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are not considered (i,e,, an investor will choose to invest more in an alternative with more favorable returns). This shortcoming may be corrected by applying LCOE to the incremental costs of the alternatives. The LCOE can be calculated using the following formula: Where: levelized cost of energy total life-cycle cost energy output or saved in year n discount rate analysis period. N Q, x LCOE c = TLCC,or (4-6) n=l (1 + d)” LC0E2’= ‘FECC+{c[Qni(1 +d)”]} Thus, the treatment of taxes in the TLCC calculation will carry over to the LCOE. For example, the LCOE can be calculated for the sarne example as was provided in the Total Life-Cycle Cost subsection fortheprivateinvestorseekinghisorherafter-taxcost. InadditiontotheassumptionsmadeinfieTLCC example, assume the investment produces 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. Recall fiom the previous example that the TLCC was calculated, after tax deductions, as $10,705. The remaining task is to calculate the discounted value of the annual energy output or energy saved; i.e., CNn=,[Qfn(1 + d)”]. Applying this formula to the example using a nominal discount rate of 12%,the discounted value of energy output is 3391 units. Thus, LCOE = $10,705 / 3,391 = $3.16 in current dollars. Once the TLCC is calculated, the LCOE can be figured in either current or constant dollars, regardless of the discount rates used to derive the TLCC. The form of the LCOE will be determined by the form ofthediscountrateusedinthedenominatoroftheequationCNnJQnf (1+d)”].Inthepreviousexample, a nomind discount rate was used in the denominator; thus, the resulting LCOE values are current values. For the same example, the LCOE based on a 8.74% real discount rate is $2.91 in constant dollars. It is important to note that if the system output (Q) or savings remains constant over time, the equation for LCOE can be reduced as follows: LCOE = (TLCC/Q) (UCRF) (4-7) Where: TLCC = total life-cycle cost Q = annual energy output or saved d(1 + d)N UCRF = the uniform capital recovery factor, which is equal to (1 -I-d)N - 1 “Even though it may appear in this formula that quantities are being discounted, this is actually a direct result of the algebra carried through Exom the previous formula in which revenues were discounted. 48 N nslPDF Image | A Manual for the Economic Evaluation of Energy Efficiency and Renewable Energy Technologies
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