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A bank has developed a new type of account called the gold account. Development and advertising costs were 50000. At the start of each of the next four years, 1000 customers are expected to open a gold account and to pay the bank 300 each year that they use it. Of the 1000 customers who open a gold account 500 are expected to close the account after one year and 500 after two years. The bank estimates it will cost 400 per customer to administer the gold account in the customer’s first year reducing to 50 per customer in the second year.
Ignoring the time value of money, what is the lifecycle profit per customer of gold account?
Why the number of customers for year 4 is 2000 instead of 1500 as in the other years.
I calculated the revenue for year 1 to be 1000 multiply by 300 = 300000
Revenue for year 2 1000*300+500*300=450000
Revenue for years 3 and 4 by performing the same calculation as that for year 2.
The costs 1000*400 + 1500*50*3
Development and advertising costs 50000
The profit 975000/5500 = 177.27 profit per customer
Where have I went wrongOver the 4 years there will be 4,000 new customers.
All of them will use the account for 1 year, but only half of them (i.e. 2,000) will use the account for a second year.
The first year loses the bank 300 – 400 = $100 per customer.
The second year makes a profit for the bank of 300 – 50 = $250 per customer.So the total profit over the 4 years is:
(2,000 x $250) – (4,000 x $100) = $100,000.
Less the advertising costs gives 100,000 – 50,000 = $50,000.
So per customer = 50,000 / 4,000 = $12.50
Alternatively you can get the same answer by saying that the profit per customer is
(0.5 x $250) – $100 = $25.The advertising cost per customer is $50,000/4,000 = $12.50
Therefore the profit per customer = $25 – $12.50 = $12.50.
You have forgotten that half of the new customers in year 4 will continue into year 5.
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