Different Overhead Allocation Bases

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The Answer is In this problem, there are three possible overhead allocation bases: direct labor (present system), machine hours (the proposed system), and number of batches. First, calculate product costs under each of the three allocation schemes:
1. Direct labor cost as the allocation base (present system):

\begin{array} { | l | r | r | r | } \hline & ext { Biuethings } & ext { Giraythings } & ext { Total } \\hline ext { Number of units } & 120,000 & 6,000 & 126,000 \\hline ext { Direct labor/unit } & .50 & .50 & \\hline ext { Direct labor cost } & \$ 60,000 & \$ 3,000 & \$ 63,000 \\hline \begin{array} { l } ext { K of total direct } \ ext { labor cost }\end{array} & 95.238 \% & 4.762 \% & \\hline ext { Overhead allocated } & 342,857 & 17,143 & 360,000 \\hline ext { Direct material cost } & \underline{60,000} & \underline{3,000} & \underline{63,000} \\hline ext { Total cost } & \$ 462,857 & \$ 23,143 & \underline{\$ 486,000} \\hline ext { Unit cost } & \$ 3.857 & \$ 3,857 & \\hline\end{array}

2. Machine hours as the allocation base (proposed system):
$In this problem, there are three possible overhead allocation bases: direct labor (present system), machine hours (the proposed system), and number of batches. First, calculate product costs under each of the three allocation schemes: 1. Direct labor cost as the allocation base (present system): \begin{array} { | l | r | r | r | } \hline & ext { Biuethings } & ext { Giraythings } & ext { Total } \ \hline ext { Number of units } & 120,000 & 6,000 & 126,000 \ \hline ext { Direct labor/unit } & .50 & .50 & \ \hline ext { Direct labor cost } & \$ 60,000 & \$ 3,000 & \$ 63,000 \ \hline \begin{array} { l } ext { K of total direct } \ ext { labor cost } \end{array} & 95.238 \% & 4.762 \% & \ \hline ext { Overhead allocated } & 342,857 & 17,143 & 360,000 \ \hline ext { Direct material cost } & \underline{60,000} & \underline{3,000} & \underline{63,000} \ \hline ext { Total cost } & \$ 462,857 & \$ 23,143 & \underline{\$ 486,000} \ \hline ext { Unit cost } & \$ 3.857 & \$ 3,857 & \ \hline \end{array} 2. Machine hours as the allocation base (proposed system): 3. Number of batches as the allocation base: \begin{array}{|l|r|r|r|} \hline & ext { Bluethings } & ext { Graythings } & ext { Total } \ \hline \begin{array}{l} ext { Number of } \ ext { units/year } \end{array} & 120,000 & 6,000 & 126,000 \ \hline \begin{array}{l} \div ext { number of } \ ext { units/batch } \end{array} & \underline{600} & \underline{30} & \ \hline \begin{array}{l} ext { Number of } \ ext { batches/year } \end{array} & 200 & 200 & 400 \ \hline \% ext { of total batches } & 50 \% & 50 \% & \ \hline ext { Overhead allocated } & \$ 180,000 & \$ 180,000 & \$ 360,000 \ \hline ext { Direct labor cost } & 60,000 & 3,000 & 63,000 \ \hline ext { Direct material cost } & \underline{60,000} & \underline{3,000} & \underline{63,000} \ \hline ext { Total cost } & \$ 300,000 & \$ 186,000 & \underline{\$ 486,000} \ \hline ext { Unit cost } & \$ 2.50 & \$ 31.00 & \ \hline \end{array} Notice that allocating overhead by either direct labor or machine hours produces identical product costs. Thus, the proposed system change will not affect decision making. There are two cost drivers in Step Up Company. Unit volume drives direct materials and direct labor, but set-ups (number of batches) appear to drive overhead costs. Allocating overhead using direct labor gives an incorrect impression of how overhead costs vary and distorts product costs. Overhead costs are incurred in set-ups. While run times per unit of thing is the same for blues and grays, batch sizes vary considerably. In fact, bluethings and graythings each required 200 batches. Therefore, each product line (as opposed to each unit of product) should be allocated an equal dollar amount of overhead. If this is done, then graythings become massive losers and bluethings are seen to be profitable, even with market price of $3 per unit. But these allocated costs using number of batches still do not necessarily represent opportunity costs. If the thing-a-majig and set-up crews are not operating at full capacity, then the opportunity cost of a batch of graythings is $30 (just variable cost). However, if the firm is reducing the number of bluethings it can produce to make graythings (production is at capacity), then the opportunity cost of a graything is the forgone margin on a batch of bluethings plus the variable costs of the graythings. Or, \begin{array} { | l | r | r | } \hline \begin{array} { l } ext { Contribution margin on batch of } \ ext { bluethings } ( \$ 4 - 1 ) imes 600 \end{array} & \$ 1800 & \ \hline \begin{array} { l } ext { Plus: Variable cost of a batch of } \ ext { graythings } ( \$ 1 imes 30 ) \end{array} & \underline{30} & \$ 1,830 \ \hline \div ext { Units of graythings per batch } & & 30 \ \hline \begin{array} { l } ext { Opportunity cost of producing a } \ ext { graything } \end{array} & & \underline{\$ 61} \ \hline \end{array} The decision to continue to make graythings depends on i) how overhead costs vary with batches and ii) whether additional bluethings can be sold if graythings are not produced. If the size and cost of the set-up crew is invariant to the number of batches, then direct labor is probably not too bad an allocation base. If more bluethings cannot be sold, again it is not optimum to drop graythings. Graythings are covering variable cost. Just because all overhead costs are incurred in set-ups does not make set-up costs variable with number of batches. Some of the overhead costs are sunk costs and do not vary with batches (e.g., depreciation of the thing-a-majig ).$
3. Number of batches as the allocation base:

