Replacement cost depreciation and cash flow requirements

In this article a framework is developed to test whether depreciation based on replacement cost meets cash flow requirements. It also indicates both the extent to which depreciation based on replacement cost can be linked to depreciation based on historical cost and the factors which should be considered in the calculation of the ratio of replacement cost depreciation to historioal cost depreciation. These aspects are of importance to most enterprises and of particular importance to price-controlled enterprises. The most significant findings are that: there is no need to provide for backlog depreciation; additional depreciation needs only be provided to the extent that equity financing is used; and the ratio of replacement cost depreciation to historical cost depreciation is a function of the inflation rate, lives of assets and the applicable gearing ratios. die meeste sake-ondernemings. Die belangrikste bevindings is: daar is geen noodsaaklikheid vir die voorsiening van agterstallige waardevermindering nie; addisionele waardevermindering hoef slegs voorsien te word in dieselfde mate as wat van finansiering met eie fondse gebruik gemaak is; en die verhouding van vervangingswaarde-waarde vermindering teenoor historiese kostewaardevermindering is 'n funksie van die inflasiekoers, die leeftyd van bates en die toepaslike hefboomverhouding.


Introduction
should be taken into account if such an approach were to be followed. A question which often arises is whether or not sufficient provision has been made for additional depreciation (replacement cost depreciation less historical cost depreciation). In the case of a price-controlled enterprise, an over-provision for additional depreciation would result in prices or tariffs being too high. This is not so in the case of an enterprise which is in competition with others. In the latter case, the price or tariff is a function of free competition and an over-provision of replacement cost depreciation will have no effect on the consumer. The correct calculation of replacement cost depreciation is therefore very important for an undertaking which is not operating in a completely free market. A related aspect is the expression of replacement cost depreciation as a ratio of historical cost depreciation. This ratio is often used in price control formulae and in some cases critical values are also calculated. The practice is probably applied to indicate that the provision for additional depreciation is not excessive. The use of this ratio could result in erroneous calculations, as replacement cost depreciation is not a function of historial cost depreciation alone.
The objectives of this article are, firstly, to develop a framework for comparing replacement depreciation with actual cash flow requirements and, secondly, to indicate both the manner in which replacement cost depreciation could be linked to historial cost depreciation and the factors which When calculating depreciation based on replacement cost. certain problems are experienced, e.g. which indices to use in determining replacement costs and the calculation of the gearing adjustment The solution of such problems is beyond the scope of this article.

Tennlnology
The replacement cost (RCjt) of asset j in year t is determined from the historical cost (HCi0 ) of asset j in the following way: where I = weighted average inflation rate per annum.
Historical cost depreciation (HDi 1 ) of asset j in year t is equal to the historical cost (HCi1) divided by the lifetime of an asset {Li), i.e.

HD.JI =
Replacement cost depreciation (RDjt) of asset j in year t (excluding backlog depreciation) is equal to the replacement S.AfrJ.Bus.MgmL1990,21(3) cost (RCjt) of asset j in year t divided by the lifetime (I,) of the asset, i.e. = From the above two f onnulae it follows that additional depreciation (ADjt) of asset j in year t; is equal to the difference between replacement 'cost depreciation and historical cost depreciation, excluding backlog depreciation, of asset j in year t, i.e.
Backlog depreciation (BDjt) of asset j in year t, also known as recovery of under-depreciation, is equal to the accumulated depreciation based on replacement value in year t, calculated by dividing the latest replacement value by the lifetime, multiplying by the age (A) of the asset and then subtracting the sum of historical cost depreciation, additional depreciation and backlog depreciation to date, i.e.
The formula for backlog depreciation could also be expressed in a simpler way. Backlog depreciation results (or is submitted to result) from the detrimental effect of inflation on accumulated depreciation. It is therefore equal to the inflation rate (I) multiplied by the accumulated depreciation of the previous year (ACDji-i ), which includes historical cost depreciation, additional depreciation and backlog depreciation, i.e.
The term updating depreciation (UDj,) is used in the 73 context of this article to describe the total of additional depreciation and backlog depreciation where a system of replacement cost depreciation has not been in operation, i.e.
Updating depreciation is calculated in order to correct the accumulated depreciation based on replacement value (including backlog depreciation).

The sufficiency of replacement cost depreciation
The sufficiency of replacement cost depreciation is analysed by means of an example in which the following assumptions are made: 1.
On I January of each year a new machine is acquired.
2. The purchase price of a machine increases by 12 per cent every year (for ease of argument it is assumed that price increases occur at the end of every year). 3.
The lifetime and the depreciation period of a machine equals five years, after which replacement with an identical machine takes place. At the end of five years five machines are on hand, each with a different age, resulting in a situation of one hundred per cent diversity. A situation of complete or almost complete diversity is quite common in large production enterprises where assets are diversified in respect of type, lifetime, age, location and investment amount. Continuous replacement takes place instead of intermittent replacement. The cash required to replace operating capacity in year t is exactly equal to replacement cost depreciation, i.e. no backlog depreciation is necessary.

4.
Equity financing is assumed initially, i.e. no loan funds are used. This assumption is changed in Table 5.

5.
The provision for updating depreciation is made in 19.5 so that a complete system of replacement depreciation can be introduced from 19.6 onwards.

