Question

Craylon Corp has two service departments, S1 and S2, and two production departments, P1 and P2.

The data for April were as follows:

		Services provided to:
Activity	Costs	S1	S2	P1	P2
S1	$100,000		25%	40%	35%
S2	$80,000	10%		55%	35%
	Fixed Costs
P1	$400,000
P2	$500,000

One of the algebraic equations in linear form for an activity using the reciprocal method is

	S2 = 80,000 +.25S1
	S1=100,000 + .25S2
	S2 = 80,000 + .35S1
	S1 = 100,000 +.10S2

Answer 1

Craylon Corp has Two Service Department S1 AND S2 & Two Production Department P1 AND P2

Activity for the months of April

Activity Cost Service provided to Production Cost

S1 S2 P1 P2

S1 100000 25% 40% 35%

25000 40000 35000

From S1 100000 (25%) goes to S2 i.e. 25000. This will be added to S2 Cost 80000 Now S2 will be 105000 allocate cost to all departments

S2 105000 10% 55% 35%

(80000+25000) 10500 57750 36750

From S2 105000 (10%) goes to S1 i.e. 10500. Now S1 10500 will be allocate cost to all the departments

S1 10500    25% 40% 35%

2625 4200 3675

From S1 10500 (25%) goes to S2 i.e. 2625. Now S2 2625 will be allocate cost to all the departments

S2 2625 10% 55% 35%

262.5 1443.75 918.75   

From S2 2625 (10%) goes to S1 i.e. 262.5. Now S1 262.5 will be allocate cost to all the departments

S1 262.5 25% 40% 35%

65.62 105 91.88

From S1 262.5 (25%) goes to S2 i.e. 65.62 Now S2 65.62 will be allocate cost to all the departments

S2 65.62 10% 55% 35%

6.56    36.09 22.97

From S2 65.62 (10%) goes to S1 i.e. 6.56. Now S1 6.56 will be allocate cost to all the departments

S1 6.56   25% 40% 35%

1.64 2.62 2.30

From S1 1.64 (25%) goes to S2 i.e. 65.62 Now S2 65.62 will be allocate cost to all the departments

S2 1.64 10% 55% 35%

0.16 0.90 0.58

We have allocated all the service cost to production

S1 = 0

S2 = 0

P1= 40000+57750+4200+1443.75+105+36.09+2.62+0.90 = 103,538.36

P2 = 35000+ 36750+3675+918+91.88+22.97+2.30+0.58 = 76,460.73

One of the algebraic equations in linear form for an activity using the reciprocal method is

Equation 1 S2 = 80000 + 0.25S1

Equation 2 S1 = 100000+0.25S2

Equation 3 S2 = 80000 + 0.35S1

Equation 4 S1 = 100000+0.10S2.

Solutions through equation

Equation 1 S2 = 80000 + 0.25S1 where as S1 = 100000 + 0.25 S2 in equation 2

S2 = 80000 + 0.25S1

S2 = 80000 + 0.25 (100000+0.25S2)

S2 = 80000 + 25000 + 0.0625S2

S2 =105000 + 0.0625S2

1 S2 - 0.0625 S2 = 105000

0.9375 S2 =105000

S2 = 105000/0.9375

S2 = 112000

Equation 2 S1 = 100000+0.25S2 where as S2 = 80000 + 0.25 S1 in equation 1

S1 = 100000 + 0.25 S2

S1 = 100000 + 0.25 (80000 + 0.25 (S1))

S1 = 100000 + 20000 + 0.0625 S1

S1 = 120000 + 0.0625 S1

1 S1 - 0.0625 S1 = 120000

0.9375 S1 = 120000

S1 = 120000/0.9375

S1 = 128000

Equation 3 S2 = 80000 + 0.35 (S1) where as S1 = 100000 + 0.10 S2 in equation 4

S2 = 80000 + 0.35 (S1)

S2 = 80000 + 0.35 (100000+ 0.10 (S2))

S2 = 80000 + 35000 + 0.035 S2

S2 = 115000 + 0.035 S2

1 S2 - 0.035 S2 = 115000

0.965 S2 = 115000

S2 = 119171

Equation 4 S1 = 100000 + 0.10 (S2) where as S2 = 80000 + 0.35 S1 in equation 4

S1 = 100000 + 0.10 (S2)

S1 = 100000 + 0.10 (80000+ 0.35 (S1))

S1 = 100000 + 8000 + 0.035S1

S1 = 108000 + 0.035 S1

1S1 - 0.035 S1 = 108000

0.965 S1 = 108000

S1 = 111917

There are three method direct method, Step down Method & Reciprocal Method

The Receiprocal method allocates support department costs to operation departments by fully recognizing the mutual services provided among all support departments. The Method is complicated in that it either requires an iteratives series of allocations or a linear programming solution to determine the final amounts to be allocated between the support department which use each other services. It provides the highest level of accruacy but its complex to implement