\begin{array}{|l|r|r|r|}\hline & ext { Bluethings } & ext { Graythings } & ext { Total } \\hline \begin{array}{l} ext { Number of } \ ext { units/year }\end{array} & 120,000 & 6,000 & 126,000 \\hline \begin{array}{l}\div ext { number of } \ ext { units/batch }\end{array} & \underline{600} & \underline{30} & \\hline \begin{array}{l} ext { Number of } \ ext { batches/year }\end{array} & 200 & 200 & 400 \\hline \% ext { of total batches } & 50 \% & 50 \% & \\hline ext { Overhead allocated } & \$ 180,000 & \$ 180,000 & \$ 360,000 \\hline ext { Direct labor cost } & 60,000 & 3,000 & 63,000 \\hline ext { Direct material cost } & \underline{60,000} & \underline{3,000} & \underline{63,000} \\hline ext { Total cost } & \$ 300,000 & \$ 186,000 & \underline{\$ 486,000} \\hline ext { Unit cost } & \$ 2.50 & \$ 31.00 & \\hline\end{array}

Notice that allocating overhead by either direct labor or machine hours produces identical product costs. Thus, the proposed system change will not affect decision making.
There are two cost drivers in Step Up Company. Unit volume drives direct materials and direct labor, but set-ups (number of batches) appear to drive overhead costs. Allocating overhead using direct labor gives an incorrect impression of how overhead costs vary and distorts product costs. Overhead costs are incurred in set-ups. While run times per unit of thing is the same for blues and grays, batch sizes vary considerably. In fact, bluethings and graythings each required 200 batches. Therefore, each product line (as opposed to each unit of product) should be allocated an equal dollar amount of overhead. If this is done, then graythings become massive losers and bluethings are seen to be profitable, even with market price of $3 per unit.
But these allocated costs using number of batches still do not necessarily represent opportunity costs. If the thing-a-majig and set-up crews are not operating at full capacity, then the opportunity cost of a batch of graythings is $30 (just variable cost). However, if the firm is reducing the number of bluethings it can produce to make graythings (production is at capacity), then the opportunity cost of a graything is the forgone margin on a batch of bluethings plus the variable costs of the graythings. Or,

\begin{array} { | l | r | r | } \hline \begin{array} { l } ext { Contribution margin on batch of } \ ext { bluethings } ( \$ 4 - 1 ) imes 600\end{array} & \$ 1800 & \\hline \begin{array} { l } ext { Plus: Variable cost of a batch of } \ ext { graythings } ( \$ 1 imes 30 )\end{array} & \underline{30} & \$ 1,830 \\hline \div ext { Units of graythings per batch } & & 30 \\hline \begin{array} { l } ext { Opportunity cost of producing a } \ ext { graything }\end{array} & & \underline{\$ 61} \\hline\end{array}

The decision to continue to make graythings depends on i) how overhead costs vary with batches and ii) whether additional bluethings can be sold if graythings are not produced. If the size and cost of the set-up crew is invariant to the number of batches, then direct labor is probably not too bad an allocation base. If more bluethings cannot be sold, again it is not optimum to drop graythings. Graythings are covering variable cost. Just because all overhead costs are incurred in set-ups does not make set-up costs variable with number of batches. Some of the overhead costs are sunk costs and do not vary with batches (e.g., depreciation of the "thing-a-majig").

Different Overhead Allocation Bases

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