Chapter 6, Problem 50P

Owl-Eye Radiologists (OR) does various types of diagnostic imaging. Radiologists perform tests using sophisticated equipment. OR’s management wants to compute the costs of performing tests for two different types of patients: those who are hospitalized (including those in emergency rooms) and those who are not hospitalized but are referred by physicians. The data for June for the two categories of patients follow:

The accountant first assigns overhead costs to two pools: overhead related to equipment-hours and overhead related to labor-hours. The analysis of overhead accounts by the cost accountant follows:

Required

1. a.      Compute the predetermined overhead rates assuming that Owl-Eye Radiologists uses equipment-hours to allocate equipment-related overhead costs and labor-hours to allocate labor-related overhead costs.
2. b.      Compute the total costs of production and the cost per unit for each of the two types of patients undergoing tests in June.

To determine

Calculate the predetermined overhead rates using equipment-hours for the allocation of equipment related overhead costs and labor-hours to allocate labor-related overhead costs.

Answer to Problem 50P

The Cost per unit is $46 for the overhead rates when using equipment-hours for allocation.

The Cost per unit is $50 for the overhead rates when using labor-hours for allocation.

Explanation of Solution

Predetermined overhead rate:

The predetermined overhead rate is the rate computed for applying manufacturing overheads to the work-in-process inventory. This rate can be computed by dividing the total amount of manufacturing overheads by the base of allocation.

Analysis of overhead accounts by the cost accountant is as follows:

Account	Amount	Related to:
Utilities	$    4,800	Equipment hours
Supplies	12,600	Labor-hours
Indirect labor and supervision	20,400	Labor-hours
Equipment depreciation and maintenance	8,400	Equipment hours
Miscellaneous	3,360	Equipment hours

Compute equipment-hours related predetermined rate:

$\begin{array}{c}\text{Predetermined}\text{rate}\text{=}\frac{\text{Utilities}\text{+}\text{Equipment}\text{depreciation}\text{\&}\text{maintenance+}\text{Miscellaneous}}{\text{Total}\text{equipment-hours}}\\ \text{=}\frac{\text{\$4,800}\text{+}\text{\$8,400}\text{+}\text{\$3,360}}{\text{360}}\\ \text{=}\frac{\text{\$28,560}}{\text{360}}\\ \text{=}\text{\$46}\end{array}$

Hence, the equipment-hours related predetermined rate is $46.

Compute materials cost related predetermined rate:

$\begin{array}{c}\text{Predetermined}\text{rate}\text{=}\frac{\text{Supplies}\text{+}\text{Indirect}\text{labor}\text{and}\text{supervision}}{\text{Total}\text{direct}\text{labor-cost}}\\ \text{=}\frac{\text{\$12,600}\text{+}\text{\$20,400}}{\text{660}}\\ \text{=}\frac{\text{\$33,000}}{\text{660}}\\ \text{=}\text{\$50}\end{array}$

Thus, the labor-hours related predetermined rate is $50.

To determine

Compute the total costs of production and the cost per unit for each of the two types of patients undergoing tests in June.

Answer to Problem 50P

For hospital patients:

Total cost:  $73,440

Cost per unit: $115

For other patients:

Total cost: $25,320

Cost per unit: $29

Explanation of Solution

Product cost:

Product cost includes all the costs that are attributed to the production of the product. All the money that has spent on the process of production or purchase of the product is known as product cost.

Product cost per unit:

The product cost per unit is determined by dividing the total of variable and fixed cost with the total number of units.

Compute the total cost of hospital patients:

$\begin{array}{c}\text{Total}\text{cost}\text{=}\text{equipment-hours}\text{related}\text{cost}\text{(1)}\text{+}\text{labor}\text{hours}\text{related}\text{cost}\text{(2)}\\ \text{+}\text{Direct}\text{labor}\\ \text{=}\text{\$11,040}\text{+}\text{\$24,000}\text{+}\text{\$38,400}\\ \text{=}\text{\$73,440}\end{array}$

Compute total cost of other patients:

$\begin{array}{c}\text{Total}\text{cost}\text{=}\text{equipment-hours}\text{related}\text{cost}\text{(3)}\text{+}\text{labor}\text{hours}\text{related}\text{cost}\text{(4)}\\ \text{+}\text{Direct}\text{labor}\\ \text{=}\text{\$5,520}\text{+}\text{\$9,000}\text{+}\text{\$10,800}\\ \text{=}\text{\$25,320}\end{array}$

Thus, the value of total cost for hospital patients and other patients are $73,440 and $25,320 respectively.

Compute cost per unit for product hospital patients:

$\begin{array}{c}\text{Cost}\text{per}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Number}\text{of}\text{units}}\\ \text{=}\frac{\text{\$73,440}}{640}\\ \text{=}\text{\$115}\end{array}$

Compute cost per unit for the product of other patients:

$\begin{array}{c}\text{Cost}\text{per}\text{unit}\text{=}\frac{\text{Total}\text{cost}}{\text{Number}\text{of}\text{units}}\\ \text{=}\frac{\text{\$25,320}}{860}\\ \text{=}\text{\$29}\end{array}$

Working note 1:

Compute equipment hours related cost for hospital patients:

$\begin{array}{c}\text{Equipment}\text{hours}\text{related}\text{cost}\text{=}\text{Equipment}\text{hours}\text{related}\text{predetermined}\text{rate}\\ \text{×}\text{Equipment-hours}\\ \text{=}\text{\$115}\text{×}\text{240}\\ \text{=}\text{\$11,040}\end{array}$

Working note 2:

Compute labor hours related cost for hospital patients:

$\begin{array}{c}\text{Labor}\text{related}\text{cost}\text{=}\text{Labor}\text{hour}\text{rate}\text{×}\text{Direct}\text{labor-hours}\\ \text{=}\text{\$50}\text{×}\text{480}\\ \text{=}\text{\$24,000}\end{array}$

Working note 3:

Compute equipment hours related cost for other patients:

$\begin{array}{c}\text{Equipment}\text{hours}\text{related}\text{cost}\text{=}\text{Equipment}\text{hours}\text{related}\text{predetermined}\text{rate}\\ \text{×}\text{Equipment-hours}\\ \text{=}\text{\$29}\text{×}12\text{0}\\ \text{=}\text{\$5,520}\end{array}$

Working note 4:

Compute labor hours related cost for other patients:

$\begin{array}{c}\text{Labor}\text{related}\text{cost}\text{=}\text{Labor}\text{hour}\text{rate}\text{×}\text{Direct}\text{labor-hours}\\ \text{=}\text{\$29}\text{×}1\text{80}\\ \text{=}\text{\$9,000}\end{array}$