Question

a company reports the following: sales (2,500 units at ₦40 each) ₦100,000 less: expenses: cost of goods sold (all variable) 45,000 sales commission 5,000 rent 5,000 fixed administrative expenses 18,000 miscellaneous fixed expenses 2,000 total expenses 75,000 net profit 25,000 required: (i) how many units must be sold before the firm can break - even? (ii) what will be the net profit if sales increased by 30% (assume no increase in selling price). (iii) if selling price is reduced by 5% how many units must be sold in order to maintain the net profit of ₦25,000?

Explanation:

Step1: Calculate total fixed costs

Total fixed - costs = Rent+Fixed administrative expenses+Miscellaneous fixed expenses
Total fixed - costs = 5000 + 18000+2000=$25000$

Step2: Calculate contribution margin per unit

Selling price per unit = $40$
Cost of goods sold per unit (variable) = $45000\div2500 = 18$
Sales commission per unit (variable) = $5000\div2500 = 2$
Total variable cost per unit = $18 + 2=20$
Contribution margin per unit = Selling price per unit - Total variable cost per unit
Contribution margin per unit = $40-20 = 20$

Step3: Calculate break - even point

Break - even point (in units)=$\frac{\text{Total fixed costs}}{\text{Contribution margin per unit}}$
Break - even point (in units)=$\frac{25000}{20}=1250$ units

Step4: Calculate new selling price

New selling price = $40\times(1 - 0.05)=38$
New contribution margin per unit = $38-20 = 18$

Step5: Calculate number of units to maintain profit

Let the number of units be $x$.
Profit = Contribution margin - Fixed costs
We want to maintain a profit of $25000$.
$25000=18x - 25000$
$18x=25000 + 25000$
$18x = 50000$
$x=\frac{50000}{18}\approx2778$ units

Answer:

(i) 1250 units
(ii) $38$
(iii) 2778 units