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Reciprocal Method of Cost Accounting with a Matrix Algebra equation

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Warren Ltd. has two production departments, Building A and Building B, and two service departments, Maintenance
and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments
for the month of June follow:
Proportion of Services Used by
  

Department Direct Costs Maintenance Cafeteria Building A Building B
  Building A $ 505,000
  Building B 315,000
  Maintenance 217,000 â?" 0.2 0.6 0.2
  Cafeteria 165,000 0.7 â?" 0.1 0.2

Required
Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Note: Due to rounding, the
cost allocations to the various departments may not add up to the total service department costs being allocated.)

Cost Allocated To:
From: Maintenance Cafeteria Building A Building B
Service Dept 217,000 165,000 0 0
Maintenance
Cafeteria
Total

Set up the equations:
Total service = Direct costs of the + Cost allocated
department costs service department to the service
department
   S1 (Maintenance) = $217,000 + 0.70 S2
   S2 (Cafeteria) = 165,000 + 0.20 S1

Substituting, the first equation into the second yields,

S2 = $165,000 + 0.20 ($217,000 + 0.70 S2)
S2 = $165,000 + $43,400 + 0.14 S2
.86S2 = $208,400
S2 = $242,326

I do not understand how S2 has been determined to be .86, can someone please explain it to me?

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Solution Summary

The following posting helps with a problem involving the reciprocal method for cost allocations.

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Advance costing for management's decisions - Amazon Beverages

Evaluate Profit Impact of Alternative Transfer Decisions
Amazon Beverages produces and bottles a line of soft drinks using exotic fruits from Latin America
and Asia.The manufacturing process entails mixing and adding juices and coloring ingredients at bottling plant,which is a part of Mixing Division
The finished product is packaged in a company-produced glass bottle and packed in cases of 24 bottles each.

Because the appearance of the bottle heavily influences sales volume,Amazon developed a unique bottle production process at the company's
container plant,which is a part of a Container Division.The Mixing Division uses all of the container plant's production.
Each division(Mixing and Container) is considered a separate profit center and evaluated as such.
As the new corporate controller,you are responsible for determining the proper transfer price to use for the bottles produced for Mixing Division.
At your request,Container Division's general manager asked other bottle manufacturers to quote a price for the number and sized demanded
by mixing Division.These competitive prices follow:

Volume Total price Price per case
400,000 equivalent cases $2,400,000 $6.00
800,000 4,000,000 $5.00
1,200,000 6,480,000 $5.40

Note :An equivalent case represents 24 bottles

Container Division's cost analysis indicates that it can produce bottles at these costs:

Volume Total cost Cost per case
400,000 equivalent cases $2,400,000 $6.00
800,000 4,000,000 $5.00
1,200,000 5,600,000 $4.67

These costs include fixed costs of $800,000 and variable costs of $4 per equivalent case.These data have caused considerable corporate
discussion as to the proper price to use in the transfer of bottles from Container Divison to Mixing Division.This interest is heightened
because a significant portion of a division manager's income is an incentive bonus based on profit center results.

Mixing Division has the following costs in addition to the bottle costs;

Volume Total cost Cost per case
400,000 equivalent cases $1,800,000 $4.50
800,000 2,600,000 $3.25
1,200,000 3,400,000 $2.83

The corporate marketing group has furnished the following price-demand relationship for the finished product:

Sales Volume Total sales Revenue Sales Price per case

400,000 equivalent cases $8,000,000 $20.00
800,000 14,400,000 $18.00
1,200,000 18,000,000 $15.00

Required
a) Amazon Beverages has used market price transfer prices in the past.USING the current market prices and costs and assuming a volume of 1.2 million cases
calculate operating profits for:
1) container Division
2)Mixing Division
3)Amazon Beverages

b) Is this production and sales level the most profitable volume for:
1) Container Division ?
2)Mixing Division?
3)Amazon Beverages?
Explain.

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