Proceedings
of the Tomsk Order of the October Revolution
and Order of the Red Banner of Labor
Polytechnic Institute named after S. M. Kirov

Vol. 290 1974

Economic Assessment of the Timing of Equipment Renewal

V. N. Shchukov

(Presented at the scientific seminar of the Department of Industrial Economics)

The increasing pace of scientific and technological progress gives rise to accelerated rates of obsolescence of machines and equipment. As machine models become morally obsolete, their economic efficiency tends to decline. As a result, it becomes necessary to transfer the machine fleet to a new technical level. The interval of time during which a reduction in social costs is ensured as a result of applying a machine model of a given technical level is the period of its economic functioning. Therefore, the task of the economic assessment of new equipment should be to determine the time boundaries of the effective use of machines of a certain technical level, that is, to substantiate economically optimal times for replacing machine models and the machine fleet.

A static approach to determining the economic efficiency of new equipment, without taking into account the rates of obsolescence and the periods of its effective functioning, leads to a smoothing out of the difference in the level of economic efficiency between slightly improved and substantially new machine models, and to an overstatement of the economic effect of machines of a low technical level. Undoubtedly, however, machine models at a higher technical level possess greater potential and actual efficiency, since they have longer periods of economic functioning and greater possibilities for further improvement.

The principal indicator recommended by the Standard Methodology [1] for selecting the most effective variant of new equipment is the indicator of annual reduced costs, the minimum of which determines the economic efficiency of the adopted variant:

\[ W_{\mathrm{p.g}} = C_i + \varepsilon_{\mathrm{n}} K_i = \min, \tag{1} \]

where \(C_i\) is annual operating costs, rubles/year;
\(K_i\) is additional capital costs, rubles;
\(\varepsilon_{\mathrm{n}}\) is the normative coefficient of economic efficiency.

Expression (1), for so-called standard objects, for which \(T_{\mathrm{sl}} \to \infty\), is identical in its economic results to the expression for total costs over a period equal to the reciprocal of the efficiency norm:

\[ W = K_i + \frac{1}{\varepsilon_{\mathrm{n}}} C_i = \min. \tag{2} \]

In reality, we are dealing with limited (finite) service lives of machines, which in this case act as the optimized quantity determining the time boundaries of their effective use. The magnitude of the total economic effect obtained depends on the particular duration of operation of the objects.

The reflection of real (finite) service lives of machines in annual reduced costs is achieved, in the opinion of a number of authors, by including depreciation charges in operating costs. In this case, it is proposed that depreciation charges for renovation be calculated not according to the traditional formula:

\[ a_{\mathrm{n}}=\frac{100}{T_{\mathrm{sl}}}\ (\%), \tag{3} \]

but according to formulas that take the time factor into account:

\[ a_{\mathrm{n}}=\frac{100\cdot \varepsilon_{\mathrm{n}}}{(1+\varepsilon_{\mathrm{n}})^{\tau}-1}\ (\%), \tag{4} \]

\[ a_{\mathrm{n}}=\frac{100\varepsilon_{\mathrm{n}}(1+\varepsilon_{\mathrm{n}})^{\tau}}{(1+\varepsilon_{\mathrm{n}})^{\tau}+1}\ (\%), \tag{5} \]

where \(\varepsilon_{\mathrm{n}}\) is the normative coefficient of economic efficiency, equal in this case to the discounting coefficient for the time factor.

A. B. Zalesskii regards the inclusion of depreciation charges, calculated by formulas (4) and (5), in operating costs (1) as a method of reducing real objects that have finite service lives to so-called standard objects. In this case, in his opinion, the quantity \(a_{\mathrm{n}}K\) reflects the influence of the limited duration of an object’s operation on its economic efficiency (2).

But the question arises: is the inclusion of depreciation charges sufficient to reflect the longevity of the compared alternatives; do they make it possible to take into account the influence of service lives on the economic efficiency of each alternative of new technology?

