If the selling price is $6.00, the break-even point will be achieved when the number of books sold is 200,000 units.
Break-even point (BEP) is a situation in which the profit is zero or the company does not gain profit or loss.
Recall that:
Profit = revenue - total cost
Since profit = 0, hence the condition for break-even point is:
revenue = total cost
Revenue = number of units sold x selling price per unit
Total cost = fixed cost + variable cost per unit x number of units sold
In the given problem, given parameters are:
selling price = $6.00
fixed operating cost = $600,000
variable cost = $3.00 per book
Let:
p = number of unit sold
Hence,
revenue = 6 x p = 6p
total cost = 600,000 + 3p
Condition for BEP:
revenue = total cost
6p = 600,000 + 3p
3p = 600,000
p = 600,000/3 = 200,000
Hence, the BEP achieved if the number of books sold is 200,000 units.
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