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Background
For this case, we are going back in time where there was no differentiation in the credit card industry: credit cards almost all were offered with a one-size-fits-all 19.8% APR, and a $20 Annual Membership Fee (AMF). In this setting, Citibank, as the market leader, decided to lower the rate they were offering (to both existing customers as well as new) to 16%. We are trying to decide how Capital One should react to increasing market pressure.

Step #1 - Conceptual Discussion
After the interviewer has explained the market and Citibank’s decision, s/he would ask something like, “What are some of the factors that would influence Capital One’s decision of whether or not to follow Citibank, and lower our rate to 16%?” or “What are some of the pros and cons of following Citibank to a lower rate?”
Good candidates would observe that:
1. If we don’t drop our rate,we may lose some customers
2. If we do drop our rate, we may lose money
3. We may increase the balance customers are willing to carry by offering a
lower rate
Since the question is about what Capital One should do on its existing base, impacts to new acquisitions are not really relevant here.
#3 is the most necessary concept for people to understand, as it feeds into the entire case

Step #2 - Translating conceptual discussion to analytics
Depending on the seniority of the candidate, they may either be provided with this information or be asked what information they want. Good candidates will see what information they need to decide on a course of action.
Avg Balance = $1000 (new information) Revenues:

Revenue
APR: 19%
AMF: 20

Expenses:
Variable Cost-Cost of Funds: 5%
Variable Cost-Defaults/losses: 4%
Fixed Cost-Operations Cost: 40

Profit: $80

Good candidates will recognize that the implication of #3 from the conceptual section is that the impact is not simply $30 (3% of $1000). They should move to calculating a break even to understand how much average balance has to increase for this to be a profitable proposition.

Good candidates will also point out that as average balance goes up, some but not all parts of revenue go up and some but not all parts of cost go up. The candidate may make some simplifying assumptions about the impacts on each element of the P&L as long as the candidate is explicit about what the assumptions are. For instance, the candidate could assume no impact on per account operations costs (even though we might get more calls on a bigger balance) and proportional impact on losses (even though the people who respond to the price drop might have a different risk profile).
One way to structure the equation is to call break-even average balance “x” and set up this
equation:
80 = (.16x + 20) – (.04x + .05x + 40) 80 = .07x – 20
x = 1428.57 OR
An alternate (simpler) approach is:
100 = (.16 - .04 - .05)x
x = 1428.57

Step #3 (Translating the analysis into decision making)
The interviewer will then ask the candidate if a 43% increase in average balance is likely. Good candidates will take a clear point of view and have a reason why. In our experience, more candidates have been able to articulate a good logic for the answer “no”, though the key here is the logic, not the specific answer. The interviewer would then ask what that means the candidate would do. Assuming the candidate said they thought 43% was unrealistic, a good candidate should say at this stage that they wouldn’t change pricing.

Step #4
The interviewer will now provide new information - if Capital One continues to price people at 19%, we will lose 20% of our customers. However, if we drop them down to 16%, we will retain them all. What should Capital One do?
Good candidates will recognize they need to redo the work from step 2 after having revised their “starting point” for how much we are making.
New starting point:
A. .8(80) = 64 (since we would make money on 20% less customers)

Revised break even given the new starting point
B. 64=.07x–20 x = 1200
Again the interviewer will ask the candidate if a 20% increase in average balance is likely and again the candidate should have some logic for their answer. There is no need to change the answer from step 3 to step 4.