Consideration of Fictitious Profit and Inflation Losses
In an economy with the constant annual inflation rate π, the stream of nominal gross return
which is generated by an investment costing C at year u can be expressed as
(8) Au = Aoe-αueπu = Aoe-(α-π)u .
In this case, the sum of annual gross return exponentially decreases at rate α but increases
at rate π over the course of time.
The size of fictitious profits and the additional corporate tax burden, which are caused
by applying the historical cost accounting method in the inflationary phase, can also be
measured on the basis of the net present value model. Such inflation losses lead to the
reduction of nominal net present value. More precisely, the amount of increased tax
burden caused by inflation can be described as the difference between the two nominal
PVs, one with depreciation measured on the basis of current (replacement) value of a
capital good and the other determined on the basis of the historical cost accounting
method.
In the case of employing the historical cost accounting method, the nominal present
value of the asset with straight-line depreciation at year 0 is
∞ Γ
(9) nPV(t)osld = (1-t) ∫ Aoe-{α-π+μ(1-t)}u du + t ∫ (C∕Γ)e-{μ(1-t)}u du
0 0
(1-t)Ao tC{1-e-μ(1-t)r}
= —————— + —————— ,
α-π+μ(1-t) μ(1-t)Γ
where the nominal interest rate μ = r + π.
On the other hand, when depreciation expense is determined on the basis of current
investment cost, the nominal value of the asset with the same depreciation method at year
0 is
(10) nPV(t)osld* = (1-t) ∞ Ao e-{ α-π+μ(1-t)}udu + t ∫(C∕Γ)e-{μ(1-t)-π}udu
0 0
(1-t)Ao tC{1-e-{μ(1-t)-π}r}
= —————— + ——————— ,
α-π+μ(1-t)
{μ(1-t)-π}Γ
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