Question

3. Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one). Suppose that a customer at a restaurant spends, on average, R per visit and comes F times each year (for example, if a customer purchases once every two years, then F = 2 = 0.5). The restaurant realizes a gross profit margin of M (expressed as a fraction) on the aver- age bill for food and drinks. In addition, the fraction of customers defecting (not returning) each year is D. a. Develop a mathematical model to compute the gross profit during a customer's lifetime in doing business with the restaurant (this is often called the economic value of a customer. b. If the average purchase per visit is $50, the gross profit margin is 0.4 (that is, 40%), customers visit

Answer 1

Answer a= The economic value of the customer is given as=

average spending = R

Number of visits= F times per year

Profit Margin= M

Profit = average spending * number of visits per year* profit margin= R*F*M

Number of defecting customer each year= D

The average lifetime of a customer = 1/D years

the average nondiscounted gross profit during a customer’s lifetime =(R*F*M)*(1/D)

Answer b= In the question

R=$50

F=6

M= 0.4

D= 0.3

The lifetime value of the customer = 50*6*0.4/0.3

The lifetime value of the customer =$400

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