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Match prior-year profit with new fixed costs

Capital OneData Scientist · Technical Screen
EasyData ScientistTechnical ScreenStatistics & Math

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This question tests the ability to model financial profitability by balancing fixed cost increases against variable profit contributions to maintain a target net income.

Scenario

A retail company currently operates with annual fixed costs of $500,000. They sell a single product with a unit selling price of $100 and a variable cost of $60 per unit. Last year, the company sold 20,000 units, resulting in a specific net profit.

For the upcoming year, the company anticipates an increase in fixed costs of $100,000 due to infrastructure upgrades. The selling price and variable cost per unit remain unchanged.

Task

  1. Calculate the total net profit earned in the previous year.
  2. Determine the number of units the company must sell in the upcoming year to achieve the exact same net profit as last year despite the increase in fixed costs.

Example

  • If fixed costs were $100,000, price was $50, and variable cost was $30, the contribution margin is $20. To cover $100,000 fixed costs, you would need 5,000 units just to break even.

Constraints

  • Assume all produced units are sold.
  • Ignore taxes and interest.
  • State your algebraic approach clearly.

Hints

Hint 1

Calculate the contribution margin per unit by subtracting the variable cost from the selling price.

Hint 2

The profit formula is (Units * Contribution Margin) - Fixed Costs = Net Profit.

Hint 3

Since the target profit remains constant, set the profit equations for both years equal to each other and solve for the new unit quantity.

Follow-up questions

  • If the company wanted to maintain the same profit without increasing sales volume, how much would they need to increase the selling price per unit?
  • How would a 10% increase in variable costs impact the break-even point in units?
  • If the product mix changes to include a second product with a lower contribution margin, how would that affect your overall target sales volume calculation?