We assume the planning horizon to be infinite. The advances
in technology are not incorporated in the model. Thus the
efficiency of the new machines in the replacement chain is the
same as that of the first machine. We assume that inflation s
is constant and that no relative price changes occur that
would affect the factors included in the model.
When discounting we use a positive discount rate iī = i + s +
is (where i is the real discount rate) that stays in real terms
constant. We assume the effect of the machine on the firmīs
real net income constant, too. Hence the model can be
optimized using the minimization of costs as the criterion.
We assume the operation and maintenance costs of the
machine to inrease and the salvage value of the machine
correspondingly to diminish as time passes. We assume no
financial limitations when financing the replacement
investment.
With these assumptions we get the NPV of the total costs
after tax for a single machine in inflationary conditions as
(S.1) PVC(n,s) = I + (1 - f)PVO(n) - fPVD(n,s) - (1 - f)PVS(n),
where I is the purchase price of the machine and f is the tax
rate. PVO(n) is the present value of the cost of operation and
maintenance. PVD(n,s) is the present value of the
depreciation allowances. It becomes a function of inflation.
PVS(n) is the present value of the salvage value.
When we consider a chain of identical machines we get the
NPV of the total costs of the chain as
(S.2) PVCH(n,s) = c(n,i)(1/i) PVC(n,s),
where c(n,i) is the annuity factor for n periods and discount
rate i.
Hence, inflation has an effect on the NPV of the total costs
only throught the effect of taxes on the depreciation
allowances. It means that inflation has influence only when
the tax rate is positive.
The general optimal replacement policy can be characterized
also in inflationary conditions as follows: As long as the
average yearly costs is greater than the marginal costs of
extending the life of the machine by one additional year,
donīt replace ; as soon as the marginal costs of the additional
yearīs service exceeds the average cost, the machine should
be replaced.
We tested the NPV model further by numerical simulation.
We chose inflation s as the basic variable and tax rate f and
the declining balance depreciation factor j as parameters
that we let vary in relevant ranges. We found out that
inflation has a lengthening effect on the optimal service life
of a machine. If we increase the depreciation factor, the
effect of inflation is diminished. An increase in tax rate has a
lengthening effect on the optimal service life, too. Under
high values of inflation and tax rate we further have a
strong interaction effect of these two factors.
(The Finnish Journal of Business Economics, 1-
1984, 60-80)