6.
The non-deductibility from taxable income of additional and backlog depreciation is ignored. It is therefore assumed that the cash flow effect of the provision for additional and backlog depreciation and that of historical cost depreciation are similar in the sense that the cash flow is equal to the provision. 7.
The straight-line method of depreciation is used. The example is illustrated in Tables 1-4. In Table 1 the statistics relating to the machines acquired and replaced are summarised. It shows the historical cost of each machine, the machines on hand and scrapped, and the accumulated historical cost and historical cost depreciation of the machines on hand. The calculations in the table are explained by means of notes to the table.
In Table 2  which is the total in column g of Table 3.
The calculation of replacement cost depreciation in 19.6, the first year after the implementation of replacement cost depreciation, appears in Table 4. In this table a clear differentiation between additional and backlog depreciation is made. To evaluate whether or not the provision for total   • tocal backlog depreciation in year L replacement cost depreciation is sufficient for replacement, an analysis is made in terms of cash flow in Table 5. The assumption of 100 per cent equity financing is relaxed and the effect of different financing mixes on cash flow is investigated. The cash inflow consists of historical cost depreciation, additional depreciation and backlog depreciation (the Jatter where applicable). The cash outflow consists of the purchase price of the replacement investment If loan capital is panially used to finance a machine, an adjustment for gearing has to be made in respect of additional and backlog depreciation. Provision should only be made for the higher replacement cost of that portion financed by equity capital. In the case of loan capital with a guaranteed source, provision for inflation is built into the interest rate over the longer term and the source automatically supplies its portion of the higher replacement cost (assuming a fixed financing ratio). If the loan capital ratio (debt/assets) is indicated by D, the cash inflow consists of: HDn = (1 -D) (ADn + BDn) and the cash outflow (application) amounts to: (1 -D)(Purchase price of new machine) + repayment of previous loan 75 Nine different combinaJions of cash inflows (sources) are analysed in Table 5 for 19.6. On the applications side only one combination (ratio) of financing is assumed, i.e. 70 per cent loan financing. It is assumed that loans are repaid on a straight-line basis over five years (interest is excluded). The redemption is equal to 70 per cent of the historical cost of the assets. In column 1 the difference between available and required funds is calculated and in column m it is expressed as a percentage of total funds required (column k).
The following conclusions are drawn from Table 5: 1. There is only one situation where there is no overrecovery of funds, i.e. where the financing assumption of the sources equals the financing assumption of the applications (70 percent loan capital) and no backlog depreciation is provided. 2. The larger the difference between the equity percentage of the sources and the equity percentage of the applications, the Jarger is the over-recovery. 3.
The larger the percentage backlog taken into account, the larger the over-recovery.

4.
The surplus can be calculated by applying the following formula:

The ratio replacement cost depreciation: hlstorlcal cost depreciation
This ratio is to a large extent a function of acquisition dates (age}, lives and specific price increases (inflation), as is clear from Table 6 which is based on the same information as Table 1 (see the previous section) and which summarises the situation after five years. The following conclusions are drawn from the table: 1. The older a machine, i.e. the shorter the remaining life, the higher is the ratio of additional depreciation to historical cost depreciation. If the lifetime of an asset increases, this ratio would also increase.

2.
The higher the price increase of the assets, the higher the ratio will be and vice versa.

3.
The ratio (r) of additional depreciation (ADjt): historical cost depreciation (HDjJ for a specific machine can be derived from the following calculated from the following foonula: where the age is three years (machine C), the ratio in Table 6 is as follows The total replacement depreciation (RDn) is equal to: (I + o.12t 2 -1 = 1.39 -1 = 0.39

RDn =
In line with the conclusion in the previous section, no povisioo has been made for backlog depreciatioo which is unneccessary in the siblation of complete diversity assumed in the example. Even if a siblation of incomplete diversity of the type, age Cl' lifetime of assets existed. there would be no need for backlog depreciation. The latter necessitates continued replacement rather than large replacements on a discontinuous basis. and the ratio:

LJ
(1 + I) -1 is equal IO the present value (PV) of an llllluity and the ratio is therefore equal 10 HDn PV of an annuity over L periods at an inflation rate of I In Table 6, the ratio HDn 5 amounts to ---3.605 = 1.39 Following the derivation of this formula a table could be compiled for different lifetimes (L) and inflation rates (I) as in Table 7.
From this table it is clear that the longer the lifetime and the higher the inflation rate, the higher n RDn the ratio HDn If the assumption regarding 100 per cent equity financing is relaxed and different gearing ratios are assumed the situation will change as in Table 8 (I = 15%).
The higher the gearing ratio, the lower RDn the ratio HDn because of the lower 'responsibility' of the suppliers of equity capital.

Practical lmpllcatlons of findings
The major findings of this article are that there is no need for backlog depreciation, that additional depreciation should only be provided to the extent that equity financing takes place and that RDn the ratio HDn is a function of the inflation rate, the life of assets and the   undertakings they have an advantage in that they do not pay lfitome tax.
Finally, a word of caution -the resulta and findings of the anicle should be viewed in the light of the underlying u1umption1.