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. [Pg.424]

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. [Pg.447]

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. [Pg.804]

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). [Pg.811]

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. [Pg.812]

The discounted-cash-flow rate of return (DCFRR) can readily he obtained approximately hy interpolation of the (NPV) for = 10 percent and = 20 percent ... [Pg.814]

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. [Pg.815]

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 ... [Pg.815]

Number of years to reach discounted-cash-flow rates of return of, say, 15 and 25 percent per year respectively... [Pg.815]

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... [Pg.815]

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. [Pg.815]

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)]. [Pg.817]

FIG. 9-13 Relationship between payback period and discounted-cash-flow rate of return. [Pg.817]

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. [Pg.821]

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. [Pg.828]

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. [Pg.828]

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. [Pg.833]

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). [Pg.834]

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. [Pg.835]

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. [Pg.837]

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). [Pg.209]

Once values have been assigned for the costs and benefits of each proposed risk-reduction modification, a variety of economic evaluation techniques may be used to choose the most attractive option. These techniques include net present value, discounted cash flow rate of return and cost-benefit ratio analyses. Most companies have a preferred method for evaluating project economics, which can be used with little or no modification. Chapter 8 of... [Pg.117]

Discounted cash-flow analysis, used to calculate the present worth of future earnings (Section 6.10.3), is sensitive to the interest rate assumed. By calculating the NPW for various interest rates, it is possible to find an interest rate at which the cumulative net present worth at the end of the project is zero. This particular rate is called the discounted cash-flow rate of return (DCFRR) and is a measure of the maximum rate that the project could pay and still break even by the end of the project life. [Pg.273]

Discounted cash-flow rate of return DCFRR % Measures performance of capital allowing for timing of cash flows No indication of the resources needed... [Pg.275]

This is found by trial-and-error calculations. The present worth has been calculated at discount rates of 25, 35 and 37 per cent. From the results shown in Table 6.8 it will be seen that the rate to give zero present worth will be around 36 per cent. This is the discounted cash-flow rate of return for the project. [Pg.278]

Calculate the cumulative net present worth of the project, at a discount rate of 8 per cent. Also, calculate the discounted cash flow rate of return. [Pg.283]

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