## Cost Accounting - Allocating Indirect Expense

METHODS OF DISTRIBUTING INDIRECT

EXPENSES

There are seven methods of distributing indirect expenses which may be considered as more or less standard. A study of methods found elsewhere under other names will show that they are more or less modifications or combinations of these seven. It is suggested that under some circumstances one of these methods may be found valuable to distribute the general operating expenses over the departments, while another method may be used more advantageously in the department itself to apply the expense to the product.

The methods are:

(1) Direct Labor Cost

(2) Direct Labor Hours

(3) Direct Labor and Material Cost

(4) New Pay Rate

(5) Old Machine Rate

(6) New Machine Rate

(7) Fixed Machine Rate

(1) Direct Labor Cost

This method is based on the principle that indirect expenses are incurred in proportion to the amount of labor involved, this amount being measured by the labor cost.

To operate the plan, the total cost of direct labor charged to the product for a def1nite period is ascertained, together with the total indirect expenses for the same period. The total indirect expense is divided by the total labor cost; and this shows what per cent the indirect expense is of the total productive labor. The amount of indirect expense assigned to any article is then found by multiplying the labor cost of the article by the rate. Adding the amount of the indirect expenses to the prime cost gives the total or factory cost. The same principle applies in finding the factory cost of any job, production order, or process.

To illustrate, suppose that the pay-rolls for a certain cost period show payments of $16,000 for direct labor, and that the indirect expenses for the same period are $14,000. These indirect expenses are 87^ per cent of the direct labor cost. Now, if a man worked on an article 5 hours at 32 cents an hour, and the cost of material was 60 cents, the total cost would be $0.60, plus $1.60, plus 871/2 per cent of $1.60, or $3.60.

The simplicity of this method is a great point in its favor, but at the same time offers a temptation to employ the method too widely. The point to consider is how far the particular conditions are in accord with the principle of the method. To fit the case perfectly, the labor should be the dominant element in the manufacturing process, and there should be a marked uniformity as to product, wages, and time of operation. These conditions rarely exist throughout a factory, but are not uncommon in single departments. The limits within which the method may be advantageously applied are therefore fairly well defined.

When the direct labor method is employed, special care must be exercised, if there are machines, to see that they are uniform as to cost and running expenses, or, if not, that there is a corresponding difference between the wages paid to the operators. The method is less accurate, and even misleading, if these uniformities do not exist. For instance, if a low-priced man is operating an expensive automatic machine, and a high-priced man is working at a cheap machine where skill amounts to more than running expense, the charges for indirect expense will not only be inaccurate, but will be actually reversed.

When the residue of unabsorbed general operating expenses is small, the direct labor method is often used to prorate it over the departments, first, because the data on which to base the distribution are easily obtained, and second, because any resulting errors, when divided up over all the output of all the departments, will hardly be appreciable. Only an examination of the circumstances in the case can determine whether theoretical accuracy may be safely put aside for the sake of practical results.

(2) Direct Labor Hours

The principle of this method is the same as that just described, except that the amount of labor is measured by time and not cost. That is to say, the indirect expenses of a plant are considered to be in keeping with the number of employees engaged, and the hours they work, rather than with the wages they receive.

The plan is to divide the total indirect expense for some definite period by the number of productive labor hours in that same period, in order to find the amount per hour to be added to the prime cost of the product. Using the example given before, suppose the number of working hours for direct labor to be 56,000, and the indirect expense to be $14,000 as before. $14,000 divided by 56,000 gives an indirect expense per hour of 25 cents. In producing the single article previously discussed, the other conditions remaining the same, the total would be 60 cents for material, plus $1.60 for labor, plus 5 x 25 cents for overhead, equaling $3.45.

An analysis of the difference between the two costs will provide the best basis of comparison between the methods. The critical point is the 32 cents per hour of the labor cost in the first example. The average wage per hour found by dividing $16,000 by 56,000 is only 28 4-7 cents per hour, and therefore the output of any man whose pay is more than 28 4-7 cents per hour has to bear more of the indirect expense in the first method than in the second.

This makes it perfectly clear why “there should be a marked uniformity as to product, wages, and time of operation” in the direct labor cost method. Evidently, differences in any of these factors tend to throw the costs out of true, unless it can be shown that there are corresponding differences in the direct costs. And this has to be shown in each particular case; for there is no essential reason why, as between two men working side by side, the output of the higher-priced man should incur more indirect expense than the other. Consideration will show that, on the whole, indirect expense is more a function of time than of labor cost. If the items that make up indirect expense are examined one by one, as interest, depreciation, light, heat, power, supervision, etc., it must be seen at once that the majority, though not all of them, accumulate according to time, and have but an incidental connection with the rate of wages.

