Net Present Value NPV

To evaluate the net present value (NPV) of a proposed plant, its cash flows are computed for each year of the projected life of the plant, including construction and startup phases. Tlien, given the interest rate specified by company management (typically 15%), each cash flow is discounted to its present worth. The sum of all the discounted cash flows is the net present value. The NPV provides a quantitative measure for comparing the capital required for competing processes in current terms. However, the result is usually quite sensitive to the assumed interest rate, with proposed processes changing favor as the interest rate varies. An 

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Net present value (NPV). Since money can be invested to earn interest, money received now has a greater present value than money received at some time in the future. The net present value of a project is the sum of the present values of each individual cash flow. In this case, the present is taken to be the start of a project. 

The sum of the annual discounted cash flows over n years SAdcf is known as the net present value (NPV) of the project ... 

The total undiscounted cash surplus (the ultimate cash surplus) is 190 m. The total discounted cash surplus ( 24.8 m) is called the net present value (NPV) of the project. Since in this example the discount rate applied is 20%, this figure would be the 20% NPV also annotated NPV(20). This is the present value at the beginning of Year 1 of the total project, assuming a 20% discount rate. 

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). 

Net Present Va.Iue, Each of the net annual cash flows can be discounted to the present time using a discount factor for the number of years involved. The discounted flows are then all at the same time point and can be combined. The sum of these discounted net flows is called the net present value (NPV), a popular profit criterion. Because the discounted positive flows first offset the negative investment flows in the NPV summation, the investment capital is recovered if the NPV is greater than zero. This early recovery of the investment does not correspond to typical capital recovery patterns, but gives a conservative and systematic assumption for investment recovery. 

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). 

The net present value (NPV) is found hy summing the values of Adcf for each year, as in Eq. (9-53). The net present value is found to he 276,210, as given hy the final entry in Table 9-5. 

Increasing use is being made of the capital-rate-of-return ratio (CRR), whiA is the net present value (NPV) divided by the maximum cumulative expenditure or maximum net outlay, -(S CF)max... 

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... 

For this simphfied case the net present value (NPV) after n years with money invested at a required aftertax compound annual fractional interest rate i is given by the equation... 

We shall use these data and the accompanying information of Table 9-5 as the base case and calculate for straight-line depreciation the net present value (NPV) with a 10 percent discount factor and the discoiinted-cash-flow rate of return (DCFRR) for the project with the following situations. 

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. 

Decision Trees In a typical decision tree, illustrated in a very simplified form by Fig. 9-24, each node represents a decision point (DP) at which one or more alternatives are available. Some quantifiable result of each alternative is chosen as a basis for comparison for example, the net present value (NPV). A value is assigned to the probability of attaining each result, either cumulative or not as required. These may be obtained by the methods just described or otherwise. The estimates are subject to the restriction that the sum of the proba-... 

In considering two investments, we shall let option B be a safe investment having a base net present value (NPV)g that is independent of any competition. We shall let option A yield a net present value (NPV) i if no competition exists and (NPV) 9 if competition exists. We shall then let the probabilities of no competition and competition be Pi andp2 respectively. Thenpo must equal (1 —p ). 

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. 

Let us consider a proposed project in which there is a probability pi that a net present value (NPV)i wih result, a probability p2 that (NPV)2 will result, etc. A weighted average (NPV),, known as the expected value, can then be calculated from... 

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. 

Example 13 Evaluation of Investment Priorities Using Prob-ability Calculations A company is considering investment in one or more of three projects, A, B, and C. We wish to evaluate the investment priorities if the prohahihties of attaining various net present values (NPV) are as listed in the third column of Table 9-11. Equation (9-105) gives the expected value for (NPV),. Hence for project A, (NPV), is computed from the data in Table 9-12 and found to be... 

Year, n Net capital expendihire, Atc Revenue from sales, Total expenses. Ate Cash income, Aci Depreciation charge. Ad Taxable income, Aci - Ad) Amount of tax at t = 0.5, A,t Net cash flow, Acf Discount factor at i = 10%, f. Discounted net cash flow, Adcf Net present value (NPV)... 

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. 

Cost of Capital The value of the interest rate of return used in calculating the net present value (NPV) of a project is usually referred to as the cost of capital. It is not a constant value since it depends on the financial structure of the company, the policy of the company toward a particular project, the local method of assessing taxation, and, in some cases, the measure of risk associated with the particular projec t. The last-named fac tor is best dealt with by calculating the entrepreneurs risk allowance inherent in the project i from Eq. (9-108), written in the form... 

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. 

Textbooks on investment present a simple model where the net present value (NPV) of an investment equals annual future revenues [R) summed and discounted at the rate r, minus the initial investment cost, I. Using t as a time subscript to denote different years, the equation is... 

Discounted cashflow (DCF). This method recognizes that 1,000 income in five years time is worth less than 1,000 receivable this year. The use of DCF in appraising two or more competing projects offers two methods of assessment the net present value (NPV) or DCF rate of return. 

The net present value (NPV) method is based on discounting of cash flows (DCF) to be realized in the future ... 

Economic analysis can determine the discounted profitability criteria in terms of payback period (PBP), net present value (NPV), and rate of return (ROR) from discounted cash flow diagram, in which each of the annual cash flow is discounted to time zero for the LHS system. PBP is the time required, after the construction, to recover the fixed capital investment. NPV shows the cumulative discounted cash value at the end of useful life. Positive values of NPV and shorter PBP are preferred. ROR is the interest rate at which all the cash flows must be discounted to obtain zero NPV. If ROR is greater than the internal discount rate, then the LHS system is considered feasible (Turton et al., 2003). 

Whenever the net present value (NPV) is positive this means the project will yield more money (assuming all income is invested at the given interest rate when it is received) than if the money expended had been invested at the interest rate initially. A positive value, then, means the plant appears to be a winner. If the net present... 

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