Since the average initial purchase was $$58,$ the analyst rounded down to $$50$ and used that to

divide the $7953$ new customers into two groups: those whose initial purchase was less than $$50,$

and those whose initial purchase was $$50$ or more. Of the total, there were $4657$ that made an

initial purchase less than $$50$ and $3296$ with an initial purchase of at least $$50.$

Next, for each group he tracked the number of repeat purchases in each of their first $5$ years as

a customer of Tuscan Lifestyles. In any given year, there were some who did not make a repeat

purchase and some who made one or more repeat purchases. Exhibits $1$ and $2$ summarize

these results. In any given frequency table, the first column represents the total number of

purchases made, the second column represents the number of customers who made the

corresponding number of purchases. In interpreting these exhibits, note that $$# orders $5$ years

ago$$ reflects orders placed during customers$$ first year as a customer, $$# orders $4$ years ago$$

reflect orders placed during customers$$ second year as a customer, and that $$# orders last year$$

reflect orders placed during customers$$ fifth year as a customer.

Finally, for each of the two groups the analyst computed the average initial order size $($in dollars$)$

and the average repeat order size for years $1$ through $5.$ This information is summarized in

Exhibit $3.($Hint: All exhibits were produced in SPSS$,$ hence the formats are comparable to

others we$$ve seen in this class.$)$

Armed with this information, Joan wants to know the average lifetime value of a customer for

each group. That is$,$ what is the average lifetime value of a customer whose initial purchase is

less than $$50?$ And what is the average lifetime value of a customer whose initial purchase is

$$50$ or greater? In making these calculations, Joan has instructed you to assume the COGS is

about $58\%$ of the revenue and to use a discount factor of $6\%(3\%$ interest x a risk factor of $2).$

Joan has turned this information over to you and scheduled a meeting to review your analysis

and conclusions. In preparation for this meeting you should determine the average lifetime value

of a customer for each of the two groups. In addition, Joan mentioned several other points that

she would like your thoughts on:

$1.$ What is the LTV over five years for customers who initially spend less than $$50?$

$2.$ What is the LTV over five years for customers who initially spend $$50$ or more?

$3.$ Based on your findings, which group of customers has higher LTV$?$

$4.$ Since when has the higher LTV group of customers become profitable?

$5.$ Should you keep sending catalogs to the lower LTV group of customers? Why or why not?

$6.$ Hand in your CLV chart for each group.