Question

Robinson Products Company has two service departments (S1 and S2) and two production departments (P1 and P2). The distribution of each service department’s efforts (in percentages) to the other departments is:

From	To
	S1		S2			P1			P2
S1	—			20	%		30	%		?	%
S2	20	%		—			?			40

The direct operating costs of the departments (including both variable and fixed costs) are:

S1		$220,000
S2		$74,000
P1		$61,000
P2		$175,000

Required:

1. Determine the total cost of P1 and P2 using the direct method.

2. Determine the total cost of P1 and P2 using the step method.

3. Determine the total cost of P1 and P2 using the reciprocal method.

***Please show all your work on how you get the answers in a working note. I would really need to understand this problem and how its solved. Please show me how you get all numbers if its not obvious from the information given. Thank you!***

Answer 1

Solution:

Distribution table
	To
From	S1	S2	P1	P2
S1	-	20%	30%	50%
S2	20%	-	40%	40%

1. Direct Method:

Under this method, the cost of service dept. are directly apportioned to production depts. , without taking into consideration any service from one service dept. to another service dept.          

Direct Method
Particulars		P1	P2	S1	S2
Total Costs		61000	1750000	220000	74000
Distribution of :
S1	(3:5)	82500	137500	-220000
S2	(1:1)	37000	37000		-74000
Total		180500	1924500	0	0

2) Step Method:   

In this method, the cost of most serviceable dept. is first apportioned to other service dept. and production depts. The next service dept. is taken up and its cost is apportioned and this process goes on till the cost of last service dept. is apportioned. The cost of last service dept. among production dept. only.  

Step Method
Particulars		P1	P2	S1	S2
Total Costs		61000	1750000	220000	74000
Distribution of :
S1	(3:5:2)	66000	110000	-220000	44000
		127000	1860000	0	118000
S2	(4:4:2)	47200	47200	23600	-118000
		174200	1907200	23600	0
S1	(3:5:2)	7080	11800	-23600	4720
		181280	1919000	0	4720
S2	(4:4:2)	1888	1888	944	-4720
		183168	1920888	944	0
S1	(3:5:2)	283	472	-944	189
		183451	1921360	0	189
S2	(4:4:0)	94	94	0	-189
		183546	1921454	0	0

3) Reciprocal Method:   

This method gives cognizance to the fact that where there are two or more service depts, they may render services to each other, and therefore these inter-departmental services are to be given due weight in distributing the expenses of service depts. There are three methods available to deal with inter service departmental transfer:                         

1) Repeated Distribution method

2) Simultaneous equation method (I am doing this one)                                                              

3)Trial and error method

Reciprocal Method
Let the total cost of Dept. S1 be "x" and that of S2 be "y"
Therefore, x = 220000 + 20% of y				y = 74000 + 20% of x
or,	x = 220000 + 0.2y…(1)			or, y = 74,000 + 0.2x…(2)
	Now, putting the value of "y" in (1), we get
	x = 220000 + 0.2 ( 74000 + 0.2x)
	x=220000 + 14800 + 0.04 x
	0.96 x = 234800
	x = 244583
and	y = 74000 + 0.2 ( 244583.3)
	y = 122917
Particulars		P1	P2	S1	S2
Total Costs		61000	1750000	220000	74000
Distribution of :
S1	(3:5:2)	73375	122292	-244583	48917
		134375	1872292	-24583	122917
S2	(4:4:2)	49167	49167	24583	-122917
		183542	1921458	0	0