## Interview Question

Interview*(Student Candidate)* Richmond, VA

`Capital One`

Answer## CASE: Cross-selling Credit Insurance to Cardholders direct

mail: .50, 1% response rate, avg balance $1000, 5% claim insurance, etc. Profitable? How make more profitable? What if response rate doubled but claims doubled? Make chart of profit curve, what does it mean if..., etc.

## Interview Answer

12 Answers

Hi Sir, Can you confirm if below is the correct answer. I believe its always unprofitable. Assume 100 direct mail offers were sent for card insurance, 1% response rate means, 1 person bought credit insurance Revenue = 1% of avg balance = (1/100)*1000 = 10$ Cost = Insurance claim Cost + Mailing Cost = (Response Count* claim rate * Avg Bal) + (No. of mails sent * Cost per mail) (1* (5/100)*1000) + (100 * 0.5) = 50 + 50 = 100 $ Selling credit insurance in this case is unprofitable even without the mkt cost. For other questions if we assume, response rate = x%, claim rate = y% with the assumption, 100 offers were sent for credit insurance Revenue = x*(1/100)*1000 = 10x Insurance Cost = x*(y/100)*1000 = 10xy Mkt Cost = 100 * 0.5 = 50 Profit = 10x-10xy-50 Assumption is that y% claim rate means, of x people who take the offer, y% of those x, file for claim, which means company has to cover their avg bal of 1000 for people who filed the claim, and hence is a loss for the company. At this point its a loss to sell credit insurance. Let me know if i am doing anything incorrectly.

Great the way you laid it out, very thorough and clearly organizing your thoughts. Remember to think out loud/explain your thinking as you write during the case. Yes, something is incorrect, very small but key, changes the whole answer: you are assuming everything is in the same time unit. When you calculate revenue to be $10, you should realize right away that would be a MONTHLY amount, while claims et all would be annual. Helps to know that credit cards in the US regularly try to entice customers to add little $5-10/month services to their bills, whether insurance, credit report monitoring, etc so that $10 couldn't possibly be yearly, ie insurance less than 0.90/month.

Thanks for your response and guidance. I knew the revenue is monthly, but i thought claim rate is also monthly and hence calculated profit for each credit insurance sold per month. In light of your clarification Profit per card insurance per year = (10*12)-50-50 = 20$ per year If we chose to calculate per month, we will need to consider monthly claim rate as (5/12) and also amortize the marketing expense over next 12 month. Profit per card insurance per month = 10-(50/12)-(50/12)= (20/12)$ per month The profitability equation (per card per year) = 120x-10xy-50 For calculating any of the break even rates (x or y assuming 1 is known), 120x-10xy-50 = 0. For graph, P = 120x-10xy-50 Let me know if my analysis/answer is accurate and up to the mark. Thanks a lot for all your guidance.

Aspirant, why did you take the revenue as 1% of the average balance? I think the average balance is the revenue. Whereas the response rate is 1%. Assuming 100 people are sent the mail: Revenue : (Response rate * 1000) = 1 * 1000 = 1000 Cost : (100 * Mailing cost) + (Response rate * claim rate * 1000) = (100 * 0.5) + (1*(5/100)*1000) = 50 + 50 = 100 Profit = Revenue - Cost = 1000 - 100 = 900 (This is for 100 mails sent) So the profit per mail sent = 900/100 = $9 Now, assuming the response rate is x% (instead of 1% as given) Revenue = 1000x Cost = (100*0.5) + (x*(5/100)*1000) = 50 + 50x Profit = 1000x - (50+50x) = 950x - 50 Profit per person = (950x - 50)/100 = 9.5x - 0.5 To make it more profitable, try to increase response rate x. Now if response rate is doubled and claims doubled, Profit = (Revenue) - (Cost) =(2000) - (50 + 100) = 1850 So profit per person = 1850/100 = $18.5 Now to make a chart of profit curve, i.e profit vs response rate, we use Profit per person = 9.5x - 0.5 plot : y= 9.5x - 0.5 Meaning : To break even, we need 9.5x - 0.5 = 0 i.e x = 0.05 (approximately) So we need a response rate of atleast 0.05% to be profitable (or 1 in 2000 people to respond)

Looks like I left out the price of the insurance: customers would pay 1% of monthly balance for insurance.

@Aspirant 2: You are using response rate as a number and at the same time using claim rate correctly as 5/100. use Response rate as 1/100 wherever applicable. Revenue should be $10 Cost = 50.50 Profit(Loss) = 10-50.50 Profit (Loss) per mail sent = (10-50.50)/100

Why isn't churn rate mentioned in here? Isn't that an important factor? Or were those number given to you without probing? Thank you! =)

@ ghachla: The response rate is 1% that is 1 out of 100. I assumed 100 people are sent the mail. Hence the response rate is 1. As for the claim rate, the people who don't respond can't make claims. So out of the people who respond, the claim rate is 5% (i.e 1 person responds in 100 and out of that 1, 0.05 make the claim); Or to make it more clearer, if we assume 10000 people are sent the mail, 100 respond (because of the 1% response rate) and 5 out of the 100 make claims (because of the 5% claim rate).

@A2: I understand what you are saying. the words were just misleading. What about the insurance rate? That's revenue to the bank, right? "By intrvw candidate: Looks like I left out the price of the insurance: customers would pay 1% of monthly balance for insurance." = monthly avg balance x 10 x # of people who made claims? and then convert to annual numbers or monthly as the case may be? How do you suggest to answer the profit: annual numbers or monthly numbers?

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This discussion was helpful, I have been thinking about this problem for a bit now. Only one thing, shouldnt equation for market cost be 50/x since if the response rate goes up, the cost per customer will go down as a function of the response rate.

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see cross selling case on CO's website