Martingales, Taxes, and Neutrality

Abstract

We analyze a general business tax in an uncertain economy. Our tax system allows for a time-dependent tax rate and to this end we incorporate a generalized allowance for corporate equity (ACE). The generalized allowance is given by a fraction of the product of interest rate and book value of the project and this fraction can be time-dependent. We determine conditions under which taking this tax into account does not distort investment decisions, i.e. under which the tax system will be neutral. To allow for investors with arbitrary risk attitude we make use of the martingale approach. We show that the after-tax capital market is arbitrage-free and complete if it is arbitrage-free and complete in a world without taxation. We furthermore derive a valuation equation under taxes that we use to specify neutral tax systems. Our tax system generalizes two well-known neutral tax systems: The taxation of economic rent and the tax with allowance on corporate equity as introduced by Boadway/Bruce (1979) and Wenger (1983). The taxation of economic rent even remains neutral if the tax rate is time-dependent and if there is a generalized allowance on corporate equity. This reveals that the assertion of Bond/Devereux (1995) that a constant tax rate is an indispensable condition for neutrality is wrong. This assertion is found to be wrong even in the model of Bond/Devereux (1995). The taxation with a generalized allowance on corporate equity even remains neutral if the tax rate is time-dependent and if the parameters which determine the fraction of the allowance are chosen in an appropriate manner. This shows that the ACE concept of neutrality is far more general then stated in the literature.