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
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
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 |
Questions:
- What are the expected value and the standard deviation of the NPV from a customer? In running the simulation, use a sufficient number of trials to estimate the expected NPV from a customer within $1 with 95% confidence (i.e., make sure that the length of 95% confidence interval does not exceed $2).
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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