Question

At Corner Bakery, the average customer in the "Young Mothers" segment brings in $101 in annual margin to the firm. In turn, Corner Bakery spends $24 per customer each year on retention communications. Acquiring a customer in this category costs the Corner Bakery an average of $64. Corner Bakery's retention rate for these customers is 83%. If the company maintains a discount rate of 12%, calculate customer lifetime value for 1 "Young Mothers" customer. Rounding: penny. Remember, the answer may be negative.

SHOW EXACT WORK HOW YOU DID EVERY STEP!

Answer 1

Solution:

Customer lifetime value for 1 customer = 232

Calculations:

Earnings from each customer yearly = 101 - 24

= 77

Average earnings from each customer yearly

= 77

Earning next year from that customer= 77* 0.83

= 63.91

This is because the probability of retention of that customer is 0.83

This earning is of next year so it has to be discounted by 12% every year this will happen

So we derive a geometric series

77 + 770.83/1.12 + 77(0.83/1.12)2 + ..........

THIS WILL BE AN INFINITE SERIES

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

here, a= 77

r = 0.83 / 1.12

r = 0.74

Sum = 77 / (1 - 0.74)

= 296

Total earning from a customer during lifetime = 296

Cost of acquiring = 64

Customer lifetime value for 1 customer = 296 - 64 = 232