L.S.E. Essays on Cost
What follows is a shortened version of a series of twelve articles published in the Accountant from 1 October to 17 December 1938 under the title 'Business Organization and the Accountant'. The omissions largely consist of illustrations of the argument and a discussion of the problems of estimating costs in practice. The suggestion for writing this series of articles came from R. S. (now Sir Ronald) Edwards. Originally the intention was to take a number of problems of business administration and to show how such problems should be tackled. It was on this basis that I began writing in the summer of 1938. However, comments from Edwards on the draft of a section dealing with vertical integration suggested that readers of the Accountant would find my discussion hard to follow without some account of the approach I was using. I therefore decided to write an introductory section in which I explained the basic concepts being employed. In the event the introductory section took up the whole of the series. This explains why the title of the series is not wholly appropriate to its contents.
The articles were written and typed each week during Wednesday night and were taken to the office of the Accountant by my wife on Thursday (while I slept). They appeared in print on Saturday. They could be written in this way because I thought of my articles simply as an exposition of views which were generally accepted by economists. The application of these views to business problems was the special interest of a group of economists at L.S.E. working under Professor (now Sir Arnold) Plant of which I was a member along with Edwards and R. F. Fowler, the two others with whom I worked most closely. That these articles proved to have more than transitory interest, and were reprinted and often referred to, was a great surprise to me. Perhaps because the outbreak of the war diverted economists from their academic studies, these articles came to represent the only extended statement in print of the approach to costs, particularly as applied to business problems, which was the common property of economists at L.S.E. in the 1930s. If Professor Buchanan's thesis about the special character of the L.S.E. approach to costs is correct, it is the fact that these articles do not represent a personal view which gives them their historical significance.
The method of approach which will be employed is probably best indicated by explaining certain basic concepts. These basic concepts are of general application and find a prominent place in modern discussions on the subject of cost accounting. The first point that needs to be made and strongly emphasized is that attention must be concentrated on the variations which will result if a particular decision is taken, and the variations that are relevant to business decisions are those in costs and/or receipts. This reasoning applies to every business decision, whether it is concerned with the opening or closing of a department, the manufacture of a new product, the introduction of more frequent style changes or an alteration in the volume of production. Whatever the character of the decision, one has to inquire into the variations in costs and receipts which will follow. Costs and receipts which will remain unchanged whatever decision is taken can be ignored. All this sounds very simple and obvious, and it may seem to certain readers that I am flogging a dead horse. Unfortunately, it would appear that this is not entirely the case. Not only is it true that businessmen do not always follow this simple method of reasoning, but in one branch of accounting, namely cost control, it seems that the consequences of this type of reasoning are ignored.
It is clear that if the information regarding costs is to be of use in facilitating business decisions it must ultimately be presented in a form which enables variations in costs to be obtained. But it seems improbable that any accounting system could continuously produce cost information which might be required for every business decision; it is certainly doubtful whether it would be profitable to do so. The problem then arises as to what cost variations are to be considered. If we are to judge by the following quotations from Mr Edwards's paper on the 'Rationale of Cost Accounting'*1 the aim of a cost-accounting system is to discover variations in costs with changes in output. Mr Edwards says that '...the most important thing about costs is the extent to which they change with output',*2 and 'I consider it the cost accountant's main job to inform the management regarding the minimum at which additional work can be taken'.*3 Many writers seem to take a wider view of the nature of cost accounting. At times, however, writers on this subject appear to consider that cost variation is no part of the job of cost accounting; they suggest, for example, that the aim is merely to find out the total cost of a unit of output in the past. It is doubtful whether this phrase can have any real meaning, and the highly arbitrary calculations which are necessary to arrive at a figure seem to support this view. But whatever the view held of the scope of present-day cost accounting it will surely be agreed that information on cost variations is essential for the making of correct business decisions and that the accountant is probably the man who is in the best position to give the required information. Those who believe that it is part of the function of a cost-accounting system to give information relating to variations in costs might well consider how far the information given should relate merely to the variations in cost through changes in output and whether it should also embrace questions such as the opening and closing of departments and the introduction or discontinuance of a product. How far the information required can be provided by the employment of the traditional accounting technique is a still wider question. As Mr Edwards says '... if the future of costing lies principally in statistical examination of marginal variations, then it may be doubted whether it can be fitted into the framework of double-entry book-keeping'.*4 It should be noted that accounting records merely disclose figures relating to past operations. Business decisions depend on estimates of the future. Accounting records cannot therefore be used as a guide for future action without considering how far the conditions which have existed in the past will continue in the future.
Our purpose will be served if attention is confined to the simple case of variations in costs through variations in output. It is possible to set out the estimated variations in costs which will result from altering output. Certain points, however, should be noted. First there is no need to distinguish between 'fixed' and 'variable' costs. By concentrating on what cost variations will occur, one avoids the necessity of dividing costs up into the categories of 'fixed' and 'variable' costs; there is indeed good reason for thinking that categories of cost which vary for some changes in output do not vary for all changes of output. Secondly it is worth noticing that variations in cost will also depend on the notice which is given of the proposed output change. The variation in costs associated with changes in output will be very different if the variations are to occur next week from what they would be if they were to be carried out next year. A third point is that these costs will also depend on the proposed output for the period after the one under consideration.
Now let us assume that a businessman is examining the variations in costs which he estimates would occur if output varied at some future date. The businessman might produce nothing. If he produces some output certain additional costs will be incurred. These we may term the avoidable costs of that output because they can be avoided by not producing it. Table 5.1 sets out hypothetical figures. In the first column is shown the number of units which might be produced in that unit period of time; in the second column is shown the avoidable costs of producing each size of output.
Unless receipts to be received from the sale of the output are more than these avoidable costs, it will not be profitable to produce that output. So far we have only considered the total avoidable costs of an output. In economic literature another concept is often employed, that of marginal cost, which may be defined as the avoidable cost of an additional unit. If one considers the figures in the table, this avoidable cost of an additional unit is the increase in the total avoidable costs when the output is increased by one. The avoidable cost of producing one unit is £10, the avoidable costs of producing an output of two units are £19; it follows that the marginal cost of the second unit is £9. Similarly, since the avoidable costs of an output of two units are £19 and of three units £27, it follows that the marginal cost of the third unit is £8. Table 5.2 sets out the marginal costs of the various units.
