Question

Assume that a customer shops at a local grocery store spending an average of ​$300 a​ week, resulting in the retailer earning a ​$40 profit each week from this customer. Assuming the shopper visits the store all 52 weeks of the​ year, calculate the customer lifetime value if this shopper remains loyal over a​ 10-year life-span. Also assume a 9 percent annual interest rate and no initial cost to acquire the customer. This customer yields ​$ per year in profits for this retailer. ​(Round to the nearest​ dollar.)

Answer 1

No of periods = 52 weeks * 10 years = 520 weeks

Revenue per week = $300

Profit per week = $40

interest rate = 9%

Weekly interest rate = 9% / 52 = 0.173%

We can find the customer lifetime value by discounting the revenues for 520 weeks using PVIFA formula

Customer Life time = (1 - (1 + weekly interest rate)^{- no of periods} / weekly interest rate) * Revenue per week

Customer Life time = (1 - (1 + (9% / 52))^-520 / (9% / 52)) * $300

Customer Life time = $102,806.414

Profits per year = Profit per week * No of weeks per year

Profits per year = $40 * 52

Profits per year = $2080