10
where the current investment cost at year u is Ceπu.
The difference between nPV(t)0sld and nPV(t)0sld* is defined as the present value of
additional corporate tax burden (inflation losses) at year 0 (ATB0sld), which is caused by
the fictitious profit. With the economic life of a capital good Γ*, therefore
1-e-{μ(1-t)-∏}Γ* ι-e-μ(1-t)Γ*
(11) ATB(Γ*)osld = tC[---] = tC(FPosld) ,
{μ(1-t) -π}Γ* μ(1-t)Γ*
where FP0sld indicates the present value of fictitious profit per monetary unit at year 0 in
the case of adopting straight-line depreciation. In order to examine whether and to what
extent generous tax depreciation provisions promote private investments in inflationary
situations, the value FP0sld (with Γ*) can be adopted as the benchmark.
When the amount of annual depreciation expense is calculated on the basis of historical
cost, the incentive effect of accelerated depreciation on private investment in an
inflationary phase can be measured by
(12) nPV(t)0ad - nPV(t, Γ*)0sld
σ{1-e-μ(1-t)} e-μ(1-t)r* - e^(1-w
= tC [—————— + ————————] = tC(IE0ad) ,
μ(1-t) μ(1-t)Γ*
where nPV(t)0ad is the nominal present value of the asset with accelerated depreciation at
year 0 and Ω* denotes the reduced tax-life of a capital good, when Γ = Γ*.
With free depreciation,
(13) nPV0fd - nPV(Γ*)0sld
1-e-μ(1-t) 1-e-μ(1-t)r
= tC{—————— - ——————} = = tC(IE0fd) ,
μ(1-t) μ(1-t)Γ*
where nPV0fd indicates the nominal present value of the asset with free depreciation at year
0.
When investment tax allowance is adopted and the tax-life of a capital good is Γ*,
(14) nPV0ita - nPV(Γ*)0sld