It should be observed that the multiplication of the marginal cost by the number of units produced does not necessarily give the total avoidable costs of that output. If one takes the output of five units, the marginal cost of the fifth unit is £5. Multiplying this by five gives a figure of £25; the avoidable costs of the total output are in fact £35. Similarly the marginal cost of the tenth unit is £13 and multiplying this by ten gives the figure £130; in fact the avoidable costs of the total output are £90. A consideration of marginal costs indicates that a further condition has to be fulfilled if the most profitable output is to be produced. Not only must the total receipts cover the total avoidable costs, but the additional receipts obtained by the sale of the marginal unit must also be greater than marginal cost. In the case of perfect competition, since the variations in the output of a single producer have no effect on price, it follows that the additional revenue from the sale of an additional unit of output (which we may term marginal revenue) is equal to the price. If, however, to sell additional units of the product, the price has to be lowered, marginal revenue will be less than the price since to sell those additional units the receipts on those units which could have been sold at a higher price are reduced. Marginal revenue is thus less than price and may even be negative. We may, however, lay down as a general rule that it will pay to expand production so long as marginal revenue is expected to be greater than marginal cost and the avoidable costs of the total output less than the total receipts.
It would be Utopian to imagine that a businessman, except by luck, could manage to attain this position of maximum profit. Indeed it may cost more to discover this point than the additional profits that would be earned. It is to be hoped, however, that the cost accountant may so refine his technique to take account of variations in cost and thus facilitate the task of the businessman.*5
Up to the present my chief aim has been to emphasize the importance to business policy of concentrating on variations in costs and/or receipts. It goes without saying that within the business organization information must be made available which enables these variations to be estimated. Before tackling the practical problem of how this information is to be obtained and presented, there are certain analytical difficulties which need to be faced. These difficulties centre around the fact that costs and receipts cannot be expressed unambiguously in money terms since courses of action may have advantages and disadvantages which are not monetary in character, because of the existence of uncertainty and also because of differences in the point of time at which payments are made and receipts obtained.
The fact that there may be non-monetary advantages and disadvantages attaching to different business policies is a difficulty which need only be dealt with briefly since it may be assumed that in most joint-stock companies and in many other businesses, this factor is of little or no significance. None the less it may at times be important. A businessman may wish at the present time not to buy German or Japanese goods quite apart from any considerations relating to their price or quality; or his views on the problems of national defence may make him desirous of, or averse from, supplying firms in the armament industries. Some attempt might be made to measure the strength of these preferences in money terms, but little benefit would seem to be gained by so doing.*6 To this extent the figures of costs and receipts produced by the accountant are incomplete, and without a knowledge of the preferences of the businessman no decisions on questions of business policy can be reached. This factor makes, for example, the computing of income in money terms more and more unreal, the more personal the entity that is considered. The increased-net-worth concept of income, discussed at length in a series of articles by Mr Edwards,*7 is essentially a monetary concept and fails to describe the situation in a realistic manner as soon as non-monetary costs and receipts have to be considered.
It can be claimed that the non-monetary factors which have just been discussed are of no importance in most businesses and can be ignored. Exactly the same analytical difficulties arise, however, in the case of a factor which cannot possibly be ignored. This factor is the existence of uncertainty. When one is estimating costs or receipts, the figures of the estimate by themselves do not show anything near the whole truth. There is the further question of how likely it is that these figures will be achieved. The figures have to be considered in relation to the probability of this result actually coming about. There is yet another difficulty, because even if the figures which are produced relate to the most probable result, it may not be this result which is of vital significance in determining the decision. A person who buys a lottery ticket is not interested in the most probable result! And all business has to some extent the characteristics of a lottery, the direction of investment being influenced by possibilities other than the most probable result. A businessman considering what will be the effect on costs and receipts of a particular decision will no doubt be contemplating a whole series of possibilities, some highly improbable, some by no means improbable and others quite likely. No single figure (even if it were considered the most likely one) would be adequate. Consider now a businessman trying to decide between alternative courses of action, each of which might produce so many different results. It is clear that the choice will depend partially on the attitude to risk-taking of the person deciding. Some businessmen will be influenced much more by possibilities of high profits which are not very probable than will others. There is no one decision which can be considered to maximize profits independently of the attitude of risk-taking of the businessman. A further point is that the correctness of the decision cannot be determined by subsequent events. If a businessman undertakes to do something which entails certain risks, he considers that the chance of gain is worth the risks he runs, and whether ultimately he succeeds or fails has no relevance to this preference.
This lack of objectivity must necessarily be disturbing to those who wish to employ the normal technique of accounting for the solution of many business problems. However a vital factor is apparently being ignored if estimates of costs and receipts make no reference to the probability of these estimates being correct. There is, of course, the extremely difficult problem of whether any numerical value can be given to the probability of the forecast being correct. If it cannot, and it would surely not be denied that in most cases this is so, the most useful way of presenting information is probably to produce several different sets of figures, each one relating to a particular group of assumptions about the course of events in the future. Just as monetary calculations become less realistic as they are applied to a more personal entity, so it is that we find that the single-figure costs and receipts of the cost-accounting textbooks become less significant the more uncertain is the future.
