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Match prior-year profit with new fixed costs

Last updated: Mar 29, 2026

Quick Overview

This question evaluates cost–volume–profit analysis, unit economics, and algebraic modeling of fixed versus variable costs in a multi-product sales mix, testing quantitative financial reasoning in the Statistics & Math domain and emphasizing practical application rather than abstract theory.

  • easy
  • Capital One
  • Statistics & Math
  • Data Scientist

Match prior-year profit with new fixed costs

Company: Capital One

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Technical Screen

Assume m = million. Year 1 (Regular-only): fixed costs $375m; sold 231m Regular at price $4, unit cost $1. Year 2 (launch Vegan): additional fixed costs: training $60m/year and supplier retainer $2.25m/month; maintain prices/costs from above and a sales mix Vegan:Regular = 2:3. How many total burgers (Regular + Vegan) must you sell in Year 2 to match Year 1 profit? Show formulas and the final number.

Quick Answer: This question evaluates cost–volume–profit analysis, unit economics, and algebraic modeling of fixed versus variable costs in a multi-product sales mix, testing quantitative financial reasoning in the Statistics & Math domain and emphasizing practical application rather than abstract theory.

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Capital One
Oct 13, 2025, 9:49 PM
Data Scientist
Technical Screen
Statistics & Math
2
0
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Target Profit Match with Product Mix and Added Fixed Costs

m = million.

You sold only Regular burgers in Year 1. In Year 2, you launch a Vegan burger while maintaining the same unit price and unit cost as in Year 1. A new training program and a supplier retainer add fixed costs in Year 2. The sales mix in Year 2 is Vegan:Regular = 2:3.

Assume both Regular and Vegan burgers have the same unit price (4)andunitvariablecost(4) and unit variable cost (4)andunitvariablecost(1).

Given

  1. Year 1 (Regular-only):
    • Fixed costs = $375m
    • Units sold (Regular) = 231m
    • Price per burger = $4
    • Unit variable cost = $1
  2. Year 2 (launch Vegan):
    • Additional fixed costs:
      • Training = $60m per year
      • Supplier retainer = $2.25m per month
    • Sales mix = Vegan:Regular = 2:3
    • Maintain the same unit price and unit cost as in Year 1 for both products

Task

How many total burgers (Regular + Vegan) must be sold in Year 2 to match the Year 1 profit? Show formulas and the final number.

Solution

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