A major advantage of the annual rate of return method is that it considers the time value of money.

Internal Rate of Return

The internal rate of return (IRR) is a rate of return on an investment. The IRR of an investment is the interest rate that gives it a net present value of 0, or where the sum of discounted cash flow is equal to the investment. The IRR is calculated by trial and error.

IRR is the best method to evaluate the economic side of an investment, because it allows a good comparison with other investment projects and financial alternatives (bank account, stocks, real estate):

X0=X1/(1+r)+X2/(1+r)2+…+Xn/(1+r)n

If the initial cash outflow occurs at time 0, it is represented by the interest rate r.

Let us perform an exercise in the IRR method. We evaluate the furnace project of the Surge Arrester Company using the internal rate of return method.

Furnace A provides a yearly constant cash flow:

Investment sum: $1,000,000

Utilization period: 8 years

Mean annual revenue: $1,150,000

Mean annual costs: $625,000

Overhead costs: $240,000

From this a payback time of 3.5 years and an annual net income of $285,000 can be calculated. According to definition, the internal rate of return is the interest rate, for which

Investment sum=Discounted cash flow

In our example, this means

1,000=285×∑n=18(1+k/100)n

3.5=∑n=18(1+k/ 100)n

With the use of a table of discounting factors (Table 7.13) and a graphical representation (Figure 7.17), this leads to an IRR of 23%.

Table 7.13. Discounting Factors for Several Interest Rates and Years

Furnace B provides varying cash flows:

Investment sum: $1,600,000

Utilization period: 10 years

Annual revenue:

Year 1–6: $1,150,000

Year 7–10: $1,380,000

Annual costs:

Year 1–6: $550,000

Year 7–10: $660,000

Overhead costs: $300,000

For this case, the calculation has to be done by iteration, starting with a realistic value of the interest rate. If the discounted cash flow is lower than the investment sum, the calculation has to be repeated with a lower interest rate. Let us start with a 16% interest rate in the first iteration. The annual net income I is for

Years1-6:I=1,150,000-550,000-300,000=$300,000

Years7-10:I=1,380,000-660, 000-300,000=$420,000

Table 7.13 shows the discounting factors for the interest rates and number of years relevant for this example. Using this table and assuming an interest rate k = 16% gives Table 7.14.

Table 7.14. Discounting Factors (DFs) at k = 16%

An analogous calculation with k = 15% yields a surplus of $54,000. Comparing the two results shows that the actual interest rate is closer to 16%. We can now compare the two furnaces and see that furnace A with an IRR of 23% is clearly more attractive than furnace B with an IRR of 16%.

Modified Internal Rate of Return (MIRR)

To resolve the potential conflicting ranking of projects by the NPV and the IRR methods, project analysts resort to the use of modified internal rate of return (MIRR). The MIRR accounts for different reinvestment rates, and it is recommended for multiple projects ranking especially mutually exclusive projects.

The MIRR is defined as the discount rate that forces the total initial investment to be equal to the present value (PV) of terminal (future) value compounded at the firm's cost of capital r%.

MIRR is determined by considering all cash inflows realized (positive inflows FPt in year t) before the end of useful life period N are reinvested at firm's discount rate r% until the end of the period (FPt(1 + r)N − t), and this amount is then discounted to the base year with the MIRR discount rate to equate to all discounted cash out flows (negative cash flows in year n FNt) at r%:

(8.30)∑t=0TFNt1+rt=∑t=0TFPt 1+rT−t1+MIRRT

where MIRR avoids the problem of multiple IRRs but can still produce conflicting results in ranking mutually exclusive projects with differing sizes. The NPV should be used in such a case.

6.5.10 Internal rate of return

This method calculates the rate of return that an investment is expected to yield. The IRR method expresses each investment alternative in terms of a rate of return (a compound interest rate). The expected rate of return is the interest rate for which total discounted benefits become just equal to total discounted costs (i.e., net present benefits or net annual benefits are equal to zero, or for which the benefit/cost ratio equals one). The criterion for selection among alternatives is to choose the investment with the highest rate of return.

The rate of return is usually calculated by a process of trial and error, whereby the net cash flow is computed for various discount rates until its value is reduced to zero. The IRR of a project is the discount rate, which makes its NPV equal to zero. It is the discount rate in the equation:

IRR=0=(CF_0)/〖(1+K)〗^0+(CF_1) /〖(1+K)〗^1+…….+(CF_ n)/〖(1+K)〗^n=∑_(t=0)^n(CF_t)/〖(1+K)〗^t

Internal Rate of Return

In most instances, the primary criteria for judging the relative merits of proposed investments should be internal rate of return (IRR). The rate of return criterion can be applied using several different methods of computation and should use compound interest methods. The IRR method of analysis has the advantage that it is more universally used and therefore comparison of energy management uses of available funds can be compared directly with competing uses of funds such as increased production, improved company operating efficiency, or manufacturing cost reduction schemes. No matter how intrinsically satisfying it may be to save energy costs by reducing energy use, corporate decision makers must choose between competing uses of funds based on maximizing return on the investments of available company monies.