The third difficulty in expressing costs and receipts in money terms is due to the time element. Payments and receipts at different times have to be summated and compared. This can, I think, be made clear by means of an example. Let us assume that an engineering concern is offered two contracts, both of which will employ the full resources of its organization and will take a considerable period of time to complete, one for the construction of a bridge and the other for the construction of an oil refinery. It is obvious that in the case of such jobs as these payments will be made continuously over a long period. It is possible to imagine cases in which receipts come when the job is completed at one particular time, but it is more realistic to consider a case in which the clients pay for the job by instalments, the times when the payments are made possibly being related to the completion of the various sections of the work. To decide whether it is worth while to undertake either of these jobs, and also which of them is the most profitable, it is necessary to take into account the fact that payments are made and receipts obtained at many different points of time. How is this to be done? In order to add payments or receipts or to make comparisons it is necessary to transform these sums into their value at a given date. The time chosen by those who have considered this problem has usually been the present.*8 The present value of the sums accruing or being disbursed at each point of time has first to be discovered. Then these sums, which will be positive for accruals and negative for disbursements, when added together represent the present value of the income which would be obtained from undertaking this particular activity. We have therefore to consider how the present value of a future payment or receipt is determined. We shall assume that estimates are made of future payments and receipts and that these estimates are treated as if they were certain. The present value is obtained by discounting the future sums accruing to or being disbursed by the business by a rate of interest. This procedure, which is of course bound up with the choice of the rate of interest, has now to be investigated. Suppose one has to make a payment now instead of at some future date. What sum would leave one in exactly the same position from the point of view of profits as if one had made the payment at the later date? Clearly it is the sum which, at the rate of interest one could obtain if one did not make the payment now, or the rate of interest one would have to pay if one were forced to borrow in order to be able to make the payment now, would amount to the future sum at the later date. Similarly, if one received a sum in the present instead of at some future date, the sum in the future to which it is equivalent is that sum plus the interest it enabled one to earn or the interest it enabled one to avoid if previously one were borrowing. The rate of interest therefore that one uses for purposes of discounting is quite determinate.*9 It is indeed unfortunate that this process is usually known as discounting. The problem is to transfer the date of a payment or receipt without altering one's profit position. This can be done if one subtracts (when a receipt is brought nearer in time or a payment is moved further off) any interest it enables one to receive or avoid paying, or adds (when a payment is brought nearer in time or a receipt is moved further off) any interest one has to forgo or interest payment one is forced to incur. The addition or subtraction of interest—the discounting—is thus merely a means of ensuring that the transfer of payments or receipts through time does not alter the profits earned.
It cannot be too strongly emphasized that calculations of present values such as have just been made depend on the assumption that the estimates of payments, receipts and the rate of interest can be treated as if they were certain. In fact, however, the introduction of the time element also brings into play the factor whose influence was discussed earlier in this article, the factor of uncertainty. The figures for payments, receipts and the rate of interest are mere estimates. Before coming to any decision, a businessman will have to consider the probability of these estimates actually proving to be accurate. When the satisfaction of a particular contract involves payments and receipts which extend over a period of time, the businessman's attitude to risk-taking, which, as I have said, is purely subjective, will be an important factor determining the decision actually taken. Since no method of accounting can reproduce on paper the mental processes of a businessman, the decision to be taken is one which no mechanical process of discounting can disclose. The only procedure which seems likely to be helpful is apparently the one which was previously suggested, namely, the preparation of several estimates based on different sets of assumptions about the future. We noted previously that the greater the uncertainty, the less significant are single-figure costs and receipts for the solution of business problems. Although the element of time by itself raises no insuperable difficulties, the fact that a lengthening of the period over which forecasts are made will tend to be associated with an increase in the uncertainty with which these forecasts are regarded presents a formidable difficulty for those who wish to present information in a useful way for businessmen.
The difficulties which have been examined up to this stage have been common both to the measurement of costs and receipts. Some attention must now be paid to the nature of costs, since their derived and indirect character is liable to cause difficulty. In this article the notion of costs which will be used is that of 'opportunity' or 'alternative' cost. The cost of doing anything consists of the receipts which could have been obtained if that particular decision had not been taken. When someone says that a particular course of action is 'not worth the cost', this merely means that he prefers some other course -the receipts of the individual, whether monetary or non-monetary, will be greater if he does not do it. This particular concept of costs would seem to be the only one which is of use in the solution of business problems, since it concentrates attention on the alternative courses of action which are open to the businessman. Costs will only be covered if he chooses, out of the various courses of action which seem open to him, that one which maximizes his profits. To cover costs and to maximize profits are essentially two ways of expressing the same phenomenon. In practice it is probably better to regard the cost of doing anything as the highest alternative receipts that might have been obtained rather than vaguely as all the alternatives that are open.
Some characteristics of cost when it is interpreted in this way should be noted. First of all costs are not necessarily the same as payments. It is this fact that makes the 'costs' disclosed by cost accountants something quite different from 'opportunity cost', for cost accounting methods would seem to be designed to 'recover' all payments that have been made for purposes of production. This point can be illustrated by considering the cost of using a particular machine for a certain purpose. Cost accountants would presumably give different answers according to the particular method of depreciation which they employ; but if cost is interpreted as opportunity cost the answer is quite simple and definite. The cost of using the machine is the highest receipts that could be obtained by some alternative employment of the machine. This may be any figure and may be unrelated to the cost of the machine. The other point that must be mentioned is the forward-looking character of the opportunity-cost concept where business decisions are concerned. It is useless to look back at the past, except as an object lesson. Of course one can say that one might have made a Wiser decision and that in this sense costs were not covered. But to employ the term in this way does not seem to be very helpful, for as Jevons reminded us, 'Bygones are forever bygones'. The only course which is open to a businessman is to make the best choice given the knowledge at his disposal, and in this ask I hope to show that the concept of opportunity cost can be of considerable assistance.
Having explained the meaning of the concept of 'opportunity' or 'alternative' cost, I now turn to the question of its application to the solution of business problems. It will be assumed that an attempt is being made to calculate the minimum price at which it pays to accept a particular job. This minimum price is, of course, the total avoidable cost of that job. In working out this total avoidable cost, the calculation of the cost items, materials, depreciation, and interest on capital will be considered as examples of the use of the 'opportunity' -cost concept in the solution of such a problem. Much that I have to say may appear obvious, but it is necessary to secure agreement on simple matters before proceeding to consider more complex questions.
