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Appendix C: Derivation of τ In order to determine the appropriate tax rate, τ, to be used in calculating the before-tax PTC value, PTC ÷ (1-τ), we must first define the following terms: f = Marginal federal income tax rate (%), s = Marginal state income tax rate (%), Rt = Revenue (cents/kWh) in year t, and PTC = Production Tax Credit (cents/kWh) available for the first 10 years of the project. Further, as in Appendix B, we define Rt’ as the required revenue in the absence of the PTC, and we define Rt’’ as the required revenue in the presence of the PTCt.15 We start by assuming that after-tax income, ATt, is held constant with or without the PTCt. to ensure that investors receive the same rate of return, By simplification we have, R' − fR' −sR' + fsR' = R'' − fR'' −sR'' + fsR'' +PTC. tttttttt R'(1− f −s+ fs)=R''(1− f −s+ fs)+PTC. tt Dividing by 1 yields, (1− f −s+ fs) Or equivalently, Such that, if and only if, R' = R'' + t t R' −R'' = t t PTC . (1− f −s+ fs) PTC . (1− f −s+ fs) PTC = PTC , (1−f−s+fs) (1−τ) τ =(1− f −s+ fs). 15 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. 14PDF Image | An Economic Valuation of a Geothermal Production Tax Credit
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