Let us consider this using the following hypothetical example. Suppose that two identical alternatives have the following economic indicators:

where \(C_{\mathrm{t}}\) denotes operating costs excluding depreciation proper. The results of calculations when varying the service lives of the compared alternatives are presented in Table 1 (with \(\varepsilon_{\mathrm{n}}=\varepsilon_{\mathrm{p.g}}=0.1\)).

As Table 1 shows, the magnitude of the annual reduced costs of each of the compared alternatives depends to a significant extent on the adopted service life. Moreover, in those cases where the most effective alternative at \(T_{\mathrm{sl}}=\infty\) and, consequently, at \(a_{\mathrm{n}}=0\), is the more capital-intensive alternative (this very case is reflected in Table 1), an inconsistency is observed in the choice of the effective alternative depending on the adopted service life under any method of calculating depreciation charges. For short service lives the less capital-intensive alternative 1 proves to be the most effective. Thus, when depreciation is calculated according to formula (3), alternative 1 wins for service lives of less than five years; when formulas (4) and

Table 1

Change in the annual reduced costs of the compared variants under different methods of accounting for depreciation charges

Note: \(\varepsilon_{\mathrm{n}}\) is taken equal to 0.1.

(5), respectively, up to four and seven years. However, no such inconsistency arises if the variant that is most effective according to formula (1) and with \(T_{\text{sl}} \to \infty\) turns out to be the less capital-intensive variant.

This circumstance leads, when service lives are short, to a relative overstatement of the economic efficiency of less capital-intensive and, as a rule, less advanced variants, and to an understatement of the economic efficiency of more expensive variants, which are usually at a higher technical level.

The table also shows that, as the service life increases, the relative reduction in the value of annual reduced costs for each of the variants being compared decreases and, for long service lives, becomes insignificant. As a result, the absolute value of the annual reduced savings at different service lives of the given variant decreases relatively. Thus, for the first variant, when the service life is increased from two to three years, the absolute value of the savings would be 16.7 rubles/year, whereas when \(T_{\text{sl}}\) is increased from 9 to 10 years it is only 9 rubles/year. For the second variant, the corresponding figures are 33.3 rubles/year and 6 rubles/year. It is difficult to explain such high rates of decline solely by the action of the time factor, especially since the service lives do not exceed 10 years. This is explained, rather, by an unsuccessful method of accounting for the durability of equipment, which is reduced merely to changing the amount of annual depreciation deductions.

As a result, the comparability of the magnitudes of the economic effect at different service lives of new equipment is violated, and ultimately this leads to a diminution of the economic efficiency of machines with longer periods of operation.

The most substantial shortcoming of the formula for annual reduced costs in the economic assessment of the timing of equipment renewal is that planned depreciation rates do not reflect the real costs required for the reproduction of machines. In essence, it is assumed that the costs of reproducing equipment correspond to the costs of producing it at the time of its creation, adjusted at best by a coefficient that accounts for the time factor. It is precisely for this reason that reproduction costs (the amount of depreciation deductions) are taken on the basis of the initial capital costs. The proposed methodology for calculating depreciation rates by formulas (4) and (5) merely helps to adjust the initial capital investments for the time factor.

In reality, however, the reproduction of machines takes place at a new technical level, to which a different magnitude of capital costs, operating expenses, machine productivity, etc., corresponds. Therefore, the formal reflection of the costs of producing equipment through depreciation rates means that the total amount of these costs does not depend on the period of operation of the machines (only its annual portion changes). But such an assumption does not correspond to the real economic process. Since there is a constant reduction of costs as a result of technical progress, consequently, the later a machine is reproduced, the smaller the amount of costs required for its reproduction. Therefore, it becomes necessary to determine directly the reproduction costs, taking into account the rates of obsolescence at the moment a new model of machine is introduced. Determination of the actual level of reproduction costs for the machine fleet being replaced can be ensured on the basis of forecasting the development of the given type of equipment.

