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Appendix B: PTC ÷ (1-τ) Mathematical Derivation 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 change in unit revenue (e.g. electricity price or real LCOE) induced by the PTC.14 In order to determine the change in unit revenue induced by the PTC, we must first define the following terms: τ = Marginal income tax rate (%), see Appendix C Rt = Revenue (cents/kWh) in year t, ITt = Income tax (cents/kWh) in year t = Rtτ, PTC = Production Tax Credit (cents/kWh) available for the first 10 years of the project, FTt = Final tax bill (cents/kWh) in year t = ITt-PTCt, and ATt = After-tax cash flow (cents/kWh) in year t = Rt-FTt. Next, we find that ATt = Rt-FTt can be reduced to ATt=Rt (1-τ)+PTCt in the following manner, ATt =Rt −FTt =Rt −ITt +PTC=Rt −Rtτ+PTCt =Rt(1−τ)+PTC. Now, to determine the change in revenue induced by the PTCt holding ATt constant to ensure that investor’s receive the same rate of return, we can define Rt’ as the required revenue in the absence of the PTC, and we can define Rt’’ as the required revenue in the presence of the PTCt. If we assume that ATt is held constant with or without the PTCt, we can determine the change in revenue using following equality, Dividing by 1 (1−τ) Or equivalently, yields, R ' (1 − τ ) = R '' (1 − τ ) + PTC tt R' =R'' + PTC t t (1−τ) R' −R'' = PTC . t t (1−τ) Thus, we find that the difference in revenue in year t (Rt’-Rt’’) with and without the PTC, while holding ATt constant, is equal to PTC . (1−τ) It is important to note that this is the maximum PTC induced unit revenue change. This value may need to be annualized over the term of the PPA depending upon project-specific conditions, and the value will be further reduced in the presence of lender imposed debt-service constraints, and/or corporate imposed Phantom Income constraints. 14 For simplicity, we have omitted debt payments, operating expenses, and tax deductions from the mathematical equations presented in this Appendix (i.e. revenue = taxable income). If these factors were included here, the complexity of the equations would be substantially increased, but the final result would remain unchanged. 13PDF Image | An Economic Valuation of a Geothermal Production Tax Credit
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