A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies

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A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies ( a-manual-economic-evaluation-energy-efficiency-and-renewable )

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at an assumed inflation rate of 3% per year thereafter; the investment is not replaced; 5-year double- declining depreciation schedule; a marginal federal income tax rate of 34%; no state income tax; production of 1000 units of energy in the first year of operation, 950 in the second, 925 in the third, and 900 in the fourth and fifth;and energy sold for $10 a unit in year zero, inflating at 3% per year thereafter. Year investment (4 0 $ 10,000 1 0 2 0 3 0 4 0 5 0 O&M Costs (b) $0 1,339 1,379 1,421 1,463 1,507 Revenues (c) Table 4-10. After-Tax IRR Net Taxable Federal Income Tax (9 = e x tax $ 1,687 2,142 2,464 2,580 2,668 After-Tax Cash Flow (9) = (c-a-b-9 7,274 6,558 6,223 6,087 6,259 Depreciation (d) 10,30Q 10,079 2,400 10,108 1,440 10,130 1,080 10,494 1,080 Income ( 0 ) = (eb-d) $I 4,961 6,300 7,247 7,587 7,847 An IRR equal to 61% is calculated when the formula is applied to the after-tax cash flow scenario (successive approximation methods can be used to find the rate that equates the present value of cash flowstozero). Inotherwords,thepresentvalueofthisafter-taxcashflowscenarioiszeroifadiscount rateof61%isassumed. Inthisscenario,iftheinvestor’shurdlerateishigherthan61%,thentheinvestor will more thanlikely invest his or her money elsewhere; whereas, if the hurdle rate is lower than 61%, the investor may view the investment as a good opportunity. It is also important to note that the 6 1%IRR is actually the nominal IRR and should be stated as such. This is the case because the cash flows on which the IRR was calculated were in current dollars. If the dollars had been constant, the IRR would have been a real IRR. The equation for IRR is a polynomial of degree N and, as such, the analyst must be aware that there are N different roots, or solutions, to the equation. However, when the investment pattern is normal (i.e., the initial investment or cash outflow is followed by a stream of cash inflows), all solutions are either negative or imaginary, except for one positive solution, On the other hand, if the cash flow is such that large outflows occur during or near the end of the life of the investment, then the possibility of multiple positive roots arises (Palm and Qayum 1985). Because of the complexity of the required calculations and multiple potential roots, some software for personal computers requires a guess at the IRR prior to calculation (Lotus 2991). For situations in which there is a close approximate value, this poses little difficulty to the analyst. However, when the analyst does not have an approximate value, this could pose a problem and add doubt to the results. IRRanalysismaynotfullyconsiderthepatternofinvestmentsandreturnsovertime. Forexample,two investment projects with an IRR of 17% might be considered equal, but if there are different analysis periods for the two projects (e.g., 20 years for project A and 3 years for project B), a decision maker mightnotbeindifferentregardingthechoiceofAorB. Thatis,aninvestormayfindasustained20-year revenue stream at 17% more desirable than a 3-year payment flow at the same rate. 53 4,000

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