Inflation diminishes the real present value of EVL
depreciation allowances, whereas JHH depreciation
amounts are sized so that inflation has no effect on the real
present value of their sum. The effect of inflation on the
present value of EVL depreciation allowances is the less the
more accelerated depreciation (the higher a rate of
depreciation) can be utilized. The upper limit of acceleration
is the writing off of the whole purchase price in the first
period. If the rate of depreciation is denoted by j(0), the real discount rate by i and the rate of inflation by s, this lump-sum
depreciation is still sufficient to provide a hedge against
inflation (compared with stable price level situation), if
s = s(1) = (1-j(0))i/(1+i)j(0). On lower rates of depreciation the
critical rate of depreciation to hedge against inflation is
j(s) = j(0) + ((1+i)j(0)/i)s.
Secondly, the paper analyses that case where the rate of
depreciation j in the declining balance method is sized to
equate the present value of EVL depreciation and that of
JHH depreciation. We obtain the JHH-equivalent inflation-
adjusted depreciation rate j = i(s)a(n,i)/(n-a(n,i)), where n is
the lenght of the service life of the investment, i(s) = i + s + is
is the nominal discount rate and a(n,i) is the present value
factor for uniform series.
Next the financing of the investment is also taken into
account in the analysis of the relations of the two
depreciation methods. We assume that debt capital is
inflation-protected (i.e. it can be paid back in nominal value).
If the fraction of equity financing is denoted by e, the JHHR
-equivalent inflation-adjusted EVL depreciation rate
becomes j(e,s) = i(s)(e a(n,i) + (i-e)a(n,i(s))/(n-e a(n,i)-(1-
e)a(n,i(s)) (JHHR depreciation = financing-adjusted JHH
depreciation).
If the investment is financed using debt capital as the sole
financing form (e = 0), we get j(0,s) = i(s)a(n,i(s))/(n-a(n,i(s)).
This last equation is by appearance of the same form as the
equation defining the JHH-equivalent inflation-adjusted j
(100 % equity financing), only the real discount rate in the
present worth factor being replaced by the nominal discount
rate i(s) = i+s+is. When the primary form of finance is debt
capital, the JHHR-equivalent rate of depreciation in
declining balance method turns up markedly lower than the
JHH-equivalent rate of depreciation, the latter being
determined without adjustment for form of finance.
(The Finnish Journal of Business Economics, 3-
1983, 286-303)