Question of the Week

For each widget that a manufacturer sells, it records a sale of $5 and a variable cost of $3. In addition, the firm has fixed expenditures of $1,000,000 per year. Which of the following statements is inaccurate in describing the company's profitability at various levels of sale?

a) The break-even point for the company occurs when it sells 500,000 units. At 1,000,000 units sold, the company would incur a profit of $1,000,000.
b) The company will break even when it sells $1,000,000 worth of widgets.
c) At its break-even point, the company's fixed costs will still be only $1,000,000.
d) The company will break even when it sells $2,500,000 worth of widgets.

Answer:

The correct answer is: b)

The break-even point can be derived as follows:
(Sales price per unit)(x) - (Variable cost per unit)(x) - Fixed Costs = 0

Where (x) is the number of units sold.

Substituting for all the variables, we get:

5x - 3x -1,000,000 =
  0
x =
  500,000 units

For 1,000,000 units sold, we can use the same equation as follows:

(5) (1,000,000) - (3) (1,000,000) - 1,000,000 =
  Profit
$1,000,000 =
  Profit


CFA Level 2 2005 LOS: 8.1.E.f