The Net Present Value and Rate of Return

CASE STUDY THE NET PRESENT VALUE AND RATE OF RETURN FOR A 150,000,000 LB/YR POLYSTYRENE PLANT USING THE SUSPENSION PROCESS 

An interest rate of 8% will be chosen. The fixed capital charges are assumed to have occurred a year before plant startup. The working capital costs occur during 

Fixed capital estimate by Guthrie s method = 13,000,000 Working capital = 2,969,000 

If the plant operates at full capacity for 11 years, the net present value in 1975 is  

The same assumptions are made as those given above for the net present value calculations. The rate of return is 13.3% after taxes. 

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Various other evaluation schemes based on the concept of time value of money are also sometimes used. These, together with the Net Present Value and Rate of Return methods, are all grouped together under the title of discounted cash flow methods. 

The calculations of the return on the investment and payout period follow. Those for the Net Present Value and Rate of Return are given following Chapter 11. 

Discounted cash flow diagram can determine the profitability criteria in terms of the payback period, net present value, and rate of return from. In the discounted cash flow diagram each of the annual cash flow is discounted to time zero for the latent heat storage system. The payback period is the time required, after construction, to recover the fixed capital investment. The net present value shows the cumulative discounted cash value at the end of useful life. Positive values of net present value and a shorter payback period are preferred. The rate of return is the interest rate at which all the cash flows must be discounted to obtain zero net present value. If rate of return is greater than the internal discount rate, then the latent heat storage system is considered feasible. 

The following example illustrates the effects of inflation on borrowing funds. This analysis is similar to any contract signed for future services because the cash flows are agreed upon and therefore represent out-of-pocket expenses. Thus, by definition, these expenses are actual doUar cash flows. The following example illustrates the required calculations to determine the net present value or rate of return for a project. 

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)... 

For a given discount rate, calculate the discount factor during the operating life of the project. Multiply the discount factor by the cash flow and obtain the net present value and the net return rate. Valle-Riesta [8] has listed alternative methods of calculating cash flow, as shown in Table 9-6. 

Be able to compute cash flows and depreciation, and use them to project the net present value and investor s rate of return (IRR) (also known as the discounted cash-flow rate of return, DCFRR), two measures that account for projections of revenues and costs over the life of the proposed process, and the time value of money. 

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. 

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... 

Example 3 Sensitivity Analysis The following data describe a project. Revenue from annual sales and total annual expense over a 10-year period are given in the first three columns of Table 9-5. The fixed-capital investment Cfc is 1 million. Plant items have a zero salvage value. Working capital C c is 90,000, and the cost of land Ci is 10,000. There are no tax allowances other than depreciation i.e., is zero. The fractional tax rate t is 0.50. For this project, the net present value for a 10 percent discount factor and straight-line depreciation was shown to be 276,210 and the discoiinted-cash-flow rate of return to be 16.4 percent per year. 

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. 

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... 

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. 

Where the calculation of the net present value was straightforward, die determination of the rate of return requires a trial-and-error procedure. An interest rate is chosen and then the net present value is determined. If it is not zero, another interest rate is chosen and the net present value is recalculated. This is continued until a zero net present value is obtained. 

Both methods assume that the money earned can be reinvested at the nominal interest rate. Suppose the rates of return calculated are after tax returns and the company is generally earning a 5% or 6% return on investment. Is it reasonable to expect that all profits can be reinvested at 23% or even 20% No, it isn t Yet this is what is assumed in the Rate of Return method. Sometimes the rate of return may be as high as 50%, while a reasonable interest rate is less than 15%. Therefore if a reasonable value for the interest rate has been chosen (this is discussed later in this chapter) and the two methods differ, the results indicated by the Net Present Value method should be accepted. 

Upon decreasing the bond sales in Example 10-20 by 100,000, two interest rates greater than zero would be obtained for which the net present value is zero. This would indicate that as long as the interest rate is not between die two values the project should be accepted. Other examples could be constructed where only if the interest rate is between the limits should it be accepted. There also could be more than two points, or no points, where the net present value is zero. If there are incomes and expenses over 8 years the equation that determines the rate of return has 8 roots. Theoretically all, some, or none of these could be positive. 

Some writers claim that an advantage of the Rate of Return method is that no interest rate needs to be chosen. It has already been illustrated that this is not true. The difference in the two measures is when, not whether, a reasonable interest rate is chosen. With the Rate of Return method it does not need to be chosen until after the rate of return is obtained. If it is too high and two processes are both found acceptable, then the net present value must be calculated to determine which is best. In doing this the interest rates for proceeds and outlays may be different. 

Since different values are usually obtained for the cost of money and the minimum return on the investment, it is desirable to use both. The former is used to determine the present value of all outlays and the latter to determine the present value of all incomes. If a positive net present value is obtained, this is an acceptable project. Then if a modified rate of return is determined, an idea can be obtained of how much better than merely acceptable it appears. This can be obtained by using the cost of money to determine the present value for all outlays and determining the interest rate for proceeds that will make the net present value zero. The advantage of the modified rate of return is that it evaluates outlays at a realistic rate. 

Calculate the net present value assuming money is worth 8% and rate of return for the following stocks in 1923 knowing the following data. Assume no dividends were paid (which is false). 

The obvious time to use computers is when some calculation is repeated over and over again. This can be in a trial-and-error calculation such as the calculation of the rate of return. As noted in Chapter 10, the best way to do this is to assume an interest rate, perform the calculations, and determine whether the net present value is zero. If it is not, another choice is made, and the net present value for this choice is calculated. This procedure is repeated until the desired answer is obtained. 

Whenever the same series of calculations is repeated a number of times, even with different sets of data, the use of a computer should be considered. For instance, the calculations of the net present value is very straightforward. It can easily be done using tables, a calculator, and/or a slide rule. However, it can also be done on a computer, and this would relieve the engineer of the responsibility of repeatedly performing the calculations. This will give him some time to analyze and compare the results. Besides this, he can also obtain from the same data the payout period and the return on the investment. He could even combine this with the program for the rate of return, and obtain all the major economic indicators for the same effort previously required to obtain any single one. 

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... 

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 ... 

Finance make projections of yearly cash flow on costs and revenues for your design, compute its net present value and internal rate of return. How do the proposed products rank in project return and security, and in corporate risk diversification ... 

Detailed economic considerations are the subject of process design courses, where you will learn about net present value, cash flow, and rate of return. Here we are concerned only with technical aspects of design such as achieving maximum production of a particular product with rniriimum reactor volume or designing a reactor with rninimrim heat input required The costs associated with these options and separation costs before and after the reactor obviously must be included to achieve maximum profit in a chemical process. 

Three methods are used to assess the value of a capital investment. They are cash payback, net present value, and internal rate of return (also known as Discounted Cash Flow-Rate of Return). 

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. 

Check the values given for the discounted-cash-flow rate of return and net present worth. If the company requires a minimum rate of return of 10 percent, which system should be chosen ... 

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