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Appendix D: Maximum Annualized PTC Value When projects are engaged in PPAs that have a longer term than the 10-year period over which the PTC is available, then the PTC induced unit revenue reduction (e.g. the change in electricity price with and without the PTC) is annualized over the length of the PPA. In these cases, the PTC induced unit revenue reduction will be less than PTC ÷ (1-τ). To determine the annualized revenue reduction value of the credit (ignoring financing limitations),16 we first compute the present value of the credit, PV(PTC). Since the credit is available for 10 years, we can calculate the present value as, Where, 10PTC 1 PV(PTC)="i=1(1−τ)x(1+dr)i , τ = Marginal income tax rate (%), PTC = Production Tax Credit (cents/kWh) available for the first 10 years of a project’s life; and dr = the real discount rate used for LCOE calculations. This can be simplified to, PTC 10 1 PV(PTC)= (1−τ)"i=1(1+dr)i . If we let dr = 5.6%, if we let PTC = 1.8 cents/kWh, and if we assume that τ is 40% then, 1.8 10 1 PV (PTC) = (1 − 0.40) "i=1 (1 + 0.056)i ≈ 3.0x7.49 ≈ 22.5. We can annualize this value over the PPA term by multiplying the PV(PTC) times the Uniform Capital Recovery Factor (UCRF) which is defined as, UCRF = dr (1+ dr )N (1+dr)N −1 Where N = the length of the PPA. If we assume that N=15, in accordance with the examples presented in this report then, 15 UCRF=0.056r(1+0.056) ≈10.1%. 15 (1+0.056) −1 We can now calculate the annualized present value of the credit, APV(PTC), as, APV (PTC) = PV (PTC)xUCRF APV (PTC) = 22.5x0.101 APV (PTC) ≈ 2.3. Thus, we can see that, under these assumptions, the annualized revenue reduction value of the PTC is approximately 2.3 cents/kWh. 16 The actual results presented in the main body of this report were developed using a detailed cost of electricity spreadsheet model. However, for illustrative purposes, in this Appendix we present a mathematical derivation of the annualization of the PTC-induced change in unit revenue. 15PDF Image | An Economic Valuation of a Geothermal Production Tax Credit
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