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Sagot :
Certainly! Let's walk through the process for both Absorption Costing and Marginal Costing step by step, based on the given data.
### Given Data
- Sales: \[tex]$16,000 - Direct materials: \$[/tex]4,000
- Direct labour: \[tex]$3,000 - Factory overheads: \$[/tex]3,000
- Selling cost: \[tex]$2,000 - Distribution cost: \$[/tex]1,000
- Administration cost: \[tex]$1,000 - Units sold: 2,000 units - Units manufactured: 2,500 units ### Additional Information - 40% of selling, distribution, and administration costs are variable. - One third of the factory overheads are variable costs. ### 1. Absorption Costing Absorption costing, also known as full costing, includes both fixed and variable costs in the cost of production. #### Step-by-Step Calculation for Absorption Costing 1. Calculate Variable and Fixed Costs - Variable selling, distribution, and administration cost: \[ (2000 + 1000 + 1000) \times 0.4 = 4000 \times 0.4 = \$[/tex]1600
\]
- Variable factory overheads:
[tex]\[ 3000 \div 3 = \$1000 \][/tex]
2. Calculate Fixed Costs
- Fixed factory overheads:
[tex]\[ 3000 - 1000 = \$2000 \][/tex]
3. Calculate Unit Cost
- Total cost per unit under absorption costing:
[tex]\[ \frac{Direct\ \text{materials} + Direct\ \text{labour} + Total\ \text{factory\ overheads}}{Units\ \text{manufactured}} = \frac{4000 + 3000 + 3000}{2500} = \frac{10000}{2500} = \$4.00/unit \][/tex]
4. Calculate Cost of Goods Sold (COGS)
- COGS under absorption costing:
[tex]\[ Unit\ \text{cost\ absorption} \times Units\ \text{sold} = 4.00 \times 2000 = \$8000 \][/tex]
5. Calculate Gross Profit and Profit
- Gross Profit:
[tex]\[ Sales - COGS = 16000 - 8000 = \$8000 \][/tex]
- Total Selling, Distribution, and Administration costs:
[tex]\[ 2000 + 1000 + 1000 = \$4000 \][/tex]
- Profit:
[tex]\[ Gross\ \text{Profit} - Total\ \text{Selling, Distribution, Administration} = 8000 - 4000 = \$4000 \][/tex]
So under Absorption Costing:
- Cost of Goods Sold = \[tex]$8000 - Profit = \$[/tex]4000
### 2. Marginal Costing
Marginal costing, also known as variable costing, only considers variable costs in the cost of production.
#### Step-by-Step Calculation for Marginal Costing
1. Calculate Unit Cost
- Total variable cost per unit under marginal costing:
[tex]\[ \frac{Direct\ \text{materials} + Direct\ \text{labour} + Variable\ \text{factory\ overheads}}{Units\ \text{manufactured}} = \frac{4000 + 3000 + 1000}{2500} = \frac{8000}{2500} = \$3.20/unit \][/tex]
2. Calculate Cost of Goods Sold (COGS)
- COGS under marginal costing:
[tex]\[ Unit\ \text{cost\ marginal} \times Units\ \text{sold} = 3.20 \times 2000 = \$6400 \][/tex]
3. Calculate Variable Selling, Administration, and Distribution Costs
- Variable selling, administration, and distribution costs:
[tex]\[ (2000 + 1000 + 1000) \times \frac{1600}{4000} = 4000 \times 0.4 = \$1600 \][/tex]
4. Calculate Total Variable Cost
- Total variable cost:
[tex]\[ COGS + Variable\ \text{Selling, Administration, and Distribution Costs} = 6400 + 1600 = \$8000 \][/tex]
5. Calculate Contribution and Profit
- Contribution:
[tex]\[ Sales - Total\ \text{Variable Cost} = 16000 - 8000 = \$8000 \][/tex]
- Fixed Costs:
[tex]\[ Fixed\ \text{factory\ overheads} + (Total\ \text{Selling, Distribution, and Administration Costs - Variable Selling, Distribution, Admin Costs}) = 2000 + (4000 - 1600) = 2000 + 2400 = \$4400 \][/tex]
- Profit:
[tex]\[ Contribution - Fixed\ \text{Costs} = 8000 - 4400 = \$3600 \][/tex]
So under Marginal Costing:
