Marginal Costing Agnew Ltd manufactures a single product - Leaving Cert Accounting - Question 8 - 2010

The variable cost per unit is calculated by dividing the total variable costs by the number of units sold:

$\text{Variable Cost per Unit} = \frac{\text{Total Variable Costs}}{\text{Units Sold}} = \frac{160,000}{40,000} = €4.00$

The contribution per unit can be calculated by subtracting the variable cost per unit from the selling price per unit:

$\text{Contribution per Unit} = \text{Selling Price} - \text{Variable Cost} = €12.00 - €4.00 = €8.00$

To determine the break-even point in units, we use the formula:

$\text{Break-even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Contribution per Unit}} = \frac{64,000}{8} = 8,000 \text{ units}$

The sales value at the break-even point is:

$\text{Sales Value} = \text{Break-even Point (Units)} \times \text{Selling Price} = 8,000 \times 12 = €96,000$

The margin of safety is calculated using the formula:

$\text{Margin of Safety (Units)} = \text{Budgeted Sales} - \text{Break-even Sales} = 40,000 - 8,000 = 32,000 \text{ units}$

For sales value:

$\text{Sales Value} = \text{Margin of Safety (Units)} \times \text{Selling Price} = 32,000 \times €12 = €384,000$

To find the level of production needed for a profit of €120,000, we use the formula:

$\text{Total Required Sales} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution per Unit}}$

Substituting the values:

$\text{Total Required Sales} = \frac{64,000 + 120,000}{8} = \frac{184,000}{8} = 23,000 \text{ units}$