The problem is a cost accounting exercise for the company SETEX. We are given the indirect costs (fixed and variable) allocated to different departments (Administration, Maintenance, Energy-Steam, Preparation, and Assembly). We need to perform the following tasks: (1) Allocate the Administration costs to other departments, considering reciprocal services between Maintenance and Energy-Steam. (2) Perform secondary distribution of fixed indirect costs using the "rational imputation" method. (3) Calculate the production cost for product P in May 1996. (4) Determine the net analytical accounting result given that the analytical result (rational imputation) including rounding is 2,041,400.

1. Problem Description

The problem is a cost accounting exercise for the company SETEX. We are given the indirect costs (fixed and variable) allocated to different departments (Administration, Maintenance, Energy-Steam, Preparation, and Assembly). We need to perform the following tasks:

(1) Allocate the Administration costs to other departments, considering reciprocal services between Maintenance and Energy-Steam.

(2) Perform secondary distribution of fixed indirect costs using the "rational imputation" method.

(3) Calculate the production cost for product P in May

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(4) Determine the net analytical accounting result given that the analytical result (rational imputation) including rounding is 2,041,

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2. Solution Steps

Step 1: Allocate Administration Costs

We need to distribute the administration costs to other sections. The basis is given in the table "Répartition secondaire". The administrative cost distribution is as follows:

- Maintenance: 10%

- Energy-Steam: 10%

- Preparation: 30%

- Assembly: 50%

Fixed Administration Costs = 1,000,000

Variable Administration Costs = 0

Fixed Cost Distribution:

- Maintenance: $1,000,000 * 0.1 = 100,000$

- Energy-Steam: $1,000,000 * 0.1 = 100,000$

- Preparation: $1,000,000 * 0.3 = 300,000$

- Assembly: $1,000,000 * 0.5 = 500,000$

After allocating the Administration costs, the new fixed costs for each department are:

- Maintenance: $160,000 + 100,000 = 260,000$

- Energy-Steam: $240,000 + 100,000 = 340,000$

- Preparation: $800,000 + 300,000 = 1,100,000$

- Assembly: $1,800,000 + 500,000 = 2,300,000$

- Administration: $1,000,000 - 1,000,000 = 0$

Step 2: Calculate Reciprocal Services between Maintenance and Energy-Steam

Let M be the total fixed cost of Maintenance after allocation, and E be the total fixed cost of Energy-Steam after allocation. We have the following relationships:

$M = 260,000 + 0.1E$

$E = 340,000 + 0.2M$

Substitute E in the first equation:

$M = 260,000 + 0.1(340,000 + 0.2M)$

$M = 260,000 + 34,000 + 0.02M$

$0.98M = 294,000$

$M = 294,000 / 0.98 = 300,000$

Substitute M in the second equation:

$E = 340,000 + 0.2(300,000)$

$E = 340,000 + 60,000 = 400,000$

So, the total fixed cost for Maintenance is 300,000, and for Energy-Steam is 400,

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Step 3: Distribute Maintenance and Energy-Steam Costs

The distribution percentages are as follows:

- Maintenance:

- Preparation: 20%

- Assembly: 60%

- Energy-Steam:

- Preparation: 40%

- Assembly: 50%

Distribution of Maintenance Fixed Costs:

- Preparation: $300,000 * 0.2 = 60,000$

- Assembly: $300,000 * 0.6 = 180,000$

Distribution of Energy-Steam Fixed Costs:

- Preparation: $400,000 * 0.4 = 160,000$

- Assembly: $400,000 * 0.5 = 200,000$

After these distributions, the fixed costs are:

- Preparation: $1,100,000 + 60,000 + 160,000 = 1,320,000$

- Assembly: $2,300,000 + 180,000 + 200,000 = 2,680,000$

Step 4: Rational Imputation and Activity Levels

Normal Activity of Preparation = 12,000 meters

Actual Activity of Preparation = 10,500 meters

Normal Activity of Assembly = 4,000 hours

Actual Activity of Assembly = 3,700 hours

Rational Imputation Rate:

Rate = Actual Activity / Normal Activity

- Preparation: $10,500 / 12,000 = 0.875$

- Assembly: $3,700 / 4,000 = 0.925$

Fixed Costs to be Imputed:

- Preparation: $1,320,000 * 0.875 = 1,155,000$

- Assembly: $2,680,000 * 0.925 = 2,479,000$

Step 5: Calculate Total Production Cost

Direct Costs:

- Textile: $10,500 \text{ meters} * 300 \text{ F/meter} = 3,150,000$

- Preparation Labor: $1,700 \text{ hours} * 435 \text{ F/hour} = 739,500$

- Assembly Labor: $3,700 \text{ hours} * 460 \text{ F/hour} = 1,702,000$

Variable Indirect Costs (already allocated):

- Preparation: 400,000

- Assembly: 1,600,000

Total Cost Calculation:

Total Cost = Textile + Preparation Labor + Assembly Labor + Variable Preparation + Variable Assembly + Imputed Fixed Preparation + Imputed Fixed Assembly

Total Cost = $3,150,000 + 739,500 + 1,702,000 + 400,000 + 1,600,000 + 1,155,000 + 2,479,000 = 11,225,500$

Cost per unit = Total Cost / Number of Articles

Cost per unit = $11,225,500 / 10,500 = 1069.10$ F

Step 6: Determine Net Analytical Accounting Result

Analytical Result (rational imputation) = 2,041,400

Total Costs = 11,225,500

Sales = Total Costs + Analytical Result

Sales = $11,225,500 + 2,041,400 = 13,266,900$

Normal Theoretical Fixed Costs: 1,320,000 + 2,680,000 = 4,000,000

Fixed Costs effectively imputed: 1,155,000 + 2,479,000 = 3,634,000

Difference (underactivity) = 4,000,000 - 3,634,000 = 366,000

Net analytical accounting result = Analytical result (rational imputation) - Cost of Underactivity

Net analytical accounting result = 2,041,400 - 366,000 = 1,675,400

3. Final Answer

Total Production Cost for articles P: 1069.10 F/article

Net analytical accounting result: 1,675,400 F