Q:
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.
A:

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

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