It should be added that the depreciation rates themselves are far from corresponding to the rates of technical progress at the present stage.

Thus, the planned depreciation rates of 1963 proceed from an average service life in machine building equal to 17 years, while for many types of machines the depreciation service life exceeds this period.

Thus, the use of annual reduced costs does not make it possible objectively to reflect the duration of the functioning of equipment. The inclusion of depreciation deductions in operating costs also does not solve this problem, since they do not correspond to the actual costs of reproducing the equipment. This leads to a distortion of the results obtained. On the other hand, it is incorrect to reduce the reflection of the duration of the functioning of equipment to one or another method of accounting for depreciation deductions in operating costs. The influence of changes in the service lives of machines is much deeper and broader and cannot be reduced only to changes in renovation norms.

From the standpoint of a dynamic approach to the economic efficiency of new equipment, the magnitude of the savings obtained over the entire period of machine operation is far from indifferent. The magnitude of the economic effect depends in the most direct way on the duration of the economic functioning of the equipment. Considerable importance attaches to taking account of the dynamics of economic indicators during the service life of machines. The costs associated with reproducing the stock of machines and the production capacities of the corresponding branches of machine building are in direct dependence on the service lives of equipment.

In this connection, it appears advisable, in the economic assessment of renewal periods, to use the criterion of total reduced costs or total reduced savings. Other authors also arrive at the necessity of determining the economic efficiency of new equipment on the basis of total costs over the service life of machines [3, 4].

Thus, L. S. Lvov proposed the following formula for calculating the total economic effect over the service life of a machine, which in simplified form may be represented as follows [4]:

\[ \Delta W(T)=\Delta K+\frac{\Delta C_T}{a_n+\varepsilon_n}, \tag{6} \]

where \(C_T\) is the annual operating costs excluding depreciation proper;

\(K\) is the price of the machine (one-time costs),

\(\varepsilon_n, a_n\) are, respectively, the depreciation coefficients and the efficiency norm.

In principle, this formula does not differ from expression (2) and proceeds from the formula of annual reduced costs. If in expression (6) we take \(T_{\mathrm{sl}}\to\infty\) and, consequently, \(a_n=0\), then it takes the form

\[ \Delta W(T)=\Delta K+\frac{1}{\varepsilon_n}\Delta C_T. \]

Consequently, expression (6) is characterized by the same shortcomings as when using formulas (1) and (2). But, unlike them, since here \(a_n>0\), expression (6) represents a certain hybrid of the total costs over the service life and a period equal to \(\frac{1}{\varepsilon_n}\).

The calculation of total costs according to the formulas:

\[ W(T)=K_i+\sum_{t=0}^{T_{\mathrm{sl}}} C_{T_i}\frac{1}{(1+\varepsilon_{n.g})^t}; \tag{7} \]

\[ W(T)=K_i+\sum_{t=1}^{T_{\text{s.l}}} C_{\text{p}i}\frac{1}{(1+\varepsilon_{\text{p.g}})^t}, \tag{8} \]

where \(C_t\) is operating costs excluding depreciation proper;
\(C_{\text{p}}\) is operating costs including depreciation;
\(\varepsilon_{\text{p.g}}\) is the coefficient of reduction by the time factor,

also has analogous shortcomings. As shown by A. B. Zaleskii, [2] expression (7) is identical to the formula for annual reduced costs with the inclusion in operating expenditures of depreciation charges calculated by expression (4), for a finite service life of the object.

The use of formulas (6), (7), and (8) to determine total costs or total savings over the service life of a machine gives a distortion of the same kind as the use of expressions (1) and (2). For short service lives the efficiency of less capital-intensive variants is relatively overstated; for long service lives the magnitude of total costs for each of the variants is relatively reduced.

The change in total reduced costs when they are calculated by different formulas is presented in Table 2. In this connection, the following economic indicators of two mutually identical variants have been adopted:

Operating costs are taken excluding depreciation charges proper. The calculation of depreciation charges is carried out by formula (3).

