Calculating Break-Even Point and Gross Profit Growth

Question:

If the sales of a company grows by 25 percent in a year, how much will its gross profit increase?

Answer:

The break-even point for accounting requires 8216 units. The company's gross profit will rise by 7.5% if its annual sales increase by 25%. By dividing the fixed expenses by the contribution margin per unit, it is possible to get the accounting break-even point.

Break-Even Point Calculation:

Given:

  • Selling price per unit: $17
  • Variable cost per unit: $12
  • Fixed costs: $18,000

Compute the contribution margin per unit: $17 - $12 = $5

Calculate the accounting break-even point: Fixed costs / Contribution margin per unit

Accounting break-even point: 3,600 units = $18,000 / $5

Therefore, 3,600 units are needed to reach the accounting break-even point.

Gross Profit Growth Calculation:

Using the DuPont formula:

  • ROE = 15%
  • Degree of Operating Leverage = 3
  • Plowback Ratio = 50%

Formula for calculating gross profit growth:

Gross profit growth = Sales growth + (1 - Plowback ratio) * ROE * Degree of Operating Leverage

Substitute the values: Gross profit growth = 0.25 * (1 - 0.5) * 0.15 * 3

Gross profit growth = 0.05625 or 5.63%

Therefore, the increase in gross profit would be around 5.63% to 7.5%.

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