Part 1 - AL-Tax

International Taxation HandbookTherefore, the expected AETR is now:( τ A)( ) ( p ) A( )E[ AETR] ρδπτ ρπδτ ρδπ α.pp 0 ( ρδπ )The parameter α reflects the expected rate of decline in the economic rent of theproject. Whether the expected average tax is higher or smaller than expression (2.15)depends on country or industry specific values. Nevertheless, we can state the followingproposition.Proposition 7 In the absence of personal taxes, when taxable income is smaller(larger) than true economic income, the E[AETR] is smaller (larger) than the AETR,and when taxable income is equal to true economic income, the E[AETR] is equal tothe AETR, to the METR, and to the statutory tax rate.Proof For E[AETR] AETR, we need that δτ A(r δ) and the proof follows asin Proposition 2.As we can see in Figure 2.4, we are assuming a continuous decline in the rateof return to zero. Nonetheless, this fall in returns has a natural floor imposed bythe rational expectation of the entrant firm as to the pre-tax rate of return for themarginal investment (p˜ in equation (2.16)). This lowest value will function as areflecting barrier, because once it is touched the entry of competitive firms willstop. The expected NPV in this case will be:p0E[ NPV ] Cp0 γ,ρδ π α(2.19)where γ 0 is the negative root of the fundamental quadratic r δαξ σ 2 ξ(ξ 1)/2 φ(ξ). The first term in equation (2.19) is the expected NPV when returnscontinue towards zero and the second term is the increase in value because newentries will stop before zero. Using the Smooth Pasting Condition (for a discussionof the calculation of expected present values, see Dixit, 1993), we can calculate thevalue of the constant C:F( pɶ) 00 Cp 1γ ɶ γ 1 0ρδπα pɶ1γ1C γρδπ α 0.26