Chapter 11, Problem 54P

 Step Method with Three Service Departments

 Model, Inc., produces model automobiles made from metal. It operates two production departments, Molding and Painting, and has three service departments, Administration, Accounting, and Maintenance. The accumulated costs in the three service departments were $250,000, $400,000, and $200,000, respectively. Management is concerned that the costs of its service departments are getting too high. In particular, managers would like to keep the costs of service departments under $3.50 per unit on average. You have been asked to allocate service department costs to the two production departments and compute the unit costs.

  The company decided that Administration costs should be allocated on the basis of square footage used by each production and service department. Accounting costs are allocated on the basis of number of employees. Maintenance costs are allocated on the basis of the dollar value of the equipment in each department. The use of each base by all departments during the current period follows:

 Direct costs of the Molding Department included $237,500 in direct materials, $337,500 in direct labor, and $112,500 in overhead. The Painting Department’s direct costs consisted of $210,000 in direct materials, $200,000 in direct labor, and $75,000 in overhead.

Required

1. a.      Using the step method, determine the allocated costs and the total costs in each of the two producing departments. Ignore self-usage (for example, ignore work done by Administration for itself). Rank order the allocation as follows: (1) Maintenance, (2) Accounting, and (3) Administration.
2. b.      Assume that 100,000 units were processed through these two departments. What is the unit cost for the sum of direct materials, direct labor, and overhead (1) for Molding, (2) for Painting, and (3) in total?
3. c.       Compute the cost per unit for the service department costs allocated to the production departments. Did the company meet management’s standards of keeping service department costs below $3.50 per unit?

To determine

Use the step method and determine the allocated costs and the total costs in each of the two producing departments. Make order the allocation as follows: (1) Maintenance, (2) Accounting, and (3) Administration.

Answer to Problem 54P

The cost allocation for molding department and painting department is $1,190,632 and $831,868.

Explanation of Solution

Step method:

Step method allows the allocation of the cost to the production department and service departments. Unlike the direct method, it also allocates the cost of the service to various service departments. Allocation of the cost starts from the department that has provided the highest proposition of service to the department that has provided the least service. Step method allows only one-way allocation of cost among service departments.

Calculate the allocation of costs:

	Department
Amount	Maintenance	Accounting	Administration	Molding	Painting
Direct costs	$200,000	$400,000	$250,000	$687,500	$485,000
Maintenance	$   (200,000)	$40,000	$2,000	$104,000	$54,000
Accounting	-	$ (440,000)	$42,128	$163,830	$234,042
Administration	-	-	$(294,128)	$235,302	$58,826
Total cost	$0	$0	$0	$1,190,632	$831,868

Table: (1)

Thus, the cost allocation for the molding department and painting department is $1,190,632 and $831,868.

Working note 1:

Calculate the allocation of maintenance cost:

Particulars	Maintenance cost (a)	Equipment value (b)	Amount $\left(\text{c = }\frac{\text{b}}{\text{Total of b}}\text{× a}\right)$
Allocation to maintenance cost :
Accounting  department	$200,000	$120.0	$40,000
Administration department	$200,000	$17.5	$2,000
Molding department	$200,000	312	$104,000
Painting  department	$200,000	162	$54,000
Total		$611.50

Table: (2)

Working note 2:

Calculate the allocation of accounting department:

Particulars	Accounting cost (a)	Number of employees (b)	Amount $\left(\text{c = }\frac{\text{b}}{\text{Total of b}}\text{× a}\right)$
Allocation to accounting cost:
Administration department	$400,000	12	$4,800,000
Molding department	$400,000	70	$28,000,000
Painting  department	$400,000	100	$40,000,000
Total		$182	$0

Table: (3)

Working note 3:

Calculate the allocation of administration department:

Particulars	Administration cost (a)	Building area (b)	Amount $\left(\text{c = }\frac{\text{b}}{\text{Total of b}}\text{× a}\right)$
Allocation to accounting cost:
Molding department	$294,128	$360,000	$235,302
Painting  department	$294,128	$90,000	$58,826
Total		$450,000

Table: (4)

To determine

Calculate the unit cost for the sum of direct materials, direct labor, and overhead cost (1) for Molding, (2) for Painting, and (3) in total.

Answer to Problem 54P

The unit cost of molding and painting is $11.91 and $8.31 respectively.

Explanation of Solution

Joint cost allocation:

Joint cost is the cost that occurs for two or more products of a business. When two or more products have the same production process then they share some common cost, that common cost is known as the joint cost of the production.

Calculate the unit cost for molding:

$\begin{array}{c}\text{Unit cost = }\frac{\text{Total cost}}{\text{Total output}}\\ =\frac{\text{\$1,190,632}}{100,000}\\ =\text{ \$11}\text{.91}\end{array}$

Calculate the unit cost for painting:

$\begin{array}{c}\text{Unit cost = }\frac{\text{Total cost}}{\text{Total output}}\\ =\frac{\text{\$831,868}}{100,000}\\ =\text{ \$8}\text{.31}\end{array}$

Thus, the unit cost of molding and painting is $11.91 and $8.31 respectively.

To determine

Compute the cost per unit for the service department costs which are allocated to the production departments. Also, identify whether the company meets management’s standards of keeping service department costs below $3.50 per unit.

Answer to Problem 54P

The unit cost of the service department for the molding and painting department is $5.03 and $3.46.

Explanation of Solution

Joint cost allocation:

Joint cost is the cost that occurs for two or more products of a business. When two or more products have the same production process then they share some common cost, that common cost is known as the joint cost of the production.

Calculate the molding cost per unit:

$\begin{array}{c}\text{Unit cost = }\frac{\text{Total cost}}{\text{Total output}}\\ =\frac{\begin{array}{r}\hfill \$503,132\text{ (4)}\end{array}}{100,000}\\ =\text{ \$5}\text{.03}\end{array}$

Calculate the painting cost per unit:

$\begin{array}{c}\text{Unit cost = }\frac{\text{Total cost}}{\text{Total output}}\\ =\frac{\begin{array}{r}\hfill \$346,868\text{ (4)}\end{array}}{100,000}\\ =\text{ \$3}\text{.46}\end{array}$

Thus, the unit cost of the service department for the molding and painting department is $5.03 and $3.46 respectively.

Working note 4:

Calculate the service department cost:

Particulars	Molding	Painting
Maintenance	$104,000	$54,000
Accounting	$163,830	$234,042
Administration	$235,302	$58,826
Total service costs	$503,132	$346,868

Table: (5)