the negative change in value of the asset in the course of time — is deducted from an
expected gross stream of return when calculating tax profits (see also Atkinson and
Stiglitz, 1980). And the TED rate is the same rate at which the gross return declines in the
course of time (i.e. the TED rate = α).
In the absence of taxation and also in the case of profit tax exemption, an equity-
financed investment project is on the margin of acceptance at the year of investment, when
(1) C = PVo = ∫∞Aoe-(α+r)u du = ——A— ,
0 α+r
where Au (= Aoe-(α+r)u ) means gross return at year u and r is the real interest rate (0 < r <
1) before imposing corporate tax. In such an equilibrium, the NPV amounts to zero.
If cash investment subsidy is provided at the year 0, the equilibrium condition of the
equation (1) changes to
(2) C - kC < PVo = ∞Ao e-(α+r)u du = ——- ,
0 α+r
where kC is the total amount of cash subsidy at the investment year. By the given PV0 this
subsidy is equivalent to the extra profit for the investor.
Accelerated depreciation is generally used in combination with the straight-line
depreciation method. Accelerated depreciation expense (as a certain percentage share of
investment cost) is tax-deductible in the first year of a capital good’s tax life.
Consequently, total depreciation expense in the first year reaches
C
(3) D1ad+sld = σC + —— ,
Γ
where σ indicates the accelerated depreciation rate (0 < σ < 1), and C∕Γ denotes the annual
sum of straight-line depreciation over Γ tax lives.
Because an extra amount of expense can be deducted in the first year, the total tax-life
of a capital good is reduced correspondingly from Γ to Ω. And
(4) Ω = (1 - σ)Γ .
The present value of the asset with accelerated depreciation at year 0 is