The previous types of economic analysis assumed an interest rate or minimum attractive rate of return. It may be more appropriate to compute a prospective rate of return on investment and compare this with the previously assumed interest rate or some other company standard.

The calculation can be done with a computer program or a spreadsheet program, or by a trial-and-error method to find the interest rate at which the present worth of the net cash flow is zero. Specifically, the process involves assuming two or more interest rates, calculating the present worth (or equivalent annual cost), and using interpolation or a graphical method to find the rate of return. The example in Table 13.9 shows the procedure for two electric motors with equal lives. Note that we first calculate the net cash flow for each year of the investment (minus signifies net cost, plus signifies net savings). Then we calculate the present worth based on various estimated interest rates. The present worth factors are found by looking them up in handbooks or an online reference, or by calculating them for the particular interest rate and period using the following expression: Uniform Annual Series Present Worth Factor=[(1+i)20−1]/[i(1+i)20].

Table 13.9. IRR analysis

Note: UASPWF refers to uniform annual series present worth factor.

This IRR analysis example shows that purchasing motor B rather than A will result in a 24.9% return on investment. From a corporate standpoint, the decision to proceed with this energy management option must be weighed against the returns of other options and other possible investments that are currently available to the firm.

In this case, we simplified the analysis by assuming the annual costs were uniform. For a nonuniform series of expenses, the analysis would be as shown in Table 13.10.

Table 13.10. Nonuniform annual cost example (US$)

The calculation has been truncated at 4 years for convenience. Normally it would be continued for the life of the project. Note each project outflow is listed as a negative (net expense) and any savings as a positive. Then each line item is converted to a present worth using a present worth factor and assumed interest rate for that year. Then the total gives the net present value. At 0% interest, the net present value is positive. Trying another rate, 10%, the net present value turns negative, so we know the IRR for the first 4 years of this investment is between 0% and 10%. Trying 5%, the result is still negative. With one final iteration (not shown), we find that with an IRR of 3%, the net present value is zero. If the series was extended to year 10 and beyond, the savings would grow and the IRR would increase.

4.2. Comparison of the methods

The payback method has the virtue of simplicity. The calculation is admittedly simple, but it is less apparent that this is a virtue since there are very serious deficiencies associated with its use. First, it does not consider the time pattern of receipts. Second, it takes no account of any earnings that may accrue to a project after the expiration of the payback period. It favors, therefore, short-term projects and ignores the possibility of long-term growth in profits. In fact it is not a profitability criterion but the embodiment of a liquidity concept; that is, it is concerned with the rapid recovery of outlays. However, where liquidity, rather than profitability, is an important business consideration the method has merit. It may also have some merit as an initial screening method. However, the most important deficiency of the method compared to the discounting methods (NPV, IRR, AM) is that it favors projects that yield immediate profits.

Concerning the differences between the various discounting methods, we have on the one hand the NPV and the AM methods, which consider the total savings, and on the other hand the IRR method that provides the return in relation to initial outlays. In the evaluation of investment opportunities two types of decisions must be made: the formal accept/reject decision and the ranking of alternative projects. In the first case the two discounting criteria produce identical answers. All projects that have yield in excess of the cost of capital must have a positive NPV when discounted at the marginal cost of capital. In other words, all projects accepted on an NPV basis have a discount rate higher than that given by the marginal cost of capital to reduce their NPV to zero. When the decision is one of ranking, however, they may not give the same results. It has frequently been argued that the IRR method does not rank projects in their true order of profitability. The reason for this is that the NPV method and the AM show absolute figures, whereas the IRR is related primarily to the amount of capital involved and the duration of the investment period. That is, a project may have a high rate of return in relation to initial investment but might yield a low absolute amount of profit. It may be argued that most decisions will be of the accept/reject type, in which the additional information generated by the NPV method will be irrelevant. However, there are situations in which the ranking projects become important, for instance, when capital rationing prevails, or when mutually exclusive choices are encountered. The term ‘capital rationing’ is used to describe a situation in which a firm cannot raise capital beyond a fixed limit. In this case the true opportunity cost of capital is clearly in excess of the market rate. Under these conditions it is impossible to calculate a well-defined cost of capital with which to evaluate projects on an IRR basis. The majority of economists also consider the NPV method to be superior. The reason for this preference is profit maximization for the investment. Therefore, the projects that produce the highest NPV, which are not necessarily those with the highest IRR, should be ranked higher.