The conclusion is clear that, other conditions being equal, the labor hour method is applicable to a wider field than the labor cost method. Certain limitations remain, viz.: The labor should be a dominant factor, and, for the most part, the product should be uniform. Where machines are used, the same precautions must be taken as in the case of direct labor cost, except that the wages of the operators may be disregarded.

(3) Direct Labor and Material Cost

Under this method of expense distribution, the cost of material is recognized as one of the factors that give rise to indirect expense. The principle and plan of operation are exactly the same as described in the direct labor cost method, if “prime cost” is substituted for “direct labor cost.”

The limitations described there all apply in this case, with the additional condition that the material cost and labor cost should be nearly equal. This method is seldom found in practice, and then almost always as an averaging method, to prorate the general expenses over the whole product. In such cases it must meet the objection to that class of methods as a whole.

If the method is used out of its special field, where the necessary uniform conditions do not exist, the results are quite unreliable.

(4) New Pay Rate

The “New Pay Rate” is still another way of utilizing the principle of direct labor cost in expense distribution. It is essentially a departmental method, and is rarely used for any other purpose.

Under this plan the indirect expenses connected with any operating department are first determined; and to these is added the department’s share of the general operating expenses, which is determined on any basis that seems best. Next, the percentage of expense to labor cost is determined as in the first method; but, in stead of this rate being added to the total labor cost, it is applied to the employee’s wage per hour. For instance, if the indirect expenses were 62 per cent of the direct labor cost, and a workman’s pay was 32 cents per hour, the new pay rate as applied to the product would be 32 cents plus 62l/2 per cent of 32 cents, or 52 cents per hour. If the man worked five hours on any one article, that article would be charged with five times 52 cents, or $2.60 for labor and indirect expense. By adding the material cost to this, the total cost is shown.

The principle involved, and the conditions of its application, have already been sufficiently discussed under the direct labor cost method. The only advantage of the new pay rate lies in the ease with which the expenses are prorated over the product. Once the rate is determined, it is a very simple matter to apply it to every article or order.

For finding costs it is just as accurate as the direct labor cost method and no more; but as a method it fails to present the data necessary to analyze costs properly. It collects charges in totals; and, in order to attain simplicity, neglects the proper classification and arrangement. However practical it may be in some cases, this last consideration disqualifies it as a part of any complete cost system.

(5) Old Machine Rate

All machine rates are based on the principle that indirect expenses accrue according to the number of hours machines are in operation. There is considerable difference in the methods employed by the different forms of machine rate in collecting and applying the charges to the product. The simplest is the “Old Machine Rate.”

Under this method, the amount of indirect expense for a certain period is divided by the number of hours the machines have been in operation during that period, and the rate per hour is applied to the product, according to the number of hours it has been in process, as its share of the overhead. In common with all other general methods, it will produce accurate results only when the conditions are substantially uniform. The machines should be alike as to cost, power, floor space, etc.; and this practically limits its scope to departmental distribution. When such conditions exist in a department, the old machine rate is both convenient and accurate, and will naturally be selected in preference to more complicated methods.

In departments where bench work is combined with machine work the method breaks down, because it makes no provision for anything outside of machine-made products. For the same reason it is almost never suitable for distributing general operating expenses.

(6) New Machine Rate

The “New Machine Rate” represents the modern application of the machine rate principle to complex conditions. It connects or welds three principles or ideas into one working system.

(1) It employs the machine rate principle, as stated. .. »

(2) It recognizes and provides for the differences in indirect expenses that arise from different kinds of machines.

(3) It is specifically devised to absorb, as direct charges, all the indirect expenses that can be associated directly or indirectly with the operation of any machine or process.

In installing the new machine rate, the department is taken as the unit whenever possible; but if a department includes different machines or processes, a further subdivision of charges must be made inside the department itself. The essential point is to reduce the unit to processes of the same kind, or to the machines used in such processes, even if this carries it down to the single machine.

The object in view is to collect the various charges against each machine or process in such a way as to know what it actually costs to run the machine per hour; ». e., what the hourly machine rate is when the operations or processes have been classified, and the charges have been made, each item being considered by itself. In making up the charge per hour only the actual number of operating hours for the cost period is considered.

In making up the machine rate, the labor cost is obtained from the time reports, as is also the actual number of operating hours.

Circumstances must determine whether the material cost should enter into the machine rate or not. If the materials operated on vary in grade or price, the rate is made up of the other expenses, and the material cost not included until after the process cost for each article or order is calculated.

