Rate of return calculations

The rate of return is often calculated for the anticipated best year of the project the year in which the net cash flow is greatest. It can also be based on the book value of the investment, the investment after allowing for depreciation. Simple rate of return calculations take no account of the time value of money. 

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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. 

Neglect interest during construction period and value-of-land effects. Note Rate of return calculations for your company must be based on discounted-cash-flow procedures to account for the time value of money. 

DISCOUNT CASH FLOW RATE OF RETURN CALCULATION... 

FORMAT (///,20X, DISCOUNT CASH FLOW RATE OF RETURN CALCULATION, /IH, 78(1H ))... 

Yield to call This method calculates the yield for the next available call date. The yield to call is determined assuming the coupon payment until the call date and the principal repayment at the call date. For instance, the yield to first call is the rate of return calculated assuming cash flow payments until first call date. When interest rates are less than the ones at issue, the yield to call is useful because most probably the bond will be called at next call date ... 

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. 

In addition, we shall calculate the discounted-cash-flow rate of return (DCFRR) with straight-line depreciation. 

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. 

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. 

Instead of using Eq. (9-113), it is unfortunately common practice to try to obtain the true or effective rate of return by calculating the nominal (DCFRR), based on actual net annual cash flows uncorrected for inflation, and then subtracting the inflation rate from it as if... 

The true rates of return L can be calculated from Eq. (9-116) to be 20, 9.09, 0, and —7.69 percent respec tively for generaf inflation rates of 0, 10, 20, and 30 percent. Thus, although the time required for a projec t with a payback period of 4 years to reach a nominal (DCFRR) of 20 percent is reduced from almost 9 years under conditions of no inflation to less than 3V2years for 30 percent inflation, the true rate of return that prevails for the latter condition is —7.69 percent, implying that the project loses money in real terms. 

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 percentage markup on cost is calculated for a known capital-turnover ratio and a desired rate of return on capital. As with absorption pricing, the percentage markup on manufac turing cost per unit of prodlic tion is calculated for a normal annual produc tion rate. If this produc tion rate is exceeded, the rate of return on capital will be higher than projected because of the decrease in unit cost. Conversely, if the... 

Using the cash flows derived from the increasing utility rates, calculating the rate-of-return would show 33.8% for a one-stage unit and 35.5% for a two-stage unit. The corresponding payback periods are 3.7 years and 3.4 years. 

Since this calculation uses trial and error to find a discount rate at which all discounted negative and positive cash flows are equal, it can be tedious without a computer. Table 3 demonstrates this calculation for a simple set of cash flows. The DCF rate of return results in a single... 

Once the economic analysis has been completed, the project should be analyzed for unexpected as well as expected impacts on the economics. This is usually done through a set of what if calculations that test the project s sensitivity to missed estimates and changing economic environment. As a minimum, the DCF rate of return should be calculated for 10% variations in capital, operating expenses, and sales volume and priee. 

There are various indicators to determine the measure of profit for a process. In the following, we describe two of these indicators return on investment and payout period. The rate of return on investment (ROI) may be calculated as follows ... 

Capital investments can also be selected on the basis of other measures of performance such as return on investment, internal rate of return, and benefit-cost ratio (or savings-to-investment ratio). Flowever, care must be taken in the application of these methods, as an incremental analysis is required to ensure consistent comparison of mutually exclusive alternatives. Also, rather than requiring a separate value to be calculated for each alternative, as in the case of the life-cycle cost method, these other methods incorporate the difference between two mutually exclusive alternatives within a single measure. For example, the net benefits measure directly pressures the degree to which one alternative is more economically desirable than another. 

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. 

Rate of return. A rate of return is calculated on the profits remaining after the initial outlay has been written off. This method suffers from the same defect mentioned in (1) above and from the use of arbitrary periods for the writing down of the initial expenditure and of arbitrary rates of interest for the calculation of the rate of return. 

Calculation document (Figure 61.5). This document provides a means of calculating the DCF rate of return or a net present value where these are required, usually where profitability of the project is of major concern. 

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. 

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. 

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. 

Calculate the expected rate of return for a plant that has a present value of — 18,000,000 at startup. The proceeds are expected to be ... 

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. 

A stock that sells for 84 has annual dividends of 2.80. It is expected that the value of the stock and the amount of the dividend will increase 5% per year. Calculate the rate of return paid by the company for issuing stock. 

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. 

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

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. 

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