Concerning the relative merits of the different methods from an ergonomic standpoint, there is insufficient information. Westlin (1989) suggests that the payback method should be limited to projects with a short economic life. This is because ergonomic measures normally take a long time to yield results. Therefore, he suggests using the NPV method. However, the higher the discount-rate, the more the long-term solutions discounted by the NPV method are discriminated (see Part 1, Table 3). There is also a lack of studies investigating the influence of ergonomic measures on accidents and diseases as a function of time. In comparison with the IRR method, the NPV method (and the Annuity Method) favor projects that produce the highest absolute amount of money. These projects are not necessarily those with the highest IRR. Since ergonomic solutions are often unique the IRR method seems preferable to other methods, at least in ranking with other types of project. However, most economists recommend the use of several quantitative methods in investment appraisal.

TECHNICAL FEASIBILITY

The technical evaluation determines whether a proposed waste minimization option will work for a specific application. The evaluation often begins with an examination of the impact of the proposed measure on process, product, production rate, safety, etc. In case there is significant deviation from the present process practices, laboratory testing and trial runs might be required to assess the technical feasibility. A typical checklist for technical evaluation is provided in Worksheet 9.

The measures which are technically not feasible due to non–availability of technology, equipment, space or any other reason should be listed separately for future studies by technical personnel. Technically feasible measures should next be subjected to an economic analysis.

Economic Viability

Economic viability often becomes the key parameter for the management to accept or reject the proposed waste minimization measure. For a smooth take–off, it is essential that the first few waste minimization measures to be reported to management are economically attractive. Such a strategy helps in creating more interest and commitment. The economic analysis can be conducted using a variety of methods, for example, the payback period method, internal rate of return method, net present value method, etc. For low–investment, short–duration measures with attractive economic viability, the simplest—the pay back period method—is usually good enough.

A typical worksheet (Worksheet 10) which would help in working out techno–economic viability is given. It may have to be modified to suit the different options, but care should be taken to keep it as simple and transparent as possible.

Worksheet 10. Economic Viability Analysis

Even measures which are not economically viable should not be dropped out. It could be possible that some of these options might have a significant impact on the environment and may, therefore, warrant implementation even if they are economically unattractive.

3.0 ECONOMIC EVALUATION TECHNIQUES

As mentioned previously, five techniques are widely used in evaluating solar energy and conservation investments: (1) total life-cycle cost analysis (TLCC), (2) net benefit (savings) analysis (B-C), (3) the savings-to-investment (SIR) or benefit-cost (B/C) ratio method, (4) the internal rate of return method (IRR), and (5) the discounted payback method (DPB). All of these techniques take into account the timing of cash flows and the associated costs of money, and all, except the discounted payback method, evaluate benefits and costs over the life cycle. The first four techniques are, comprehensive techniques of economic analysis that can be used to evaluate investments in solar energy and conservation systems, taking into account their high first costs and their savings spread out in the future and changing in amount over time. The fifth technique, the discounted payback period method, is included even though it does not take a comprehensive life-cycle approach. This technique is included because designers sometimes have clients who require a rapid turnover of their investment fund and may request the use of a payback techniques.

Each of these five techniques is defined below, both verbally and in abbreviated algebraic form. Following the definitions, the advantage and disadvantages of each technique are discussed, and recommendations are given for the appropriate uses of each technique.

The cost of money is included in each of the five techniques through a process called discounting. This process is described later on. In the following descriptions of techniques, for simplicity, the algebraic discounting expressions are not shown explicitly. Similarly, the detailed algebraic expressions required to account for tax effects and incentives are not shown. The emphasis here is distinguishing among the five techniques in their particular method of benefits and costs to derive a measure of the economic attractiveness of an investment.

