Question

The following information relates to Osceola Corporation for the past accounting period.

	Direct costs
Service Dept A	$80,000
Service Dept B	60,000
Producing Dept C	15,000
Producing Dept D	20,000

Proportion of service by A to:		Proportion of service by B to:
B	10%	A	30%
C	60%	C	20%
D	30%	D	50%

Using the reciprocal method, Department B's cost allocated to Department C is:

		$29,021
		$14,021
		$13,192
		$7,794

Answer 1

	Under reciprocal method it is assumed that cost from other service departments is included in the cost of individual service departments
	Total cost of a service department=Direct cost of the service department+Cost allocated to the service department
	Let's assume that cost of service dept A=a
	Let's assume that cost of service dept B=b
	Ratio for allocation from service dept B to service dept A=30%=0.30
	a=80000+0.30b …………. 1
	Ratio for allocation from service dept A to service dept B=10%=0.10
	b=60000+0.10a …………. 2
	Apply 1 in 2
	b=60000+0.10*(80000+0.30b)
	b=60000+8000+0.03b
	b=68000+0.03b
	b-0.03b=68000
	0.97b=68000
	b=68000/0.97=70103
	Apply b in 1
	a=80000+(0.30*70103)101031
	Total cost to be allocated for service dept B=$ 70103
	Cost allocated to department B to C=70103*20%=$ 14021
	Answer is
	2nd option. $ 14021