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	$	265,000
S2		83,000
P1		70,000
P2		220,000

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.

(Do not round intermediate calculations.)

	Total Cost Allocated Production department 1 Production department 2

Answer 1

Distribution Table
	To
From	S 1	S 2	P 1	P 2
S 1	-	20%	30%	50%
S 2	20%	-	40%	40%

1) Direct Method :
	Total Cost Allocated
Production Department 1	$ 210,875
Production Department 2	$ 427,125

Explanation :
1) Direct Method :
Particulars	P 1	P 2	S 1	S 2
Total costs	$ 70,000	$220,000	$ 265,000	$83,000
Distribution of :
S 1	$99,375 {$265,000*30/80}	$165,625 {$265,000*50/80}	($265,000)
S 2	$41,500 {$83,000*40/80}	$41,500 {$83,000*40/80}		($83,000)
Total Costs Allocated	$ 210,875	$ 427,125	$ 0	$ 0

2) Step Method :
	Total Cost Allocated
Production Department 1	$ 214,671.20
Production Department 2	$ 423,328.80

Explanation :
2) Step Method :
Particulars	P 1	P 2	S 1	S 2
Total costs	$ 70,000	$220,000	$ 265,000	$83,000
Distribution of :
S 1	$79,500 {$265,000*30/100}	$132,500 {$265,000*50/100}	($265,000)	$53,000 {$265,000*20/100}
	$ 149,500	$ 352,500	$0	$ 136,000
S 2	$54,400 {$136,000*40/100}	$54,400 {$136,000*40/100}	$27,200 {$136,000*20/100}	($136,000)
	$ 203,900	$ 406,900	$ 27,200	$ 0
S 1	$8,160 {$27,200*30/100}	$13,600 {$27,200*50/100}	($27,200)	$5,440 {$27,200*20/100}
	$ 212,060	$ 420,500	$ 0	$ 5,440
S 2	$2,176 {$5,440*40/100}	$2,176 {$5,440*40/100}	$1,088 {$5,440*20/100}	($5,440)
	$ 214,236	$ 422,676	$ 1,088	$ 0
S 1	$326.40 {$1,088*30/100}	$544 {$1,088*50/100}	($1,088)	$217.60 {$1,088*20/100}
	$ 214,562.40	$ 423,220	$ 0	$ 217.60
S 2	$108.80   {$217.60/2}	$108.80   {$217.60/2}		($217.60)
Total Costs Allocated	$ 214,671.20	$ 423,328.80	$ 0	$ 0

3) Reciprocal Method :
	Total Cost Allocated
Production Department 1	$ 214,666.70
Production Department 2	$ 423,333.30

Explanation:

Let the Total Cost of Department S 1 = X

Let the Total Cost of Department S 2 = Y

Therefore , X= $ 265,000 + 20 % of Y                     Y = $83,000 + 20 % of X

X= $ 265,000+0.2Y ….(1)                                   Y= $83,000+0.2X …. (2)

Put Value of Y in (1)

so, X= $265,000 + 0.2 ($83,000+0.2X )

X = $ 265,000+ $ 16,600 + 0.04 X

X- 0.04 X = $ 281,600

0.96 X = $ 281,600

X = $ 281,600 / 0.96

X = $ 293,333

X= $ 293,333 in (2)

so, Y= $ 83,000 + 0.2 ($293,333)

Y = $ 83,000 + $58,667

Y = $ 141,667

3) Reciprocal Method :
Particulars	P 1	P 2	S 1	S 2
Total costs	$ 70,000	$220,000	$ 265,000	$83,000
Distribution of :
S 1	$87,999.90 {$293,333*30/100}	$146,666.50 {$293,333*50/100}	($293,333)	$58,666.60 {$293,333*20/100}
	$ 157,999.90	$ 366,666.50	($ 28,333)	$ 141,667
S 2	$56,666.80 {$141,667*40/100}	$56,666.80 {$141,667*40/100}	$28,333 {$141,667*20/100}	($141,667)
Total Costs Allocated	$ 214,666.70	$ 423,333.30	$ 0	$ 0