Maintain profit margin with new product line

Q: Maintain profit margin with new product line

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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Question

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 = $60m/year; supplier =$ 2.25m/month.
Prices and unit variable costs remain: Regular price $4, cost$ 1; Vegan price $4, cost$ 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

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.
Provide the numeric answer by plugging in your Year 1 margin m1.

Maintain profit margin with new product line

Year 2 volume needed to maintain Year 1 profit margin after adding Vegan line

Solution

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Maintain profit margin with new product line

Overview

Year 2 volume needed to maintain Year 1 profit margin after adding Vegan line

Solution

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