The determination of the cost of materials for a job for which the materials have not yet been bought is simple. It is the estimated amount of money to be spent on their purchase. This accords exactly with the 'opportunity'-cost concept since, if the materials were not purchased, that amount of money would be available for the business. A more difficult problem arises, however, if the materials which are to be used have to be drawn from stock. What is the cost of using them? In the ordinary cost-accounting text-books are to be found a multiplicity of methods of calculating the cost of materials. There is the method by which this is taken to be the amount paid for the oldest part of the stock; another way of making this calculation is to discover the average amount paid for the existing stock; apparently at times the market price of the materials when they are issued is used, while yet another method is to take as one's basis the amount paid for the highest-priced stock. And, as readers will know, this list is not exhaustive. Some writers expressly point out that their figures are not to be used for estimating. It is not, however, always quite clear whether what is meant is that the price one quotes must to some extent depend on demand conditions, or whether these cost-accounting methods do not give one the minimum price at which it pays a business to take a job. Some writers—those, for example, who claim that cost-accounting methods enable one to eliminate unprofitable lines—seem to imply that it is the minimum price which is achieved, and it is therefore necessary to consider whether or not these methods do give one the figure that is required.
Our aim is to discover what allowance has to be made for the cost of materials when a calculation of total avoidable cost is being made. If the 'opportunity'-cost concept is employed, the question that has to be asked is what one would do with the material if it were not used on this job. It could either be sold or used on some other job. The cost of using the material is therefore either 1) the price if sold minus the costs of selling, or 2) the expense that would be avoided if the material were used on some other job; that is, the payment that would have been made for materials minus the cost of holding the existing materials until they are required.*10 Whichever of these two amounts is the greater may be regarded as the cost of using the material.
I shall now illustrate the proposition which has just been developed by means of an example. First of all let us suppose that a company has entered into a long-term contract for the supply of a certain raw material at £ 10 per ton, it being agreed that a minimum quantity of 1,000 tons will be taken each year. Let us also assume that the amount of material which is consumed is in fact slightly less than 1,000 tons. What will be the cost of using the material? Since, as I have said, the amount consumed is less than 1,000 tons, it follows that there is in fact always material which is available for production. The possibility of using material on another job if it is not used for this one does not therefore arise. The 'opportunity' cost of the material must therefore be the price in the open market less the costs of selling, or possibly, if this were higher, £ 10 minus the sum the suppliers would accept or plus the sum they would pay to set aside the contract.
The idea that entering into a long-term contract at a fixed price for a material in some sense avoids fluctuations in the cost of that raw material (a notion which would certainly be derived from a study of many of the usual cost-accounting methods) is one which I believe to be erroneous. The main result of entering into such a contract is to make profits higher than they would be if the price during the period is on balance greater than £ 10, and lower if the price is on balance less than £ 10. 'Opportunity'-costs, however, will continue in such a case to fluctuate with price movements on the open market.*11 The vigilance of those concerned with seeing that the best use is made of the firm's resources must not be relaxed because of the existence of such a contract. A numerical example will, I think, make this perfectly clear. Let us reconsider the policy of the company which we had supposed to have entered into a long-term contract for the supply of a material at £ 10 per ton. Suppose that the market price of the material is £ 18 per ton, and that the costs of selling are £ 1 per ton. The receipts from selling a ton of the material would be £17 per ton.
Now let us suppose that a contract is offered which will entail avoidable costs of £ 150 and will also require ten tons of the material. If one reckons the cost of the materials at £ 10 per ton, which is the amount actually paid for the material, the total avoidable cost would come to £ 250. Suppose that the price which is offered for the job is £ 300. It would appear on the basis of this calculation that the business concerned would earn a profit of £ 50 from carrying out this contract. On the other hand, if the calculations were made, using as the basis for the material cost £ 17 per ton, the total avoidable cost would have amounted to £320. The job would then have appeared unprofitable, since the receipts from the jobs would not have covered the total avoidable cost. My view is that this calculation gives a correct result and in fact it would be more profitable for the firm to refuse the contract. It can, I think, be demonstrated that it would have been in a better position through doing so. If the job were actually carried out, the receipts and payments would be as shown in Table 5.3.
If the contract were not carried out and the materials were sold, the figures of receipts and payments would then be as shown in Table 5.4.
A point that does not need much emphasizing is that the cost-accounting methods for the pricing of materials which were discussed earlier do not give one the 'opportunity' cost of materials. Most of the methods—for example, the use of the price of the oldest stock or of an average price paid for materials in stock—are determined by past payments or payments which have been agreed upon in the past. As we have seen, there is no reason for supposing that the price one has paid for materials, or a figure derived from a calculation based on the prices one has paid, will give one the 'opportunity' cost of using materials. Even the method by which materials are charged out at market prices, and which implies a break with the idea that cost calculation must be linked up with payments, is unsatisfactory. On the one hand it ignores the expenses involved in reselling materials one has purchased—expenses which may be quite considerable; on the other hand it does not take into account the value of the materials if used for some other job. I do not wish to suggest that there may not be many purposes which are served admirably by modern cost-accounting methods. My sole aim in this section is to point out that these methods do not give one 'opportunity' costs and do not enable one to calculate avoidable costs. This being so, it seems to me that any claim that modern cost accounting (at any rate in the form in which it is to be found in the textbooks) enables unprofitable lines to be discovered and eliminated is misleading. It is only possible to discover whether or not a particular activity is profitable by comparing the avoidable costs with the receipts. And this, as I understand it, is a task which modern cost-accounting methods do not enable one to perform.
This subject is one which it is difficult to treat, if only for the reason given by Professor Hatfield when he said that 'accountants are not of one voice on the subject, nor have they all learned to make satisfactory exposition'.*12 I do not, however, propose to put forward a precise definition of depreciation and I shall content myself with saying, and I believe there can be little doubt about this, that the problem of depreciation arises from the fact that assets may fall in value. As I understand it, much of the accounting literature on the subject considers depreciation from one of two points of view. The first is concerned with the problem of valuation for the purpose of measuring profits, and the second with determining the amount of reinvestment which is necessary if capital is to be 'maintained intact'. These are, however, problems of financial and investment policy and need not, I think, be considered by those who are concerned with the ordinary run of business decisions.
