annual cash flows, discounted to the present, equal to zero. As shown in Figure 2, the IRR for Project Chem-A is 38.3%/yr. 

Discotic liquid-crystal phase, 13 371 Discotic liquid crystals, 15 96 Discotic mesogens, 20 79 Discounted cash flow return rate (DCFRR), 9 544-545... 

Discounted cash-flow rate of return. Discounted cash-flow rate of return is defined as the discount rate i which makes the NPV of a project zero (curve 3 in Fig. A.2) ... 

The value of i given by this equation is known as the discounted cash-flow rate of return (DCFRR). It may be found graphically or by trial and error. 

Ref 91. Discounted cash-flow models account for use of capital, working capital, income taxes, time value of money, and operating expenses. Real after-tax return assumed to be 12.0%. Short-rotation model used for sycamore and poplar. Herbaceous model used for other species. Costs ia 1990 dollars. Dry tons. 

This gives two choices ia interpreting calculated NRR values, ie, a direct comparison of NRR values for different options or a comparison of the NRR value of each option with a previously defined NRR cutoff level for acceptabiUty. The NPV, DTC, and NRR can be iaterpreted as discounted measures of the return, iavestment, and return rate, analogous to the parameters of the earher example. These three parameters characterize a venture over its entire life. Additional parameters can be developed to characterize the cash flow pattern duting the early venture years. Eor example, the net payout time (NPT) is the number of operating years for the cumulative discounted cash flow to sum to zero. This characterizes the early cash flow pattern it can be viewed as a discounted measure of the expected operating time that the investment is at risk. 

Internal Return Rate. Another rate criterion, the internal return rate (IRR) or discounted cash flow rate of return (DCERR), is a popular ranking criterion for profitabiUty. The IRR is the annual discounting rate that makes the algebraic sum of the discounted annual cash flows equal to zero or, more simply, it is the total return rate at the poiat of vanishing profitabiUty. This is determined iteratively. 

The relationships among the various annual costs given by Eqs. (9-1) through (9-9) are illustrated diagrammaticaUy in Fig. 9-1. The top half of the diagram shows the tools of the accountant the bottom half, those of the engineer. The net annual cash flow Acp, which excludes any provision for balance-sheet depreciation Abd, is used in two of the more modern methods of profitability assessment the net-present-value (NPV) method and the discounted-cash-flow-rate-of-return (DCFRR) method. In both methods, depreciation is inherently taken care of by calculations which include capital recoveiy. 

The ways of assessing profitabihty to be considered in this section are (1) discounted-cash-flow rate of return (DCFRR), (2) net present value (NPV) based on a particiilar discount rate, (3) eqmvalent maximum investment period (EMIP), (4) interest-recovery period (IRP), and (5) discounted breakeven point (DEEP). 

Equation (9-54) may be solved for i either graphically or by an iterative trial-and-error procedure. The value of i given by Eq. (9-54) is known as the discounted-cash-flow rate of return (DCFRR). It is also known as the profitability index, true rate of return, investor s rate of return, and interest rate of return. 

The discounted-cash-flow rate of return (DCFRR) can readily he obtained approximately hy interpolation of the (NPV) for = 10 percent and = 20 percent ... 

Discounted-cash-flow rate of return (DCFRR) has the advantage of being unique and readily understood. However, when used alone, it gives no indication of the scale of the operation. The (NPV) indicates the monetary return, but unlike that of the (DCFRR) its value depends on the base year chosen for the calculation. Additional information is needed before its significance can be appreciated. However, when a company is considering investment in a portfoho of projects, individual (NPV)s have the advantage of being additive. This is not true of (DCFRR)s. 

When considering future projects, top management will most likely require the discounted-cash-flow rate of return and the payback period. However, the estimators should also supply management with the following ... 

Number of years to reach discounted-cash-flow rates of return of, say, 15 and 25 percent per year respectively... 

Comparisons on the basis of interest can be summarized as (1) the net present value (NPV) and (2) the discounted-cash-flow rate of return (DCFRR), which from Eqs. (9-53) and (9-54) is given formally as the fractional interest rate i which satisfies the relationship... 

These (NPV) data are plotted against the cost of capital, as shown in Fig. 9-12. The discounted-cash-flow rate of return is the value of i that satisfies Eq. (9-5). From Fig. 9-12, (NPV) = 0 at a (DCFRR) of 11.8 percent for project C and 14.7 percent for project D. Thus, on the basis of (DCFRR), project D is more profitable than project C. 

Figure 9-13 is a plot of Eq. (9-61) in the form of the number of years n required to reach a certain discounted-cash-flow rate of return (DCFRR) for a given payback period (PBP). The figure is a modification of plots previously published by A. G. Bates [Hydrocarbon Process., 45, 181-186 (March 1966)], C. Estrup [Br Chem. Eng., 16, 171 (February-March 1971)], and F. A. Holland and F. A. Watson [Process Eng. Eeon., 1, 293-299 (December 1976)]. 

FIG. 9-13 Relationship between payback period and discounted-cash-flow rate of return. 

Risk and Uncertainty Discounted-cash-flow rates of return (DCFRR) and net present values (NPV) for future projects can never be predicted absolutely because the cash-flow data for such projects are subject to uncertainty. Therefore, when stating predicted values of (DCFRR) and (NPV) for projects, it is also desirable to give a measure of confidence in the predictions. 

Numerical Measures of Risk Without risk and the reward for successfully accepting risk, there would be no business activity. In estimating the probabilities of attaining various levels of net present value (NPV) and discounted-cash-flow rate of return (DCFRR), there was a spread in the possible values of (NPV) and (DCFRR). A number of methods have been suggested for assessing risks and rewards to be expected from projects. 

The same questions may then be asked for different values of the probabilities p and po. The answers to these questions can give an indication of the importance to the company of P at various levels of risk and are used to plot the utility curve in Fig. 9-25. Positive values are the amounts of money that the company would accept in order to forgo participation. Negative values are the amounts the company woiild pay in order to avoid participation. Only when the utihty value and the expected value (i.e., the straight line in Fig. 9-25) are the same can net present value (NPV) and discounted-cash-flow rate of return (DCFRR) be justified as investment criteria. 

In this equation, (DCFRR) can be viewed as the nominal discounted-cash-flow rate of return uncorrected for inflation and can be thought of as the true or real discounted-cash-flow rate of return. 

If there is no inflation, then the middle hne pertains. Because there is no inflation, the nominal (DCFRR) is equal to or identical with the real discounted-cash-flow rate of return, as can be seen from the relationship expressed in Eq. (9-113). 

It is also possible to combine (MSF) considerations with evaluation of the true discounted-cash-flow rate of return (DCFRR) by using Eq. (9-62). The relationship of Eq. (9-59) is independent of inflation if all money values are based on those prevailing in the startup year. For this case, Fig. 9-34 shows the true (DCFRR) reached in a given time, expressed as the number of elapsed payback periods for various values of the payback period. 

The method of allocating overheads can seriously affect the assigned costs of a project and hence the apparent cash flows for that project . Since these cash flows are used to assess profitability by the net-present-value (NPV) and discounted-cash-flow-rate-of-return (DCFRR) methods, unfair allocation of overhead costs can result in a wrong choice between alternative projec ts. 

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. 

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