Question

At 'break-even point'

• A. Constant expenses = Profits
• B. Total sales = variable expenses
• C. Variable expenses - Profits = Total sales
• D. None of the above

Hint:

At break-even point, Contribution Margin (Total Sales - Variable Expenses) exactly equals Fixed Costs. Always start from the fundamental identity: Profit = Sales - (Fixed Costs + Variable Costs) = 0.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question explores the concept of Break-Even Analysis, a fundamental tool in industrial engineering and business management. The break-even point (BEP) represents the specific volume of production or level of sales where a business neither makes a profit nor incurs a loss. It is the "neutral" point in financial operations. We need to evaluate the given algebraic relationships to see if any of them correctly define the state of a company at its break-even point.
Step 2: Key Formulas and approach:
The basic profit equation is:
1. Profit = Total Revenue (Sales) - Total Costs.
2. Total Costs = Fixed Costs (Constant Expenses) + Variable Costs (Variable Expenses).
At the Break-Even Point, Profit is exactly zero.
Therefore, the defining equation for BEP is:
Total Sales = Fixed Costs + Variable Costs.
Equivalently, Total Sales - Variable Costs = Fixed Costs. (This difference is also known as the Contribution Margin).
Step 3: Detailed Explanation:

Let's test Option (A): Constant expenses = Profits. At BEP, profits are zero, but constant expenses (like rent or salaries) are almost never zero. Thus, this is false.

Let's test Option (B): Total sales = variable expenses. If this were true, it would imply that Fixed Costs are zero (since Sales = Fixed + Variable). In reality, sales must cover both variable AND fixed costs to reach break-even. Thus, this is false.

Let's test Option (C): Variable expenses - Profits = Total sales. Since Profit = 0 at BEP, this becomes Variable expenses = Total sales, which is the same incorrect logic as Option (B).

Analysis: The actual condition is Total Sales = Fixed Costs + Variable Costs. None of the provided mathematical statements capture this requirement accurately.

The "Contribution Margin" (Sales - Variable Costs) must equal the "Fixed Costs" for the business to break even. None of the options A, B, or C reflect this fundamental identity.

Step 4: Final Answer:
Since none of the provided equations correctly describe the break-even condition, the correct choice is (D) None of the above.

Answer 2

Break-even analysis is built around one identity: the money left over after covering variable costs (the contribution margin) must exactly cover the fixed costs, with nothing left as profit or loss.

1. Building the true identity: Contribution Margin = Total Sales - Variable Expenses. At break-even, this margin covers Fixed (Constant) Expenses exactly, so: Total Sales - Variable Expenses = Constant Expenses, or equivalently Total Sales = Constant Expenses + Variable Expenses.
2. Comparing to option (A): "Constant expenses = Profits" swaps out Total Sales and Variable Expenses entirely and replaces them with Profits, a completely different quantity (and Profits is 0 at break-even, while Constant Expenses generally isn't). This doesn't match the true identity.
3. Comparing to option (B): "Total sales = variable expenses" keeps the correct left-hand side but drops the Constant Expenses term from the right-hand side entirely, effectively assuming fixed costs don't exist. This contradicts the true identity, which needs both cost terms.
4. Comparing to option (C): "Variable expenses - Profits = Total sales" rearranges terms in a way that, once Profits is set to 0 (as it must be at break-even), reduces right back to option (B)'s flawed identity, so it carries the same mismatch.

None of the three explicit options reduce to the true identity, Total Sales = Constant Expenses + Variable Expenses, so the correct choice has to be the option that acknowledges this.

Therefore, the correct answer is None of the above.