The RBC case describes two methods for computing the lifetime value of a customer. One method (Markov Chain and Transition matrices) takes into account the expected likelihood that a customer holding a particular product portfolio will migrate to another portfolio or leave the bank in the future.

Assume that RBC has only two products: Car Loan (CL) and Credit Card (CC). The annual profitability for each of the two products is (-$100) (i.e., $100 loss) for CL and +$1000 for CC.

RBC has made the following observation for customers in the 25-30 year segment:

• If they have a car loan at the end of a given year, the probability of also acquiring a credit card during the following year is 50%
• The probability of losing even this one product during the following year is 20%
• The probability that the customer retains only the car loan during the following year is 20%
• The probability that the customer drops the car loan but acquires a credit card during the following year is 10%

Similar observations can be made for individuals who begin the year with only a credit card, both products, or neither product. These observations are summarized in the following matrix of probabilities.

Probabilities for year t+1 product mix for all possible combinations of product mixes for year t.

		Product mix in year t+1
Product mix in year t		CL		CC		CL+CC		None
CL		0.2		0.1		0.5		0.2
CC		0.1		0.5		0.2		0.2
CL+CC		0.1		0.1		0.7		0.1
None		0		0		0		1

Answer the following questions using a 8% discount rate:

1. Consider a customer who has only a credit card in year t. What is
   1. The expected profit generated by this customer in year t+1?
   2. The present value of expected profits from this customer for both years combined?
2. Consider a customer who has both a car loan and credit card in time t. What is
   1. The expected profit generated by this customer in year t+1?
   2. The present value of expected profits from this customer for both years combined?
3. Discuss how these results will be useful for you to design a market strategy. Be specific in your suggestions and provide concrete suggestions.