The depreciation per hour is found by dividing the cost of the machine by the total estimated number of working hours in the life of the machine.

Most of the floor space charges, and those resting on the value of the machine, as interest, insurance, etc., are steady, or annual, charges, and accumulate whether the machine is idle or not. These charges for the cost period are made a part of the machine rate by being divided by the number of actual working hours. If there is very much idle time on the part of a single machine, it may be best to make the annual charges for such machine a part of the department indirect, and so spread the cost over the department, instead of centering it on the small amount of product actually going through the machine.

Power charges must be determined by taking an indication of power. Allowance for horse-power lost in transmission may be made if there are marked inequalities, or if great exactness is desired. If no such allowance is called for, the first step in determining power charges is to calculate the total horse-power hours of all machines as actually operated. Multiplying the horse-power of a machine by the number of hours the machine is operated gives the horse-power hours for that machine; and the total for the plant is found by adding the results for each machine. The power generated at the engine but not indicated in the above total is simply considered as unutilized power, the cost of which is borne pro rata by all the machines. The total power charge of the power department of the plant is then divided by the total horse-power hours, which gives the cost of power per horse-power hour. Multiplying this by the horse-power hours of each machine gives the machine power cost per hour for actual operating time.

After all the charges possible have been made directly, the residue of indirect expenses must be considered. There are two classes of these—expenses that can be identified with certain departments, and general operating expenses for the plant as a whole.

First, the general operating expenses are distributed over the departments. Second, each department adds to this share of the general expense its own departmental indirect expense, and proceeds to distribute the total over its own product, the method depending on the basis of the cost system.

If the departmental costs are based on a unit of measure, as the ton or gallon, the total indirect expense of the department is divided by the total output, giving the rate per unit, and the rate so obtained is distributed among the machines or processes by multiplying the number of units of product operated on by the rate per unit.

If the costs are based on time, the departmental expense is divided by the total number of machine-operating hours; and this rate is added to the direct rate already established, which gives the complete or final rate per hour with which to charge the product of that department.

In special cases, the department indirect may be distributed over the machines or processes on the basis of labor cost or labor hours, the justification lying in the circumstances.

It may be well now to review the method as outlined.

(1) All expenses which can possibly be charged direct to machines or processes are so charged.

(2) The general operating expenses are distributed over the departments as units, and become a part of the several departmental indirect expenses.

(3) The total departmental indirect expenses are distributed over the machines or processes of the department.

(4) Combining the charges of 1 and 3, the total machine rate is determined.

Suppose an article now to pass through several departments or processes. Multiply the number of hours it is operated on in each process by the machine rate for that process, and the cost of the various processes so calculated will, when added together, give the total process cost.

If the material cost constitutes a part of the machine rate, this result is also the final factory cost; if not, the material cost must be added to the process cost to get the final result.

The scope of the new machine rate method should be clear from the foregoing description. It can be used when all operations are performed by machines, but it cannot be applied to general bench work and miscellaneous forms of hand labor.

(7) Fixed Machine Rate

The “Fixed Machine Rate” is characterized by three special features:

(1) The rate itself is an estimate, and is made in advance.

(2) The rate is estimated on the basis that every machine in the shop will run full time.

(3) All charges unabsorbed by the estimated fixed rate are distributed through a supplementary rate, the special feature in this being its relation to idle time.

In practice, the fixed machine rate is employed in various forms, and with sometimes quite essential differences. For instance, it is sometimes used departmentally, and sometimes it covers the whole machine production of a plant, each machine having its own rate, and there being no class of expenses recognized as departmental. Again, the rate may be considered as a single rate covering all forms of expense, or it may be constructed as a total rate composed of component rates, each rate representing the estimate for a certain class of expenses. The particular method chosen, in conjunction with the conditions of manufacture, will affect the accuracy of the results to a considerable degree.

We will first consider it as a single rate. The estimate is made either by a careful analysis of all the elements of expense, or by referring to the results of past experience. In the latter case the average results of a period of years are generally taken. In either case it is supposed to include all production expenses incident to the operation of each machine.

The total expense assigned to each machine is then divided by the maximum number of operating hours for any chosen period to find the machine rate per hour; i. e., the estimated cost of running the machine one hour. This rate is then charged against the machine, irrespective of the actual cost per hour, or the actual time of operation.

The sum of all the rates or machine charges in any department is charged against that department in the departmental expense account, or, if no departments are considered, the total of all estimates is charged against a general factory expense account. Whatever difference appears between the estimated charges and the actual expenses for the period is adjusted over the factory through a supplementary rate, which may be applied departmentally or over each machine separately.