The reason why depreciation has to be considered when the notion of 'opportunity' cost is being examined is that the value of an asset is sometimes affected by the use to which it is put. At this stage some reference is necessary to the meaning which I attach to the phrase 'the value of an asset'. By this phrase I mean the present value of the net receipts which it is estimated will be obtained from ownership of that asset. If future receipts and/or payments may be altered by the way in which an asset is used in the present, it is clear that the value of the asset, in my sense, depends to some extent on how it is used. It is this fact that I wish to take into account. If the value of an asset, as this phrase is used by accountants, has no relation to future payments and receipts, but is equal to the original cost of the asset reduced by the application of some mechanical rule, then changes in that value clearly have no connection with the cost which I am examining. It should be noted that, even if the value of an asset is calculated in the way I have suggested, it is only those changes in value which result from use that are relevant when one is deciding whether or not to take on a particular job. Let us assume that if a machine is not used, its value will fall from £100 to £80 and that, if it is used, its value will fall from £100 to £75. In this case depreciation through use is £5 and it is this figure with which we are concerned when we are discussing depreciation as an 'opportunity' cost. What I have termed 'depreciation through use' Mr Keynes calls user cost.*13
Let us now return to our problem. The choice between using or not using a machine, or between using a machine for one purpose and using it for another, will be influenced by the effect such uses have on future payments and receipts. It is possible to calculate the present value of future receipts and payments by discounting them by a rate of interest, a process that I have already described. The cost which we are considering is measured by the change in the present value of an asset which results from use. Examples of this cost can easily be found. If a machine is used in the present instead of leaving it idle, it may well be that its life is shortened. This means that profits that would have been earned at the end of its life will now no longer be received. This loss of profits in the future through the use of a machine in the present is a cost of using the machine which must be taken into account. Similarly the increased use of a machine may imply higher costs of maintenance in the future, or may render the machine unsuitable for purposes which otherwise it would have served and thus raise costs and/or lower receipts on jobs on which it is employed. These are examples of depreciation through use. It is clear that this cost is dependent on estimates of the future. Since, however, the future is uncertain, the allowance that will be made for this factor will be partially dependent on the attitude to risk-taking of the businessman. Although it will to some extent depend on subjective factors, depreciation through use is a cost which will have to be taken into account in calculating 'opportunity' cost.
I shall endeavour to show, by means of an example, the significance of what I have termed 'depreciation through use' and others call 'user cost'. In the case of many industrial concerns it may be that depreciation through use is of little importance; the same, however, cannot be said of mining companies or other concerns with assets of a similar character. This is very clearly brought out by Mr F. W. Paish in an article on 'Causes of Changes in Gold Supply',*14 He says:
In most types of production we have to consider the problem of the optimum rate of application of variable factors, including raw materials, to certain fixed equipment of which the useful life does not greatly vary with the intensity of utilization. In other words, the proportion of marginal cost, which consists of user cost, is relatively small, and even substantial differences in estimates of user cost would have very little effect on total marginal costs and on the rate of output. In the case of a mine, however, the position is the exact opposite. There is a given stock of raw material of which the rate of output, and therefore the length of life, is almost infinitely variable according to the amount of fixed capital and other resources which are applied to its exploitation. In this case every ton of ore extracted means a ton of ore less to be extracted at some future date; and if the deposit is a valuable one, which is expected to show a large profit over costs of extraction, the greater proportion of marginal cost may be the user cost of the deposit.
The fact which Mr Paish brings out, namely that in the case of a mine an increase in output will reduce future receipts, is one which has to be taken into account when output policy is being considered. A numerical example is bound to be somewhat of a simplification, but it may clarify the argument. We shall suppose that we are considering the output to be produced from a given mine. One assumption that will be made is that each additional ton produced in the current year reduces the output that can be produced in the tenth year by one ton. The net receipts from production in the tenth year accrue at the end of that year. We shall also assume that the estimates that are made are regarded with certainty. Marginal cost may be taken to be the cost of an additional ton and marginal receipts the receipts from the sale of an additional ton (see Table 5.5).
Let us suppose that producing 197 tons instead of 196 tons in the current year means that it is only possible to produce 199 tons in the tenth year and not 200 tons. Similarly let us suppose that producing 198 tons in the present year, instead of 197 tons, means that it is impossible to produce 199 tons in the tenth year, but only 198 tons; and similarly with other changes in output. If 197 tons are produced instead of 196 tons, £50 that would have been received at the end of ten years will not now be obtained. If 198 tons are produced in the current year instead of 197 tons, £90 that would have become available at the end of the tenth year will now not do so. If we assume that the interest rate that we have to use for discounting is five per cent per annum, the user cost is in these cases the present value of £50 and £90 in ten years at five per cent per annum. The costs-and-receipts position for the first year may be set out once again including depreciation through use or user cost (see Table 5.6).
It can be seen by looking at Table 5.6 that it will not pay to produce an output greater than 199 tons, because marginal cost (including user cost) for a larger output is greater than marginal receipts. Had depreciation through use been ignored, it would have appeared as if an output of at least 200 tons would have been profitable. But to ignore depreciation through use would mean ignoring the effect changes in output have on future receipts. Depreciation through use is part of 'opportunity' cost, because if that output were not produced, certain other receipts would accrue—although in the future. The fact that these receipts accrue in the future involves the difficulty which was discussed earlier, the comparison of receipts at different points of time. The method by which this difficulty can be overcome is to compute the present value of these future receipts by discounting, although, as I said, this makes the process seem too mechanical and obscures the reasons why this process produces significant results. There is a further point to which I have continually drawn attention. Since estimates of future receipts and future rates of interest cannot be made with certainty, all that it is possible to do on paper is to produce for the guidance of the businessman different estimates of what depreciation through use would be if various groups of assumptions about the future were realized. The actual choice that the businessman makes will then depend to some extent on subjective factors.
