A company has fixed costs of N2,000,000. Variable cost per unit is N20 and selling price per unit is N30. Calculate the break-even point in units and sales revenue. Also calculate the units needed to

Given Data:

• Fixed Cost = N2,000,000
• Variable Expense per unit = N20
• Selling Price per unit = N30

Step 1: Calculate Contribution Margin per unit
The contribution margin per unit is the selling price per unit minus the variable expense per unit.

$$\text{Contribution Margin per unit} = \text{Selling Price per unit} - \text{Variable Expense per unit}$$ $$\text{Contribution Margin per unit} = \text{N}30 - \text{N}20 = \text{N}10$$

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a) The number of units and amount to be manufactured and sold to:

i) Break-even
To break even, total contribution margin must equal total fixed costs.

• Number of Units: $$\text{Break-even Units} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per unit}}$$ $$\text{Break-even Units} = \frac{\text{N}2,000,000}{\text{N}10/\text{unit}} = \text{200,000 units}$$
• Amount (Sales Revenue): $$\text{Break-even Sales Revenue} = \text{Break-even Units} \times \text{Selling Price per unit}$$ $$\text{Break-even Sales Revenue} = 200,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}6,000,000$$ To break even, Hallelujah Ltd needs to manufacture and sell 200,000 units for a total sales revenue of N6,000,000.

ii) Earn a profit of N20,000
To earn a target profit, the total contribution margin must cover fixed costs plus the target profit.

• Number of Units: $$\text{Units for Target Profit} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin per unit}}$$ $$\text{Units for Target Profit} = \frac{\text{N}2,000,000 + \text{N}20,000}{\text{N}10/\text{unit}} = \frac{\text{N}2,020,000}{\text{N}10/\text{unit}} = \text{202,000 units}$$
• Amount (Sales Revenue): $$\text{Sales Revenue for Target Profit} = \text{Units for Target Profit} \times \text{Selling Price per unit}$$ $$\text{Sales Revenue for Target Profit} = 202,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}6,060,000$$ To earn a profit of N20,000, Hallelujah Ltd needs to manufacture and sell 202,000 units for a total sales revenue of N6,060,000.

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b) What additional unit and amount would be needed to increase the above profit by N10,000.
The "above profit" is N20,000. Increasing it by N10,000 means a new target profit of N30,000.

• Additional Units: Each additional unit sold contributes N10 to profit. To increase profit by N10,000, the additional units needed are: $$\text{Additional Units} = \frac{\text{Additional Target Profit}}{\text{Contribution Margin per unit}}$$ $$\text{Additional Units} = \frac{\text{N}10,000}{\text{N}10/\text{unit}} = \text{1,000 units}$$
• Additional Amount (Sales Revenue): $$\text{Additional Sales Revenue} = \text{Additional Units} \times \text{Selling Price per unit}$$ $$\text{Additional Sales Revenue} = 1,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}30,000$$ To increase the profit by N10,000, an additional 1,000 units must be sold, generating an additional sales revenue of N30,000.

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c) Verify your answer to (a) and (b) mathematically.

• Verification for a) i) Break-even (200,000 units):

  $$\text{Total Sales Revenue} = 200,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}6,000,000$$ $$\text{Total Variable Costs} = 200,000 \text{ units} \times \text{N}20/\text{unit} = \text{N}4,000,000$$ $$\text{Total Contribution Margin} = \text{N}6,000,000 - \text{N}4,000,000 = \text{N}2,000,000$$ $$\text{Profit} = \text{Total Contribution Margin} - \text{Fixed Costs}$$ $$\text{Profit} = \text{N}2,000,000 - \text{N}2,000,000 = \boxed{\textbf{N0}}$$

• Verification for a) ii) Earn a profit of N20,000 (202,000 units):

  $$\text{Total Sales Revenue} = 202,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}6,060,000$$ $$\text{Total Variable Costs} = 202,000 \text{ units} \times \text{N}20/\text{unit} = \text{N}4,040,000$$ $$\text{Total Contribution Margin} = \text{N}6,060,000 - \text{N}4,040,000 = \text{N}2,020,000$$ $$\text{Profit} = \text{Total Contribution Margin} - \text{Fixed Costs}$$ $$\text{Profit} = \text{N}2,020,000 - \text{N}2,000,000 = \boxed{\textbf{N20,000}}$$

• Verification for b) Total profit N30,000 (203,000 units):

  $$\text{Total Sales Revenue} = 203,000 \text{ units} \times \text{N}30/\text{unit} = \text{N}6,090,000$$ $$\text{Total Variable Costs} = 203,000 \text{ units} \times \text{N}20/\text{unit} = \text{N}4,060,000$$ $$\text{Total Contribution Margin} = \text{N}6,090,000 - \text{N}4,060,000 = \text{N}2,030,000$$ $$\text{Profit} = \text{Total Contribution Margin} - \text{Fixed Costs}$$ $$\text{Profit} = \text{N}2,030,000 - \text{N}2,000,000 = \boxed{\textbf{N30,000}}$$