As can be seen from Table 2, for short service lives the less capital-intensive variant I is preferable. The use of one or another expression for calculating total costs changes only the periods of equal efficiency of the variants.

The calculation of total costs when expressions (6), (7), and (8) are used gives a significant difference in the absolute values of these costs for identical service lives. Thus, total costs according to expression (8) exceed the costs, for one and the same service life, calculated by formulas (6) and (7), by approximately 1.5 times, which is explained by the inclusion of depreciation charges. Such a divergence in the absolute values of total costs may be of decisive importance in determining the optimal operating periods of machines.

Another shortcoming of determining total costs (or total savings) is the incorrect commensuration of reduced one-time investments and total current savings. Therefore, a formula is sometimes proposed in which the annual magnitude of capital costs \(\varepsilon_{\text{n}}K\) is commensurated with the magnitude of current costs over the service life of the machine:

\[ W(T)=\varepsilon_{\text{n}}K+\sum_{t=1}^{T} C_t\frac{1}{(1+\varepsilon_{\text{p.g}})^t}. \tag{9} \]

Naturally, in this case the influence of differences in one-time costs for the variants being compared will be insignificant, which leads to a substantial distortion of the final results.

Since \(\varepsilon_{\text{n}}K\) represents the annual magnitude of the normative effect corresponding to the annual magnitude of current costs (or

Table 2

Change in total costs over the service life of the compared variants under different methods of calculating them, with \(\varepsilon_n=0.12;\ \varepsilon_{pg}=0.08\)

annual savings in operating costs), consequently, total costs for one period or another must be compared with the corresponding magnitude of the normative effect that must be ensured when additional one-time expenditures are tied up. Then the expression for the total costs over the service life of the machine, reduced with allowance for the time factor, will take the form (without taking into account the costs of its reproduction)

\[ W(T)=\sum_{i=1}^{T}\left(C_{t_i}+\varepsilon_{\mathrm{n}}K_i\right)\frac{1}{(1+\varepsilon_{\mathrm{p.g}})^{\tau}}, \tag{10} \]

where \(C_t\) is the annual operating costs, excluding depreciation proper;

\(K\) — one-time expenditures (the cost of the machine);

\(\varepsilon_{\mathrm{n}}\) — the normative coefficient of economic efficiency;

\(\varepsilon_{\mathrm{p.g}}\) — the coefficient of reduction by the time factor.

Expression (10) has the advantage over other methods of calculating total costs (6), (7), (8) that it gives a more uniform increase in the absolute magnitudes of total costs as the service life increases. Table 2 shows that the second variant, as the most effective one, has lower total costs regardless of the adopted service life. Moreover, its advantage increases with an increase in \(T_{\mathrm{sl}}\) (the magnitude of total costs decreases relatively more rapidly). The absolute values of total costs for each of the compared variants correspond to a greater degree to the real economic process. Thus, if for the first variant the total costs calculated by expression (6) increased, with an increase in \(T_{\mathrm{sl}}\) from two to 10 years, by a little more than two times, then when calculated by formula (10) they increased almost fourfold.

Thus, the total reduced costs determined by expression (10) are in a more objective relationship with changes in the service life of machines. Their use in the economic assessment of the timing of equipment renewal does not give the distorting results that occur when (1), (2), (6), (7), (8), (9) are used. At the same time, however, it is necessary to take into account additional costs for the reproduction of machines, for the expansion of production capacities, etc., according to the actual conditions at the time of reproduction.

REFERENCES

1. Standard Methodology for Determining the Economic Efficiency of Capital Investments. Academy of Sciences of the USSR, 1969.

2. A. B. Zalesskii. Comparative Efficiency of Planned Decisions. Moscow, Ekonomika, 1968.

3. E. K. Smirnitskii. Economics and the Machine. Moscow, Ekonomika, 1970.

4. Economic Problems of Improving Product Quality. Academy of Sciences of the USSR, 1970.