The problem of whether or not to include interest on capital in the calculation of cost is one of the most controversial in cost accounting. The usual method of approach is, however, a somewhat peculiar one. Instead of treating the problem directly, writers on cost accounting commonly list the advantages and disadvantages of considering interest as a cost and then give their own opinion as to whether or not the advantages outweigh the disadvantages. As a result, several quite distinct questions are discussed at the same time. There is not only the question of whether interest is a cost, there is also the problem of whether it can be easily calculated or whether, even if it is calculated, it is of sufficient importance to be worth bothering about. It is thus possible for a conclusion to be reached that interest on capital should not be included in the cost accounts without thorough discussion as to whether it is a cost. The conclusion may be reached because, for example, the author thinks that even if it is a cost, it would be much too complicated a matter to calculate it. In this way the main question is avoided. Although this procedure is no doubt quite adequate for the purpose these writers have in mind, it seems to me unfortunate, since a concentration on the fundamental question of whether interest is a cost would have indicated the characteristics of the 'actual cost' which modern cost accounting aims at disclosing.
Before proceeding to consider the more fundamental question, we must take account of those technical problems which have made many writers on cost accounting decide on the exclusion of interest from their calculations. First of all there is the belief that if interest is to be included it will not be possible to do so within the framework afforded by double-entry book-keeping. This if I understand him right, is the view of Mr W. W. Bigg. He says:
...there is no reason why the cost accounts should be encumbered with a mass of calculations which merely tend to complicate the results achieved thereby. The result of including interest may be ascertained with the minimum of difficulty by the preparation of statistical statements quite apart from the cost accounts and from such statements the necessary information can be obtained to enable an economic price to be fixed. To this treatment the majority of the objections to the inclusion of interest in the cost accounts do not apply.*15
It may well be that double-entry book-keeping has its limitations, but it would seem to be quite another matter to argue—and Mr Bigg does not argue—that because double-entry book-keeping cannot handle a particular problem, it is therefore no concern of the accountant. The problem we are discussing may still be a matter of lively interest to accountants, even if it cannot be solved within the confines of modern cost accounts.
A subsidiary objection to the inclusion of interest as a cost, which seems connected with the point we have just discussed, is that cost accounts should deal with actual money payments. It may, of course, be true that cost accounts in fact only deal with actual money payments; it may even be true that the particular technique employed is incapable of any modification to enable interest to be included. What it does not determine is whether interest is a cost. It is also said that to include interest on capital (when this is not paid to someone outside the business) would mean anticipating profits in the valuation of stocks. There seems, however, to be no reason why the procedure adopted for the valuation of stocks should in any way depend on the answer given to the question we are examining.
The arguments which are used to support the inclusion of interest in cost calculations are fairly straightforward. It is pointed out that capital is just as much a factor of production as labour and that if labour costs are included so should interest on capital. It would obviously be foolish to decide whether to substitute machinery for labour in production without taking into account interest. As it is said in Mr Bigg's book, 'if £2,000 is expended upon the purchase of a machine, it must be remembered that in the first year of its life it has cost, at five per cent, £100 in respect of interest lost on the money expended....'*16
Similarly, when the profitability of different operations is being compared, the argument is used that quite erroneous results would be reached if account were not taken of the fact that some jobs require more capital equipment or take longer and tie up more money in work in progress. It is difficult to find in the literature counter arguments to these views. Assertions such as 'interest is the reward of capital as much as wages are of labour is one of economics, not of costing,' and 'to include interest paid on borrowed capital only cannot be accepted, because it has no more connection with manufacturing than all the capital invested in the business. Interest in both cases is a matter of finance, not of manufacturing',*17 are hardly to be taken seriously. There is, however, one answer to these arguments which is of some substance. It is to be found in Professor T. H. Sanders's Cost Accounting for Control. He says that interest 'is not really a cost, but only an opportunity forgone; and the capital in buildings and equipment for a certain industry having been once invested, that capital is no longer free for investment elsewhere'. There would seem to be little doubt that if one were considering whether or not to take on a particular contract which involved the actual purchase of capital equipment, that interest on the amount expended would reckon as a cost. Professor Sanders's objection applies, however, once the machinery has been installed. First of all it is clear that the net receipts contributed by the machinery must be estimated to be greater than the interest that could be obtained on the amount of money represented by the secondhand value of the equipment minus the costs of selling it. But if it is decided that the machinery is not to be sold, this factor is of no relevance when the cost of using the equipment for a particular job is being calculated. Nor is any allowance for interest on the original cost of the machinery. All that need be considered is the alternative net receipts that would be obtained if the machine were employed on some other job. If there is no other job on which the equipment could be used, the cost of using the maching (if we exclude depreciation through use) will be nil. It is not therefore possible to say whether any allowance should be made for the use of the capital; this depends on the facts of the case. It is, however; somewhat misleading to talk about this cost as interest on capital. It is merely the highest alternative net receipts that could be obtained if the particular job under consideration were not taken. The problems of how one determines the value of the capital and the interest rate to employ if one is to include interest on capital in one's cost calculation are avoided. Similarly it is shown to be a matter of no importance for our problem whether the money which was spent on the purchase of the equipment was obtained by the issue of debentures or was money provided by the business itself. It is also clear that in those cases where an allowance is made for interest on capital, in, for example, the uniform cost systems of trade associations, it is most improbable that the 'opportunity' cost of using capital is obtained.
I stated earlier that I would illustrate the 'opportunity'-cost concept by considering the three items of cost, materials, depreciation and interest on capital. The 'opportunity' cost of using materials in stock we found to be either the price if sold minus the cost of selling, or the expense that would be avoided if the material were used on some other job. Depreciation considered as an 'opportunty' cost could be taken to be depreciation through use or the present value of the future profits lost through use. Interest on capital, if it is to be interpreted as 'opportunity' cost, must be regarded as the alternative net receipts that could be obtained by the use of the machinery.
IX SOME CRITICS ANSWERED*18
I now propose to pause, and review the theory which I have been discussing. A pause will at the same time present an opportunity for examining certain criticisms which have been made of the theory.
