Question

Logan Products has two production departments—assembly and finishing. These are supported by two service departments—sourcing (purchasing and handling of materials and human resources) and operations (work scheduling, supervision, and inspection). Logan has the following labor hours devoted by each of the service departments to the other departments.

	Total Labor Hours Used by Departments
	Sourcing	Operations	Assembly	Finishing
Sourcing	-	20,000	40,000	60,000
Operations	10,000	-	60,000	50,000

The costs incurred in the plant are as follows:

Departments	Departmental Costs
Sourcing	$	174,000
Operations		220,000
Assembly		416,000
Finishing		261,000
Total	$	1,071,000

Required:

Use four decimal places (e.g., 33.3333%) in your calculation of percentages.

1. What are the costs allocated to the two production departments using (a) the direct method, (b) the step method, when the sourcing department that provides the greatest percentage of services to other service departments goes first), and (c) the reciprocal method?

2. What are the total costs in the production departments after allocation?

Answer 1

1)

a)	Direct Method
	Particulars			Sourcing	Operations	Assembly	Finishing
	Service department costs			$ 1,74,000.00	$ 2,20,000.00
	Allocating costs of:
	Sourcing			$ -1,74,000.00		$    69,600.00	$ 1,04,400.00
	Operations				$ -2,20,000.00	$ 1,20,000.00	$ 1,00,000.00
	Costs allocated					$ 1,89,600.00	$ 2,04,400.00

b)	Step Method
	Particulars			Sourcing	Operations	Assembly	Finishing
	Service department costs			$ 1,74,000.00	$ 2,20,000.00
	Allocating costs of:
	Sourcing			$ -1,74,000.00	$      29,000.00	$    58,000.00	$    87,000.00
	Balance			$                    -	$ 2,49,000.00	$    58,000.00	$    87,000.00
	Operations				$ -2,49,000.00	$ 1,35,818.18	$ 1,13,181.82
	Costs allocated					$ 1,93,818.18	$ 2,00,181.82

c)	Reciprocal method

Particulars			Sourcing	Operations	Assembly	Finishing
Service department costs			$   1,74,000.00	$   2,20,000.00
Allocating cost of:
Sourcing			$ -1,95,033.00	$      32,505.50	$    65,011.00	$    97,516.50
Operations			$      21,041.50	$ -2,52,498.00	$ 1,26,249.00	$ 1,05,207.50
					$ 1,91,260.00	$ 2,02,724.00

Workings:

Let the total cost of Sourcing and Operations be x and y
x	=	$ 174000 + 0.0833 y		(i)
y	=	$ 220000 + 0.1666 x		(ii)
Putting the value of x in equation (ii), we get
y	=	$ 220000 + 0.1666 ($ 174000 + 0.0833 y)
y	=	$ 220000 + $ 28988 + 0.0139 y
0.9861 y	=	$ 248988
y	=	$ 252498
and x	=	$ 174000 + 0.0833( $ 252498)
	=	$ 195033

2)	Total cost in the production departments after allocation
			Assembly	Finishing
a)	Direct Method		$ 6,05,600.00	$ 4,65,400.00
b)	Step Down Method		$ 6,09,818.18	$ 4,61,181.82
c)	Reciprocal Method		$ 6,07,260.00	$ 4,63,724.00

Note: There might be some differences in the answer that has been computed under reciprocal method. Please let me know if you find anything incorrect. Thank you