- Cost of Goods Sold = \[tex]$6400 - Profit = \$[/tex]3600
### Given Data
- Sales: \[tex]$16,000 - Direct materials: \$[/tex]4,000
- Direct labour: \[tex]$3,000 - Factory overheads: \$[/tex]3,000
- Selling cost: \[tex]$2,000 - Distribution cost: \$[/tex]1,000
- Administration cost: \[tex]$1,000 - Units sold: 2,000 units - Units manufactured: 2,500 units ### Additional Information - 40% of selling, distribution, and administration costs are variable. - One third of the factory overheads are variable costs. ### 1. Absorption Costing Absorption costing, also known as full costing, includes both fixed and variable costs in the cost of production. #### Step-by-Step Calculation for Absorption Costing 1. Calculate Variable and Fixed Costs - Variable selling, distribution, and administration cost: \[ (2000 + 1000 + 1000) \times 0.4 = 4000 \times 0.4 = \$[/tex]1600
\]
- Variable factory overheads:
[tex]\[ 3000 \div 3 = \$1000 \][/tex]
2. Calculate Fixed Costs
- Fixed factory overheads:
[tex]\[ 3000 - 1000 = \$2000 \][/tex]
3. Calculate Unit Cost
- Total cost per unit under absorption costing:
[tex]\[ \frac{Direct\ \text{materials} + Direct\ \text{labour} + Total\ \text{factory\ overheads}}{Units\ \text{manufactured}} = \frac{4000 + 3000 + 3000}{2500} = \frac{10000}{2500} = \$4.00/unit \][/tex]
4. Calculate Cost of Goods Sold (COGS)
- COGS under absorption costing:
[tex]\[ Unit\ \text{cost\ absorption} \times Units\ \text{sold} = 4.00 \times 2000 = \$8000 \][/tex]
5. Calculate Gross Profit and Profit
- Gross Profit:
[tex]\[ Sales - COGS = 16000 - 8000 = \$8000 \][/tex]
- Total Selling, Distribution, and Administration costs:
[tex]\[ 2000 + 1000 + 1000 = \$4000 \][/tex]
- Profit:
[tex]\[ Gross\ \text{Profit} - Total\ \text{Selling, Distribution, Administration} = 8000 - 4000 = \$4000 \][/tex]
So under Absorption Costing:
- Cost of Goods Sold = \[tex]$8000 - Profit = \$[/tex]4000
### 2. Marginal Costing
Marginal costing, also known as variable costing, only considers variable costs in the cost of production.
#### Step-by-Step Calculation for Marginal Costing
1. Calculate Unit Cost
- Total variable cost per unit under marginal costing:
[tex]\[ \frac{Direct\ \text{materials} + Direct\ \text{labour} + Variable\ \text{factory\ overheads}}{Units\ \text{manufactured}} = \frac{4000 + 3000 + 1000}{2500} = \frac{8000}{2500} = \$3.20/unit \][/tex]
2. Calculate Cost of Goods Sold (COGS)
- COGS under marginal costing:
[tex]\[ Unit\ \text{cost\ marginal} \times Units\ \text{sold} = 3.20 \times 2000 = \$6400 \][/tex]
3. Calculate Variable Selling, Administration, and Distribution Costs
- Variable selling, administration, and distribution costs:
[tex]\[ (2000 + 1000 + 1000) \times \frac{1600}{4000} = 4000 \times 0.4 = \$1600 \][/tex]
4. Calculate Total Variable Cost
- Total variable cost:
[tex]\[ COGS + Variable\ \text{Selling, Administration, and Distribution Costs} = 6400 + 1600 = \$8000 \][/tex]
5. Calculate Contribution and Profit
- Contribution:
[tex]\[ Sales - Total\ \text{Variable Cost} = 16000 - 8000 = \$8000 \][/tex]
- Fixed Costs:
[tex]\[ Fixed\ \text{factory\ overheads} + (Total\ \text{Selling, Distribution, and Administration Costs - Variable Selling, Distribution, Admin Costs}) = 2000 + (4000 - 1600) = 2000 + 2400 = \$4400 \][/tex]
- Profit:
[tex]\[ Contribution - Fixed\ \text{Costs} = 8000 - 4400 = \$3600 \][/tex]
So under Marginal Costing:
- Cost of Goods Sold = \[tex]$6400 - Profit = \$[/tex]3600
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