Invariant Valuation When Tax Rates Change Over Time

Abstract

Samuelson (1964) proved that if and only if depreciation for tax purposes is equal to economic depreciation will any two taxpayers with different tax rates value an asset equally.' He referred to this condition as invariant valuation; that is, the valuation of an asset with a given stream of receipts is independent of the tax rate of the individual. Under this condition, the tax system does not provide any one taxpayer a greater or lesser incentive to undertake investment than any other taxpayer. Samuelson's proof pertained only to the case of taxpayers with different, but constant, tax rates. As he noted, All of this analysis presupposes a tax rate that is uniform over time for each person. Obviously, if a man is to be subject to different rates, with [the tax rate] being a function of time, his optimal decision will be distorted by this fact. A proper system of carry-forwards and carrybacks, which makes [the tax rate] average out to a constant and which takes account of just when a man pays the tax accruing to him, will avoid such distortions (p. 605). Under many circumstances, taxpayers' statutory tax rates may change over time. Individuals and corporations are subject to graduated tax rates, minimum tax rules, and restrictions on tax losses. It is shown in Section I that if tax rates are allowed to change over time, but Samuelson's other assumptions are maintained, economic depreciation continues to result in invariant valuation without the need for carryforwards or carrybacks.2 That is, if tax rates vary across taxpay-