Question

Assume that a customer shops are a local grocery store spending an average of $400 a week, resulting in the retailer earning a $30 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 7 percent annual interest rate and no initial cost to acquire the customer. The customer yields $ per year in profits for this retailer.

Answer 1

Answer:

a. The customer lifetime value=$10,956.77

b. The customer yields $1,560 per year in profits for this retailer

Explanation:

a.

In order to calculate the customers life-time value, the net present flow is determined from all the future profit cash flows profits. This can be expressed as;

NPV=  R/(1+r)^t

where;

NPV=net present value

R=net cash flow during a certain period

r=annual interest rate

t=period

In our case;

NPV=unknown

R=profits per year=profit per week×number of weeks=$30×52=$1,560

r=7%=7/100=0.07

t=varies from 0 to 10 years

Consider the table below;

Year                   Future cash flows                    Net present value

  1                            1560                                     1560/{(1+0.07)^1}=1,457.94

​   2                            1560                                     1560/{(1+0.07)^2}=1,362.56

  3                            1560                                     1560/{(1+0.07)^3}=1,273.42

  4                            1560                                     1560/{(1+0.07)^4}=1,190.12

  5                            1560                                     1560/{(1+0.07)^5}=1,112.26

  6                           1560                                     1560/{(1+0.07)^6}=1,039.49

  7                            1560                                     1560/{(1+0.07)^7}=971.49

  8                            1560                                     1560/{(1+0.07)^8}=907.93

  9                           1560                                     1560/{(1+0.07)^9}=848.54

  10                          1560                                     1560/{(1+0.07)^10}=793.02

Total NPV= 1,457.94+1,362.56+1,273.42+1,190.12+1,112.26+1,039.49+971.49+907.93+

848.54+793.02=$10,956.77

The customer lifetime value=$10,956.77

b.

The Profit yields per year can be determined using the expression below;

P=p×n

where;

P=annual profits

p=profits per week

n=number of weeks in a year

In our case;

P=unknown

p=$30

n=52 weeks

replacing;

P=30×52=$1,560 per year

The customer yields $1,560 per year in profits for this retailer