It has been suggested that I was 'confusing charges against profit with costs'. It was further stated that: 'One of the great advantages to be derived from cost accounts is the explanations which they afford of the financial results disclosed by the normal trading and profit-and-loss account'.*19 I trust I have not misunderstood the point, but judging from the rest of the letter, it seems that the argument is that we must allocate 'oncosts' to departments in order to discover the profits contributed by each of them. My answer to this is that it is not possible (except in most unlikely circumstances) to divide up total profits and to decide how much is to be attributed to each department. Of course the methods which involve allocation of 'oncosts' do result in a figure for profits being associated with each department, but it is suggested that if a logical method is adopted for discovering the profits which result from the existence of each department, it will in general be found that adding together the profits contributed by each department separately does not give a figure equal to the total profits of the business. To explain this point, I shall work in some detail through an example. I shall assume that we are investigating the affairs of a department store with four departments: piece goods, men's and women's wear, furniture and a restaurant. Table 5.7 gives particulars relating to this business. The departmental expenses for materials and sales assistants would cease if that department were closed down.
The total sales for the period were £3,550 while the total expenses were £3,030. We may therefore assume that the profits were £520. The problem we are considering is whether it is possible to divide up this sum and say how much was contributed by each department. It would seem logical to define the contribution to profits of a particular department as the addition to profits due to having it. We have seen that profits with all four departments were £520; if the withdrawal of a particular department would have caused profits to fall to £400, it would seem reasonable to say that the profits contributed by that department are £120. If we assume that this is the basis for calculating the profits of each department, we have to estimate the effect of closing each one in turn. We shall also suppose that there is no possibility of leasing the space that is freed.
Let us start with the piece-goods department. In the case of the particular department store we are considering, we may assume that it is one which attracts many customers to the store and that a most important result of closing down the piece-goods department would be that fewer customers come to the store. The effect of this is so great that in spite of the additional room that is available for display, it is estimated that the sales of all the remaining departments would fall. The estimated operating results if the piece-goods department were closed down are shown in Table 5.8.
It will be seen that the total sales would be £2,480 and the total expenses £2,420. The profits would therefore be £60. As the profits including the piece-goods department were £520, the profits resulting from having that department are £460.
Now let us suppose that it is the department selling men's and women's wear that is closed down. Piece-goods require a great deal of space and the additional room can be used by that department. It is estimated that there would be an increase in sales by the piece-goods department, but a fall in the sales of the others. These results are set out in Table 5.9.
The total expenses would be £2,500, while sales would amount to £2,590; a profit of £90 would be shown. The profits contributed by the men's and women's wear department would therefore seem to be £430.
We can now consider the effect of closing down the furniture department. The space that it occupies could be used to some extent by the piece-goods department which, it is estimated, would result in a rise in sales; the other departments, however, would show slight falls. Table 5.10 shows the estimated operating results had the furniture department been closed down.
The profit under these circumstances would be £35, since sales are estimated at £2,545 and expenses at £2,510. The furniture department therefore adds to profits a sum of £485.
And now we come to a consideration of the last department, the restaurant. The loss of this department would mean, it is estimated, a slight fall in the sales of the others. But it would also result in a large fall in general and miscellaneous expenses. The estimated figures after the close of the restaurant are set out in Table 5.11.
The profits in this case would be much higher; actually they would be £210. Sales would be £2,580 and expenses £2,370. The amount of the profits that seem to be attributable to the existence of the restaurant is £310.
Thus it is that if we calculate the profits contributed by each department on what seems to me to be the only basis on which this can be done, the individual profits of the departments work out at £460, £430, £485 and £310. The total of these figures is £1,685. The actual profits were £520. It seems clear that it is not possible to divide up total profits among the different departments and to say how much each one contributes. The only case in which it is possible to do this is that in which there are no economies in having one particular combination of departments. The point that I am making is not dependent on the fact that possessing certain departments affects the sales of others (as it does in a department store), but applies equally well to manufacturing business in which this factor might be of no importance.
A final example (Table 5.12) will, I hope, make this quite clear. suppose that we are examining a manufacturing business which is producing unbranded radios and refrigerators. We may also assume that sales would remain the same whether the production of these two products is combined or not.
The total of other expenses may be taken to be £2,500 if the manufacture of these two products is combined but £2,000 for each product if either of them is produced separately. Thus profits are £1,500 if manufacture is combined, but no profits at all would be earned if production were separate. How is it possible to say how much of the profits are contributed by each department? Without either of them there would be no profits. As will be seen from this example, the mere fact that one could discover the profits of a department if it were run as a separate business does not enable one, if there are economies in having several departments, to say how much is contributed to profits by each department if in fact they are combined within a single business.
It will perhaps indicate most clearly the nature of the approach to business problems discussed if emphasis is placed on its close connection with the making of decisions. The technique which has been examined is one which aims at aiding businessmen in making decisions. One can discuss the meaning of the term 'avoidable costs' but what costs are avoidable and their actual measurement can only be determined with reference to a particular decision. It is for this reason that I dislike a classification of costs which divides them into 'fixed' and 'variable' costs—depreciation, interest on capital and the managing director's salary being, for example, regarded as fixed costs while wages and the cost of materials are regarded as variable costs. Instead of speaking of fixed and variable costs, some writers use the terms overhead and prime costs while others distinguish between indirect and direct costs. The difficulty of using such a rigid classification is that whether a particular category of cost is likely to vary depends solely on the decision which is being taken. If the effect of enlarging a certain department is being considered, the costs that will prove to be variable are likely to be quite different from those that would vary if the introduction of a new product is being contemplated. It seems best therefore not to make any attempt to segregate costs into the classes 'fixed' and 'variable' but merely to try to discover what costs would be avoidable if a particular course of action were taken or, looking at the problem the other way round, what additional costs would be incurred if that action were carried out. The same procedure applies of course to receipts.
This linking of cost analysis to particular decisions makes any mechanical classification of costs almost impossible. The costs whose variations are of significance for one decision will be of no significance for others. There are innumerable decisions and each one may require a different classification. In fact this difficulty has not been very apparent in modern cost accounting, partly because its function has been taken to be the ascertainment of 'actual cost' in the past without reference to the use to be made of this figure, but also because, in so far as these results were thought to have relevance to business decisions, it was a particular set of decisions that cost accountants had in mind. It would seem that the figures produced were thought to be of use in such decisions as those relating to output changes, or in deciding whether to accept a certain contract or close a department. Other decisions—and possibly even these—would require special investigations to provide the information on which the decision is to be based. The problem of what information is to be collected, how far it is to be presented regularly and how far it is to be collected as part of a special investigation are practical points of obvious importance but about which little can be learnt in the cost-accounting textbooks.
