Maintain profit margin with new product line

Quick Overview

This question evaluates competence in cost-volume-profit analysis, algebraic modeling of profit margins, and unit economics when adding a new product line.

Maintain profit margin with new product line

Company: Capital One

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Technical Screen

Assume m = million. In Year 2 you add Vegan with fixed costs: training $60m/year and supplier $2.25m/month. Maintain prices/costs from earlier (Regular: $4 price, $1 cost; Vegan: $4 price, $2 cost) and mix Vegan:Regular = 2:3. What total number of burgers must you sell in Year 2 to keep the same profit margin as Year 1 (from the previous question)? Provide the general formula and the numeric answer.

Quick Answer: This question evaluates competence in cost-volume-profit analysis, algebraic modeling of profit margins, and unit economics when adding a new product line.

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Oct 13, 2025, 9:49 PM
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Year 2 volume needed to maintain Year 1 profit margin after adding Vegan line

Context

  • m denotes million dollars.
  • In Year 2, you add a Vegan burger line with new fixed costs: training = 60m/year;supplier=60m/year; supplier = 2.25m/month.
  • Prices and unit variable costs remain: Regular price 4,cost4, cost 1; Vegan price 4,cost4, cost 2.
  • Year 2 sales mix: Vegan : Regular = 2 : 3 (i.e., 40% Vegan, 60% Regular).
  • Let m1 denote your Year 1 overall profit margin (profit ÷ revenue) from the prior question.

Task

  1. Derive a general formula for the total number of burgers to sell in Year 2 to keep the same profit margin m1 as in Year 1.
  2. Provide the numeric answer by plugging in your Year 1 margin m1.
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