Case Type: math problem; new business; finance.
Consulting Firm: Capital One 2nd round job interview.
Industry Coverage: automotive, motor vehicles; retail; financial services.
Case Interview Question #00334: Our client CarMax (NYSE: KMX) is a used car retailer and dealership headquartered in Richmond, Virginia, USA. Their business has been stagnating in recent years. They are located in a low to middle-income area and in the past 
have only sold cars to customers who are willing to pay 100% of the cost up-front or can obtain bank financing. In order to boost sales, CarMax is considering offering car loans to customers that the dealership itself will finance.
To be eligible for a loan, customers must undergo a complete credit check (which we assume to be accurate). The credit check rates potential car buyers on a scale of 0 to 100, where 0 corresponds to a 0% chance of paying off the loan and 100 corresponds to a 100% chance of paying the loan in full. Each loan only lasts 1 year in which payments are made monthly and the entire loan will be paid off in 1 year’s time. Buyers ultimately fall into two categories, those that pay off the loan entirely, and those that default.
The Question: What should be the cutoff level where CarMax decides to give potential buyers the loan? What issues might cause you to alter this cutoff-level?
Additional Information: (to be given to you when asked)
- Average cost of a used car to CarMax: $6,000.
- Average price of car sold to customer: $7,000.
- Minimum down payment for all customers: $1,000.
- Average loan defaulter makes three months of payments before defaulting.
Possible Answer:
Although this case looks like a typical “starting a new business/service” case, I did not really use any framework because this case is more of a question of establishing where the break-even marks would lie. I did all the calculations on the average.
Candidate: So what is the average cost of each car and how much does our client CarMax sell them for?
Avg Cost of car = 6000
Avg Price of car = 7000
Avg min down payment = 1000
Term of loan = 12 months
Avg defaulter defaults after making 3 payments
Costs: Car cost, Loan Financing, Operations
Assume financing costs & operating costs for the loan program = 0
Assume 0% interest on loans
Assume X% default:
Total revenue = 1000 + (X/100)*(500*3) + {(100-X)/100}*(500*12)
Total Cost = 6000
Breakeven => 6000 = 1000 + (X/100)*(500*3) + {(1-X)/100}*(500*12)
500,000 = 1500X + 600,000 – 6000X
100,000 = 4500X
X = 22.22%
Therefore, with a 22.22% default rate, minimum score = 77.77%
I looked at the problem in a different way. Correct me if I am wrong.
For the company to break even with Cost price, they need customers who should pay the minimum balance + 10 months of due = 1000+ 10*500 = 6000$. So, the credit rating for one such customer is 10 months/12 months = 83.33%.
In this case the average default rate of 3 months is not a required data.
Its also important to define credit cut off – is it the ratio of good loans to total loans, or full payment months/ total months (12 in this case). I defined the credit cut off as in the second scenario.
Hi Raj, in your way of doing this math, you implies that every bad loan starts from the very beginning rather than from the fourth month (the assumption in this case).
Correct me if I’m wrong: net profit = $1000 for good loan, net loss = $3500 for bad loan, so it needs 3.5 good loan for 1 bad loan in order to break even. Therefore, the credit rate cutoff should be set to: 3.5/(3.5+1) = 78%. Why do you need to round 3.5 into 4 anyway?
Hey George,
Normally while solving case we take round off figure so as ease our calculation part.