Rates of return

Like NPV, internal rate of return (IRR) is a quantitative method used for project selection. IRR is popular among managers because it is easy to use. Unlike selecting a discount rate for NPV analysis, IRR is the discount rate that forces NPV to equal 0. If an analyst tries to find a discount rate using trial and error for an NPV calculation to make the present value of future cash flows 0 (NPV = 0), this discount rate would be the IRR. 

Using the previous NPV example, IRR equals 36.31%. If a discount rate of 36.31% was assigned for the previous NPV example, NPV would equal 0. 

Projects should be pursued if IRR is greater than the required rate of return, which encompasses the cost of capital and project risk. The required rate of return is also referred to as the hurdle rate. If IRR hurdles or is higher than the required rate of return, the project should be selected. Hurdling the required rate of return implies that there will be a surplus of funds after repaying the capital. The surplus of funds creates wealth for shareholders. 

IRR does have drawbacks. One disadvantage of using IRR is that it assumes all cash flows will be reinvested at the projects IRR (discount rate). In reality these rates fluctuate, especially with longer term projects. IRR can be modified to mitigate this shortfall. Modified internal rate of return (MIRR) assumes that all cash flows are reinvested at the company s cost of capital, which is a more realistic view. IRR has another drawback when cash flows turn positive and negative multiple times over the life of the project, as is the case for long-term projects, IRR does not provide an accurate picture. 

So far examples have focused on independent projects. Independent projects are those whose cash flows do not affect one another. Mathematically, the NPV and IRR calculations will lead to the same accept or reject conclusions in these instances. Logically, one would choose the projects with positive NPVs or rank the projects first and select the projects with the highest NPVs. Likewise, projects with IRRs above the hurdle rate would be chosen or the projects would be ranked and the projects with the highest IRRs above the hurdle rate selected first. 

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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. 

Keywords economic model, shareholder s profit, project cashflow, gross revenue, discounted cashflow, opex, capex, technical cost, tax, royalty, oil price, marker crude, capital allowance, discount rate, profitability indicators, net present value, rate of return, screening, ranking, expected monetary value, exploration decision making. 

If the company is fully self-financing for its new ventures, then the appropriate discount rate would be the rate of return of the alternative investment opportunities (e.g. other projects) since this opportunity is foregone by undertaking the proposed project. This represents the opportunity cost of the capital. It is assumed that the return from the alternative projects is at least equal to the cost of capital to the company (otherwise the alternative projects should not be undertaken). 

The IRR column is the internal rate of return of the project at the relevant oil price, and is a measure of what discount rate the project can withstand before the NPV is reduced to 0. This indicator will be discussed in a moment, but is included here as a recommended part of this presentation format. 

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). 

Another useful profitability indicator is the internal rate of return (IRR), already introduced in the last section. This shows what discount rate would be required to reduce the NPV to zero. The higher the IRR, the more robust the project is, i.e. the more risk it can withstand before the IRR is reduced to the screening value of discount rate. Screening values are discussed below. 

Option Investment Sale Return Rate of return... 

Option A has the lowest investment at risk, B has the highest rate of return on investment, and C has the highest return. In general, the objective would be to maximize either the rate of return or the return, within the limits of available investment funds. 

Before a decision is made, all three items, ie, investment, return, and rate of return, would be examined, as would the current cash position, perceived risk, other venture opportunities, and a variety of subjective criteria. Eor this elementary situation, economists would also employ an incremental approach analogous to the above, based on the tenet that each increment of investment should itself make an adequate return. Rarely is there a unique correct decision. Only future events determine the wisdom of the selection even then, the results that another decision would have produced are rarely known. This is the essence of profitabiHty analysis. 

In multiyear process ventures, the money flows are more compHcated and must be discounted to a common point in time before they can be combined. However, the three basic parameters, investment, return, and rate of return, should be retained in some logical and consistent manner. 

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. 

Fig. 3. Profitabihty diagram for Venture A. (a) Simple diagram. NRR is net return rate IRR, the internal rate of return, is a given fixed point, (b) Three NRR cutoff lines for Venture A where B, C, and D represent NRR values of 15, 10, and 5%/yr, respectively. For example, at a discount rate of 10% per year, the NRR cutoff for Venture A could be as high as 10.74% per year for marginal acceptance (point X). Acceptable levels are to the left of NRR cutoff...

Capital ratio defined by Eq. (9-134) Capital-rate-of-return ratio defined by Eq. (9-56)... 

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. 

FIG. 9-1 Relationship between annual costs, annual profits, and cash flows for a project. A d — annual depreciation allowance Acf — annual net cash flow after tax Ac/ = annual cash income Age = annual general expense Aqp = annual gross profit A/r = annual tax A e = annual manufacturing cost Avc/ = annual net cash income Avvp = annual net profit after taxes A/ p = annual net profit As = annual sales Apc = annual total cost (DCFRR) = discoiinted-cash-flow rate of return (NPV) = net present value. 

Rate-of-Retttrn Methods Although traditional rate-of-return methods have the advantage of simplicity, they can yield veiy misleading resiilts. They are based on the relation... 

The fractional interest rate of return based on the net annual profit after tax and the original investment is... 

AbdICtc is arbitrarily assessed. Its value will affect the fractional rate of return considerably and may lead to erroneous conclusions when making comparisons between different companies. This is particularly true when making international comparisons. 

FIG. 9-6 Effect of straight-line depreciation on rate of return for a project. Abd — annual depreciation allowance A c/ = annual net cash income after tax Awwp = annual net profit after payment of tax Cj = total capital cost. 

FIG. 9-7 Effect of douhle-declining depreciation on rate of return for a project. 

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. 

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... 

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. 

From the difference in cash flows between the projects, the dis-counted-cash-flow rate of return (DCFRR) for project (J-K) can be shown as 12.4 percent. This is significantly lower than for either project J or project K. Thus, if the 3000 can be invested to give a return greater than 12.4 percent, project K should be chosen in preference to projertj. 

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. 

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. 

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