I have already pointed out that if we are to judge from writers on cost accounting the business decision for which the figures disclosed in the cost accounts are of most significance is that relating to the output to be produced. It is, of course, a general criticism of modern cost control that it does not concern itself with calculating avoidable costs. When, however, information is prepared for the purpose of determining output, a further criticism must be added, since the figures provided relate to average rather than marginal cost. Marginal cost I defined as the avoidable cost of an additional unit of output. Some attempt must be made to estimate marginal cost if the output which yields the greatest profits is to be chosen. As an example of the use of the marginal-cost concept, we may examine the case of an electricity-supply undertaking which owns a coal mine and which has to determine how much to produce in its own mine.*20 The most profitable policy for this undertaking would be to produce coal in its own mine so long as total avoidable costs were covered and marginal cost was not greater than the cost of purchasing the coal on the open market. There are then two questions which the management would have to ask constantly. First of all it would have to consider whether the expenses that it would save by not producing anything (the avoidable cost) are greater or less than the amount it would have to pay for the same quantity. The other question is whether the cost of producing one more unit is greater or less than the expense of buying it. If it is less, then it would pay to increase production from the mine; if greater, it might be profitable to contract. To serve as an example, Table 5.13 gives the costs.
If the price of a 100-ton lot is £150, it is clear that for all amounts shown in the table, the total avoidable costs are less than the expense involved in buying these quantities on the open market. On the other hand, it would not be profitable to produce more than 1,200 tons, since, if 1,300 tons were produced, the extra 100 tons would have involved the business in additional expenses of £169 whereas the same quantity could be obtained for £150 by purchase on the open market.
The marginal-cost table shows the costs of producing further units of output from the undertaking's own mine, and it seems clear that this has to be compared with the costs of purchasing coal if the economical level of production is to be reached. A real difficulty arises, however, if marginal costs do not move regularly as in my table but, after rising with every increase in output, start to fall and then recommence rising. In such a case a mechanical application of the rule I gave would suggest that there are several outputs at which profits are a maximum. When this is so, it is necessary to choose out of these outputs that one which is most profitable for the undertaking. Let us consider a case in which the marginal costs have this characteristic. Assume that the cost figures for the coal mine have been as they are set in Table 5.14.
We may assume that the consumption of coal is estimated at 1,800 tons. If the price of coal is £150 per 100-ton lot, how much of the 1,800 tons required will be produced in the mine? It would seem to be either 400 or 1,100 tons or 1,700 tons. If the output is increased from 400 to 1,100 tons, total avoidable costs rise from £400 to £1,375. The additional 700 tons will therefore cost £975. To purchase this amount on the open market at a price of £150 per 100-ton lot would cost £1,050. It is therefore more profitable for the undertaking to produce 1,100 rather than 400 tons. If, however, 1,700 tons are produced instead of 1,100 tons, total avoidable costs will increase by £1,185. To purchase 600 tons on the open market would cost £900. It follows that of the three outputs mentioned, it would be most profitable to produce 1,100 tons.
One correspondent suggested that it would be preferable for the undertaking to produce that output at which average costs are at a minimum. If, however, the cost of purchasing additional units of output on the open market is grater than the costs of producing these units from the undertaking's own mine, it seems clear that it will pay to expand production whatever happens to average costs.
It is worth while emphasizing that the concept of marginal cost can only be employed when decisions relating to output are under consideration; the notion of avoidable costs is, however, of universal application.
Notes for this chapter
R. S. Edwards, 'The Rationale of Cost Accounting', reprinted here, pp. 71-92.
Edwards, 'The Rationale of Cost Accounting', p. 76.
Edwards, 'The Rationale of Cost Accounting', p. 88.
Edwards, 'The Rationale of Cost Accounting', p. 89.
There followed a section in the original articles which illustrated the use of the concepts of marginal cost and opportunity cost by considering an electricity-supply undertaking which owned a coal mine and which discussed when the undertaking should buy coal on the open market [footnote added].
A manufacturer of pig iron, who prefers to supply armament firms, might reckon his preference in money terms at 10s (50P) per ton. He would therefore add 10s (50P) per ton to his receipts when his pig iron is sold for this purpose.
Originally published in the Accountant (2 July-24 September 1938) and reprinted in Studies in Accounting, ed. W. T. Baxter, pp. 227-320.
There is of course no reason why some other date should not be chosen if it is thought that this will prove more convenient.
In practice, since the interest rate would probably vary with the amount one lent or borrowed, there would not necessarily be a single rate.
The other job may be a similar one at a later date or of quite a different character. The material displaced may actually be a less expensive one. Another cost that may have to be deducted is the expense of transforming the material in to the form in which it is required for the other job.
The absolute movements in cost, assuming that selling expenses are unchanged, will be the same. But since in this case 'opportunity' costs is equal to the price minus the selling expense, the percentage variation in cost will be greater than the percentage variation in the price.
H. R. Hatfield, 'What they say about Depreciation', Accounting Review (March 1936). Reprinted in Studies in Accounting, ed. W. T. Baxter, pp. 337-50.
See The General Theory of Employment, Interest and Money, p. 53.
Economica (November 1938), p. 384.
W. W. Bigg, Cost Accounts (1932), pp. 84-5. A similar point is made in Wheldon, Cost Accounting and Costing Methods, pp. 128-9.
Bigg, Cost Accounts, p. 82.
Both are to be found in Wheldon, Cost Accounting and Costing Methods, p. 128.
What follows was an attempt to answer criticisms of my approach which had been made in correspondence printed in the Accountant (footnote added).
In a letter written by Mr W. W. Bigg, the Accountant (15 October 1938).
This example had been discussed earlier in the original articles but this section has been omitted in this condensation [footnote added].
Essay 6, The subjective theory of value and accounting 'cost'
End of Notes
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