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

Answer 2

The retailer earns a profit of $1669.2 in per year from this consumer in profits. As a part of sales the annual sales include $20800. This will be taxable in the hands of the retailer.

The retailer employed zero capital to acquire such customer and hence no initial costs of pickup will be required by the retailer to attract this number of sales by the consumers.

• Consumer purchases groceries of 400 dollars each week and has not missed a single week during the lifetime span of 10 years of him visiting the store resulting in sales of $20800 each year and overall sales of $208000.

• It is given that the retailer earns $30 per week from such sales and hence the profits made by the retailer will be $1560.

$30 *52= 1560$

and the overall profits of the retailer over the life of 10 years will be

$1560*10=15600$

• 16692 dollars profits in 10 years will be earned by the retailer after adding 7% interest earned over the amount invested.

Hence, the retailer earns a profit of $1669 each year by such sales considering a 7% interest received.

To know more about profit from sales, refer to the link below.

https://brainly.com/question/1913058