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 asks for the true mathematical relationship that defines the "break-even point" in business or industrial economics.


Step 3: Detailed Explanation:
The break-even point (BEP) is defined as the level of production or sales at which total revenues exactly equal total costs, resulting in a net profit of strictly zero.
The fundamental economic equation is: \[ \text{Total Sales (Revenue)} = \text{Total Costs} \] Total Costs can be broken down into Fixed Costs (Constant expenses) and Variable Costs (Variable expenses). \[ \text{Total Sales} = \text{Constant expenses} + \text{Variable expenses} \] Let's evaluate the given options based on this defining equation (where Profit = 0):
• (A) Constant expenses = Profits: Incorrect. At BEP, Profit is exactly 0, while constant expenses are typically a positive baseline value.
• (B) Total sales = variable expenses: Incorrect. This statement implies that constant expenses are zero (\(\text{Total Sales} - \text{Variable expenses} = 0\)), which ignores fixed costs entirely.
• (C) Variable expenses - Profits = Total sales: Since Profit = 0 at BEP, this equation simplifies to Variable expenses = Total sales, which is identical to option (B) and is therefore incorrect. Since none of the statements A, B, or C correctly describe the break-even condition, the correct choice must be "None of the above".


Step 4: Final Answer:
None of the listed equations correctly define the break-even point.

Answer 2

A good way to double check this kind of conceptual accounting question is to plug in a concrete, simple example of a business at its break-even point and see which equation actually holds.

Suppose a business has fixed (constant) costs of 100, and it sells enough units that variable costs come to 150, making total costs 250. At break-even, by definition, total sales must exactly equal total costs, so sales = 250, and profit = 0.

1. Constant expenses = Profits: Here, constant expenses are 100, but profit is 0. Since \(100\neq0\), this equation fails for our example.
2. Total sales = variable expenses: Here, total sales are 250, but variable expenses are only 150. Since \(250\neq150\), this equation fails too, because it ignores the 100 in fixed costs that sales also have to cover.
3. Variable expenses - Profits = Total sales: Here, variable expenses minus profit is \(150-0=150\), while total sales are 250. Since \(150\neq250\), this equation fails as well, for the same reason as the previous one.
4. None of the above: Since all three explicit equations failed our concrete numerical test, and the actual relationship that holds is Total sales = Fixed costs + Variable costs (\(250=100+150\)), which isn't listed as an option, this is the only consistent choice.

Testing all three specific equations against a concrete break-even scenario shows that none of them hold, confirming that the real relationship, sales equal to the sum of fixed and variable costs, simply isn't among the listed choices.

Therefore, the correct answer is None of the above.