If all the machines run full time, it is obvious that all the charges as estimated will be absorbed into the product; but this is very rarely the case. Besides the idleness due to dull times, there are often machines that, because of great capacity or peculiar product, are used only a fraction of the whole time. The question arises as to what to do with the charges written against a machine for the time that it is idle, which seem to apply to nothing-. If they are added to the cost of the product, they increase it out of all proportion. For example, if a machine were busy only one day in a week, the product made that day would, under such a rule, have to bear the expenses of the whole week, including charges that do not apply to it in any possible way. The result would be inaccurate on the face of it.

To avoid such an evident fallacy, the costs, as determined by applying the rate to actual running time, are subtracted from the estimated cost to find the amount still unabsorbed. This is considered as an indirect expense estimated but not actually incurred, so it is subtracted from the departmental, or from the general factory expense account, as the case may be, in order to make the proper adjustment.

This principle in itself is wrong. The plan of deducting the rate of idle machines from the general expenses implies that there are no direct expenses connected with the machines when they are not working. But this is not true; for interest, insurance, floor space charges, and certain other items go on just the same.

Evidently, the fixed rate will be unsatisfactory unless provision is made for the fixed or annual charges that accrue whether the machines are idle or not; and these charges must be distinguished from the charges arising out of actual operation, which may be designated as operating charges. Of course, allowances may be made afterwards by adjusting the supplementary rate, but this would be a direct contradiction to the principles and purposes of the method itself.

To avoid these difficulties, separate fixed rates may be calculated for the different classes of expense, and the total of these rates regarded as the maximum rate for operating time. For instance, one rate may stand for the operating charges only, while another may represent the annual charges assignable to any particular machine or department. A third rate could be fixed to include a pro rata share of the estimated general operating expenses. If it is desired to analyze the expenses according to rates, the total rate could be divided into as many component rates as desired.

Allowances for idle time would now be made as follows: The maximum number of operating hours is multiplied by the total rate for each machine, which gives the total amount charged against that machine. The sum of all these charges constitutes the total estimated factory charge. The number of idle hours for each machine is then multiplied by the “operating expense rate” only, which represents the expense charged against the machine but not actually incurred. When the sum of all allowances for idle time is subtracted from the total estimated factory charge, the result is the net estimate of all charges. The difference between the net estimate and the actual expense is then adjusted through the supplementary rate.

In such case the supplementary rate becomes far more important, because it is no longer limited only to adjusting mistakes in the estimates, but also becomes the indicator of idleness in the factory, and provides the means for distributing the resulting burden over the whole product manufactured. The supplementary rate, which distributes these expenses, reflects in actual figures the fact that idleness in one part of a plant is a burden on the rest of it.

The “Fixed Rate” as a method is adapted only to shops where the greater part of the work is done by machines. The drawbacks are that it is primarily an estimate at best, and that it is too rigid to reflect all the fluctuating phases of actual production.

Miscellaneous Methods

Various modifications and combinations of methods for the distribution of expense have been devised to meet special conditions in different lines of business. For the most part they are “percentage” plans in some form or other. It has been shown that accurate costs cannot be obtained from an arbitrary percentage added to the prime cost of the product, except in the most elementary conditions, where there is only one class of product, and all processes are the same. This, however, does not forbid the application of a percentage to the output of a department for the distributing of purely departmental expenses. In fact, the direct labor cost is a percentage plan, only it is not an arbitrary percentage plan, since it uses for a base one of the factors of production.

The departmental condition where an arbitrary percentage may be safely used for distribution of expense must be judged by direct observation. In any case the percentage method will fall short of the desired standard in the matter of analyzing expense into the different items of which it is composed.

In shops where the material constitutes much the larger part of the prime cost, and where the processes are uniform, experience has shown that the indirect expenses may be distributed either on the tonnage basis, or per hundred, on the number of articles.

In similar conditions, where the material does not differ in grade or price to any considerable degree, or where the business is really little more than assembling finished parts bought in the market, the cost of the material may be substituted for the quantity as the unit of distribution. However, such special conditions rarely exist in a business of much size.

There are also cases where the principle of the machine rate is applied to the operator of the machine instead of to the machine itself. It may be used where the wages of the operators are different, and where operators go from one machine to another.

The same principle is sometimes extended to cover a whole department; that is, a rate is made for the total productive labor hours of all the men in the department. It has been called the “Sold Hour” plan and was originally devised to apply to the printers’ trade. It is adapted to industries where any man in a department may be called on to do any job coming to that department.

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