1. **Problem Statement:** We are given various cost components and production data for ABC Limited and asked to determine: a) The break-even point and profit before tax for 4,000 units sold. b) The required units to produce and sell to achieve a target profit before tax of 12,000,000. --- 2. **Given Data:** - Salaries = 4,000,000 - Raw materials = 25,000,000 - Electricity = 1,500,000 - Fuel = 7,800,000 - Total Cost = 45,300,000 - Production units = 2,500 - Proposed selling price per unit = 45,000 - Salaries detail: 25% casuals worked 18 days, rest permanent - Generator consumes 90% fuel - Machines consume 90% electricity, 10% is factory lighting --- 3. **Step 1: Calculate variable and fixed costs** - Casual salaries = 25% of 4,000,000 = $1,000,000$ (paid for 18 days out of 30 approx) - Permanent salaries = 75% of 4,000,000 = $3,000,000$ Assuming casual salaries are variable (cost changes with production days) and permanent salaries are fixed. - Fuel for production = 90% of 7,800,000 = $7,020,000$ (variable) - Fuel for car = 10% of 7,800,000 = $780,000$ (fixed? Assume fixed since it's for manager car) - Electricity for machines = 90% of 1,500,000 = $1,350,000$ (variable) - Electricity for lighting = 10% of 1,500,000 = $150,000$ (fixed) - Raw material = $25,000,000$ (variable) --- 4. **Step 2: Calculate total fixed and variable costs** Fixed costs = Permanent salaries + car fuel + lighting electricity $$ \text{Fixed} = 3,000,000 + 780,000 + 150,000 = 3,930,000 $$ Variable costs = casual salaries + raw materials + fuel for production + electricity for machines $$ \text{Variable} = 1,000,000 + 25,000,000 + 7,020,000 + 1,350,000 = 34,370,000 $$ --- 5. **Step 3: Compute variable cost per unit** Production units = 2,500 $$ \text{Variable cost per unit} = \frac{34,370,000}{2,500} = 13,748 $$ --- 6. **Step 4: Contribution margin per unit** Selling price per unit = 45,000 $$ \text{Contribution per unit} = 45,000 - 13,748 = 31,252 $$ --- 7. **Step 5: Calculate break-even point (units)** $$ \text{Break-even units} = \frac{\text{Fixed costs}}{\text{Contribution per unit}} = \frac{3,930,000}{31,252} \approx 126 $$ --- 8. **Step 6: Profit before tax for 4,000 units sold** $$ \text{Profit} = (\text{Contribution per unit} \times 4,000) - \text{Fixed costs} = (31,252 \times 4,000) - 3,930,000 = 125,008,000 - 3,930,000 = 121,078,000 $$ --- 9. **Step 7: Units to produce for target profit 12,000,000** Formula: $$\text{Target units} = \frac{\text{Fixed costs} + \text{Target profit}}{\text{Contribution per unit}}$$ $$ = \frac{3,930,000 + 12,000,000}{31,252} = \frac{15,930,000}{31,252} \approx 510\text{ units} $$ --- **Final Answers:** - Break-even units = 126 units - Profit before tax at 4,000 units = 121,078,000 - Units needed for 12,000,000 profit = 510 units