Mathematical Nuance in Model 300 "Profit Margin" Question

Question

Hey everyone,

Just wanted to share an observation on the final question for the Model 300 math. The question asks how to keep the "profit margin" stable, and the answer gives 80% . You can check earlier threads regarding the 80% solution (for example, here).

If we stay true to definitions, the question that should be asked to get to 80% answer is:

Which percentage of customers has to buy the warranty to keep the total dollar contribution from the Model 300 stable?

If you are trying to write out a strict percentage margin formula here, you'll drive yourself crazy because we don't have the base manufacturing cost of the car. If you map it out rigorously, you'll see why the math breaks:

For stable profit Margin: Original Margin = New Margin

You will need to solve for X:

(51,000 - C) / 51,000 =(50,000 - C + 1,250X) / (50,000 + 2,350X)

(Where C is the Manufacturing Cost of the car, and X is the warranty take-rate percentage)

As you can notice, the new variables change the underlying averages:

Average Revenue per car = 50,000 + 2,350X
Average Cost per car = C + 1,100X
Average Profit per car = 50,000 - C + 1,250X

The 80% solution only works if you balance flat profit dollars per car, not percentage margins.

Answer 1

Hi Galina,

I would be happy to share my thoughts on your question:

First of all, you are right here and it is a nice catch, the 80% keeps the dollar contribution per car stable, not the percentage margin, so the wording of the official answer is too loose.
Moreover, in an interview setting, I would advise you to not spend valuable time on this kind of wording - what the interviewer wants to see is that you keep the math clean and say your assumptions out loud, the label margin versus contribution matters less than showing you understand the difference.

If you would like a more detailed discussion on how to best prepare your application files, for your upcoming pre-interview assessments and/or interviews, please don't hesitate to contact me directly.

Best,

Hagen

Answer 2

hey Galina,

You’re right to flag this. The famous “80%” answer in Model 300 is based on keeping profit dollars per car stable, not on keeping the true profit margin percentage constant. The moment you treat it as a strict margin question, you run into missing information: you don’t know the manufacturing cost of the car, and the warranty take‑rate changes both average revenue and average cost, so the actual margin percentage will move. In practice, the question is loosely phrased and really means: “what warranty take‑rate keeps total profit per car unchanged?”, under that interpretation, 80% works; under a rigorous margin definition, it doesn’t.

Alessa