question archive As the manager of a credit card services at Bank of Hanover (BOH), you are aware that the average profitability of a credit card customer grows with the number of years they have used the credit card
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As the manager of a credit card services at Bank of Hanover (BOH), you are aware that the average profitability of a credit card customer grows with the number of years they have used the credit card. Two probabilistic factors affect actual profitability. The mean profitability function is given in the table below, which has been gathered from data on BOH customers. The actual profit in a given year follows a normal distribution, with a standard deviation equal to 20% of the mean profit.
In addition, there is a probability that a customer will continue to use the card during year t. This probability is sometimes called the retention rate. For instance, an 85% retention rate means that, during any year, there is a 15% chance that the customer will cancel their credit card. Assume that if a customer cancels during year t, then the cancellation occurs at the end of the year, and BOH still gets the profit from year t but no more profits after year t. The current retention rate has been estimated at 85%. BOH uses a discount rate of 10% to calculate net present values.
Year |
Mean Profit |
1 |
40 |
2 |
66 |
3 |
72 |
4 |
79 |
5 |
87 |
6 |
92 |
7 |
96 |
8 |
99 |
9 |
103 |
10 |
106 |
11 |
111 |
12 |
116 |
13 |
120 |
14 |
124 |
15 |
130 |
16 |
137 |
17 |
142 |
18 |
148 |
19 |
155 |
20 |
161 |
What are the expected value and the standard deviation of the NPV from a customer?
b. What is the probability that the NPV for a given customer will exceed $100?
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