To solve this problem, we'll need to calculate several components: the contribution margin ratio, break-even quantity, break-even value, margin of safety in units, margin of safety ratio, and finally, a marginal costing income statement.
Let's break down each requirement:
Given Information:
- Selling price per unit: R80
- Direct material per unit: R15
- Direct labour per unit: R14
- Variable overheads per unit: R8
- Fixed overheads: R350,000
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Calculate Contribution Margin per Unit: \[ \text{Total Variable Cost per unit} = \text{Direct material} + \text{Direct labour} + \text{Variable overheads} \] \[ = R15 + R14 + R8 = R37 \]
\[ \text{Contribution Margin per unit} = \text{Selling Price} - \text{Total Variable Cost} \] \[ = R80 - R37 = R43 \]
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Contribution Margin Ratio: \[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per unit}}{\text{Selling Price}} \times 100 \] \[ = \frac{43}{80} \times 100 = 53.75% \]
Blank 1: 53.75
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Break-even Quantity: \[ \text{Break-even Quantity} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin per unit}} \] \[ = \frac{350,000}{43} \approx 8130.23 \] Rounding gives us 8130.
Blank 2: 8130
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Break-even Value: \[ \text{Break-even Value} = \text{Break-even Quantity} \times \text{Selling Price} \] \[ = 8130 \times 80 = R650,400 \]
Blank 3: 650400
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Calculate Margin of Safety:
- Sales level = R1,200,000
- Selling price per unit = R80 \[ \text{Expected Sales Quantity} = \frac{\text{Sales Level}}{\text{Selling Price}} = \frac{1,200,000}{80} = 15,000 \text{ units} \]
Margin of Safety in Units: \[ \text{Margin of Safety in units} = \text{Expected Sales Quantity} - \text{Break-even Quantity} \] \[ = 15,000 - 8130 = 6860 \text{ units} \]
Margin of Safety Ratio: \[ \text{Margin of Safety Ratio} = \frac{\text{Margin of Safety in units}}{\text{Expected Sales Quantity}} \times 100 \] \[ = \frac{6860}{15000} \times 100 \approx 45.73% \]
Blank 4: 6860
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Marginal Costing Income Statement (for 12,000 units):
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Sales Revenue: \[ \text{Sales Revenue} = \text{Selling Price} \times \text{Sales Quantity} = R80 \times 12,000 = R960,000 \]
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Variable Costs: \[ \text{Variable Cost per unit} = R37 \quad (\text{as calculated earlier}) \] \[ \text{Total Variable Costs} = \text{Variable Cost per unit} \times \text{Sales Quantity} = R37 \times 12,000 = R444,000 \]
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Contribution Margin: \[ \text{Contribution Margin} = \text{Sales Revenue} - \text{Total Variable Costs} = R960,000 - R444,000 = R516,000 \]
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Fixed Costs: \[ \text{Total Fixed Costs} = R350,000 \]
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Net Profit: \[ \text{Net Profit} = \text{Contribution Margin} - \text{Total Fixed Costs} = R516,000 - R350,000 = R166,000 \]
The marginal costing income statement can be structured as follows:
Marginal Costing Income Statement \[ \begin{align*} \text{Sales Revenue} & : R960,000 \ \text{Less: Variable Costs} & : R444,000 \ \hline \text{Contribution Margin} & : R516,000 \ \text{Less: Fixed Costs} & : R350,000 \ \hline \text{Net Profit} & : R166,000 \ \end{align*} \]
Blank 5: Net profit: R166,000
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Final Answers:
- Contribution margin ratio (Blank 1): 53.75
- Break-even quantity (Blank 2): 8130
- Break-even value (Blank 3): 650400
- Margin of safety unit (Blank 4): 6860
- Marginal costing income statement profit (Blank 5): R166,000
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