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%.