At Corner Bakery, the average customer in the \"Young Mothers\" segment brings i

Question

At Corner Bakery, the average customer in the "Young Mothers" segment brings in $90 in annual margin to the firm. In turn, Corner Bakery spends $21 per customer each year on retention communications. Acquiring a customer in this category costs the Corner Bakery an average of $68. Corner Bakery's retention rate for these customers is 77%. If the company maintains a discount rate of 10%, calculate customer lifetime value for 1 "Young Mothers" customer. Rounding: penny. Remember, the answer may be negative.

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THE SPECIFIC SUBJECT OF THIS QUESTION IS MARKETING METRICS.

Explanation / Answer

earnings from each customer yearly= 90-21=69

taverage earnings from each customer yearly= 69

earning next year from that customer= 69* 0.77=53.13

this is because the probability of retention of that customer is 0.77

this earning is of next year so it has to be discounted by 10%

every year this will happen

so we derieve a geometric series

69 + 69*0.77/1.10 + 69*(0.77/1.10)2 + ..........

THIS WILL BE AN INFINITE SERIES

sum of infinite geometric series= a/(1-r)

here, a= 69

r= 0.77/1.1=0.7

sum= 69/(1- 0.7)= 230

total earning from a customer during lifetime = 230

cost of acquiring = 68

customer lifetime value for 1 customer= 230-68= 162

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