11.10.4 Financial justification

The type of economic analysis used will often be a matter of company policy and may involve an evaluation of return on investment or discounted cash flow, but, in practice, most assessments are based on the simple payback period.7 In the case of structural steel fabrication, the labour cost often accounts for the major part of the total cost of welding. The primary cost savings are therefore associated with improvements in the operating factor for the process (the ratio of effective to non-effective time) and the consequent reduction in labour cost. For example, a manual GMAW operator may achieve an operating factor of 15–20%, whereas, with a tractor-mounted system, an operating factor of 30–40% may be possible and fully automated systems are likely to achieve 80–90%. Secondary cost savings can also be expected from improved control of weld size; which, in turn, saves time, reduces consumable costs and improves control of operating technique; which produces more consistent quality, reduces defect levels and decreases repair costs. A preliminary evaluation of the economic factors associated with the automation of a given application is straightforward, particularly if one of the many commercial weld-costing software packages8 is used. Examples of simple cost comparisons made with the NIL COSTCOMP software are shown in Table 11.2 and Fig. 11.10: a comparison of manual and mechanized welding approaches to one of the most common weld configurations is shown in Table 11.2. The cost of the simple tractor involved would be recovered after only 315 m of weld had been performed. In the same way, the high cost of a dedicated CNC unit may be offset by improvements in operating factor and improvements in quality (reduction in reject and repair rate).

Table 11.2. Example of costing spreadsheet output showing the influence of £20000 investment in welding automation on the cost of making a butt weld in steel with GMAW, 1.0-mm-diameter filler wire. The left-hand column shows the original cost for manual GMAW, and the right-hand column shows the estimated effect of automation on the capital cost, operating factor (arc on time) and weld quality (rejection rate). The totals show the reduced cost per weld and increased productivity to be expected.

3.2.4 IRR approach

Internal rate of return (IRR) method also considers the time value of money. It is used to study an investment project by comparing the internal rate of return to the minimum required rate of return of the project [49]. Morrone et al. [49] implemented the financial analyses of energy pile systems over 20 years of operation in Naples and Milan, Italy. The main economic indicators including the NPV, IRR and Profitability Index (PI) are given as:

(56)∑k=1DPBSk(1+i)-k=OC

(57) NPV=∑k=1N-1Sk(1+i)-k-OC

(58)0=∑k=1N-1Sk(1+IRR)-k-OC

(59) PI=NPVOC

where Sk is the economical saving per annum (€/year); OC is the whole expense of the alternative system to the conventional one (€); i is the yearly discount rate (%).

Fig. 44 presents the yearly savings of the horizontal GHP at different discount rates of 2.5%, 5% and 7.5% in Naples and Milan for 20 years’ operation. The NPV trend in Naples is similar to the one in Milan, but the economic performance in Milan is much better than that in Naples. Specifically, in Milan, the PI is 243% in terms of a discount rate of 5%, which stands for a wonderful economic performance, and the IRR shows a high value of 28.2%, by contrast in Naples, the PI of the investment with a discount rate of 5% is around 70%, which indicates the IRR index is equivalent to 12.4% displaying that the margin of revenue is quite limited [49].

Ghoreishi-Madiseh and Kuyuk [50] implemented an economic analysis of the GHP by means of the NPV and IRR methods.

The NPV is written as:

(60)NPV=∑t=0nCFt(1+IRR)t

where CFt is the cash flow at time t (£); IRR is the interest rate (%); n is the years of operation (year).

Fig. 45 describes the influences of heat pump COP on the IRR and NPV values. The IRR is largely a discount rate that brings the NPV to zero, thereby the IRR is able to be calculated by an NPV versus discount rate curve as shown in Fig. 46 [51]. These results conclude that the predictable growth rates that vary from 25.6% to 33.5% are higher than the said discount rate (15%), which discloses the proposed deployment scheme of the GHP should be quite attractive in terms of the investment perspective.

3.2 Assessment methods and economic parameters

This study employs three economic evaluation approaches according to China's the Economic evaluation methods and parameters of construction projects (third edition) [57]: net present value method, internal rate of return method, and minimum biodiesel sale price when the animal feed sale price is set and the net present value equals 0.

Net present value represents the economic competitiveness of a project. When using the net present value method to evaluate a project, the profitability result of the project depends, to a certain extent, on the selected discount rate. In this study, the weighted average cost of capital cost method is used to calculate the discount rate and is expressed as follows:

(1)WACC=KeE E+D+KdEE+D,

where WACC is the weighted average capital cost and equals the discount rate; Ke is the equity cost, Kd is the debt cost, E is equity and D is debt. Ke and Kd are calculated as follows:

(2)Ke=Rf+R,

(3)Kd=Rf+R+Rm,

where Rf is the risk-free interest rate, R is a company's credit, and Rm is market risk premium. According to Eqs. (1)–(3) and parameters in Table 4, the discount rate is 7.34%.

Table 4. Main economic parameters.

This study adopts economic parameters from existing studies to evaluate the economic feasibility of microalgae biodiesel. The inflation rates for 2015, 2016 and 2017 are 1.44% [58], 2.01% [58] and 1.55% [59] respectively. Table 4 presents the main economic parameters.