The accounting for overall joint costs of production (direct materials, direct labor, and overhead) is no different from the accounting for product costs in general. It is the allocation of joint costs to the individual products that is the source of difficulty. Still, the allocation must be done for financial reporting purposes to value inventory carried on the balance sheet and to determine income. Thus, an allocation method must be found that, though arbitrary, allocates the costs on as reasonable a basis as possible. Because judgment is involved, equally competent accountants can arrive at different costs for the same product. There are a variety of methods for allocating joint costs. These methods include the physical units method, the weighted average method, the sales-value-at-split-off method, the net realizable value method, and the constant gross margin percentage method. These are covered in the following sections.
Physical Units Method
Under the physical units method, joint costs are distributed to products on the basis of some physical measure. These physical measures may be expressed in units such as pounds, tons, gallons, board feet, atomic weight, or heat units. If the joint products do not share the same physical measure (e.g., one product is measured in gallons, another in pounds), some common denominator may be used. For example, a producer of fuels may take gallons, barrels, and tons and convert each one into BTUs (British thermal units) of energy.
Computationally, the physical units method allocates to each joint product the same proportion of joint cost as the underlying proportion of units. So, if a joint process yields 300 pounds of Product A and 700 pounds of Product B, Product A receives 30 percent of the joint cost and Product B receives 70 percent. An alternative computation is to divide total joint costs by total output to find an average unit cost. The average unit cost is then multiplied by the number of units of each product. Although the method is not wholly satisfactory, it has a measure of logic behind it. Since all products are manufactured by the same process, it is impossible to say that one costs more per unit to produce than the other. For example, suppose that a sawmill processes logs into four grades of lumber totaling 3,000,000 board feet as follows:
Total joint cost is $186,000. Using the physical units method, how much joint cost is allocated to each grade of lumber? First, we find the proportion of the total units for each grade; then, we assign each grade its proportion of joint cost.
We could also calculate the average unit cost of $0.062 ($186,000/3,000,000) and multiply it by the board feet for each grade. For example, manufacturers of forest products may add the average cost of logs entering the mill to the average conversion cost to arrive at an average finished product cost. This cost is applied to all finished products, no matter their type, grade, or market value. This method serves the purpose of product costing.
The physical units method may be used in any industry that processes joint products of differing grades (e.g., flour milling, tobacco, and lumber). However, a disadvantage of the physical units method is that high profits may be reflected from the sale of the high grades, with low profits or losses reflected on the sale of lower grades. This may result in incorrect managerial decisions if the data are not properly interpreted. The physical units method presumes that each unit of material in the final product costs just as much to produce as any other. This is especially true where the dominant element can be traced to the product. Many feel this method often is unsatisfactory because it ignores the fact that not all costs are directly related to physical quantities. Also, the product might not have been handled at all if it had been physically separable before the split-off point from the part desired.
Weighted Average Method
In an attempt to overcome the difficulties encountered under the physical units method, weight factors can be assigned. These weight factors may include such diverse elements as amount of material used, difficulty to manufacture, time consumed, difference in type of labor used, and size of unit. These factors and their relative weights are usually combined in a single value, which we might call the weight factor. In the canning industry, the weight factor is used in the calculation of a basic case.
An example of the use of weight factors is found in the canning industry.3 One type of weight factor is used to convert different-size cases of peaches into a uniform size for purposes of allocating joint costs to each case. Thus, if a basic case contains 24 cans of peaches in size 21/2 cans, that case is assigned a weight factor of 1.0. A case with 24 cans in size 303 (a can roughly half the size 21/2 can) receives a weight of 0.57, and so on. Once all types of cases have been converted into basic cases using the weight factors, joint costs can be allocated according to the physical units method. Peaches can also be assigned weight factors according to grade (e.g., fancy, choice, standard, and pie). If the standard grade is weighted at 1.00, then the better grades are weighted more heavily and the pie grade less heavily. For example, suppose that a peach-canning factory purchases $5,000 of peaches; grades them into fancy, choice, standard, and pie quality; and then cans each grade. The following data on grade, number of cases, and weight factor apply.
The physical units method may be used in any industry that processes joint products of differing grades (e.g., flour milling, tobacco, and lumber). However, a disadvantage of the physical units method is that high profits may be reflected from the sale of the high grades, with low profits or losses reflected on the sale of lower grades. This may result in incorrect managerial decisions if the data are not properly interpreted. The physical units method presumes that each unit of material in the final product costs just as much to produce as any other. This is especially true where the dominant element can be traced to the product. Many feel this method often is unsatisfactory because it ignores the fact that not all costs are directly related to physical quantities. Also, the product might not have been handled at all if it had been physically separable before the split-off point from the part desired.
Weighted Average Method
In an attempt to overcome the difficulties encountered under the physical units method, weight factors can be assigned. These weight factors may include such diverse elements as amount of material used, difficulty to manufacture, time consumed, difference in type of labor used, and size of unit. These factors and their relative weights are usually combined in a single value, which we might call the weight factor. In the canning industry, the weight factor is used in the calculation of a basic case.
An example of the use of weight factors is found in the canning industry.3 One type of weight factor is used to convert different-size cases of peaches into a uniform size for purposes of allocating joint costs to each case. Thus, if a basic case contains 24 cans of peaches in size 21/2 cans, that case is assigned a weight factor of 1.0. A case with 24 cans in size 303 (a can roughly half the size 21/2 can) receives a weight of 0.57, and so on. Once all types of cases have been converted into basic cases using the weight factors, joint costs can be allocated according to the physical units method. Peaches can also be assigned weight factors according to grade (e.g., fancy, choice, standard, and pie). If the standard grade is weighted at 1.00, then the better grades are weighted more heavily and the pie grade less heavily. For example, suppose that a peach-canning factory purchases $5,000 of peaches; grades them into fancy, choice, standard, and pie quality; and then cans each grade. The following data on grade, number of cases, and weight factor apply.
By multiplying the number of cases by the weight factor, we obtain the weighted number of cases. Then, the physical units method can be applied as the percentage of weighted
cases for each grade is obtained and multiplied by the joint cost to yield the allocated joint cost. The effect is to allocate relatively more of the joint cost to the fancy and choice grades because they represent more desirable peaches. The pie grade peaches, the good bits and pieces from bruised peaches, are relatively less desirable and are assigned a lower weight. Frequently, weight factors are predetermined and set up as part of either an estimated cost or a standard cost system. The use of carefully constructed weight factors enables the cost accountant to give more attention to several influences and, therefore, results in more reasonable allocations. The real danger, of course, is that weights may be used that are either inappropriate in the first place or become so through the passage of time. Obviously, if arbitrary rates are used, the resulting costs of individual products will be arbitrary.
cases for each grade is obtained and multiplied by the joint cost to yield the allocated joint cost. The effect is to allocate relatively more of the joint cost to the fancy and choice grades because they represent more desirable peaches. The pie grade peaches, the good bits and pieces from bruised peaches, are relatively less desirable and are assigned a lower weight. Frequently, weight factors are predetermined and set up as part of either an estimated cost or a standard cost system. The use of carefully constructed weight factors enables the cost accountant to give more attention to several influences and, therefore, results in more reasonable allocations. The real danger, of course, is that weights may be used that are either inappropriate in the first place or become so through the passage of time. Obviously, if arbitrary rates are used, the resulting costs of individual products will be arbitrary.
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