$(1)CLV=$$$M[\frac{1}{1+i-r}]$

CLV $=$ Customer Lifetime Value

$$M=$ Customer cash margin per period

$r=$ Customer retention rate per period

Shannon's Brewery continues to grow its customer base but is also concerned with enhancing loyalty and

associated repeat business from its existing customer base. Shannon realizes that it is generally cheaper to maintain

a cadre of loyal customers than it is to recruit new customers. To this end, Shannon wants to experiment with a

loyalty$/$rewards program that encourages more frequent visits to the brewhouse along with added consumption per

visit. The rewards program, to be implemented next month, consists of an "app" along with in$-$store kiosks that will

better track customer visits and purchases. The app also will offer rewards based on past purchases per visit and

number of visits. Rewards will be in the form of free products and discounts on select products. Email promotion,

limited direct mail, social media, and web promotions on its own website and Facebook page will be extensively

employed to create buzz and disseminate promotion information.

Question $1$

$10$ pts

Q$1$: Shannon's Brewery currently boasts a customer base of $1,750$ customers that frequent the

brewhouse on average twice per month and spend $$28$ per visit. Shannon's current variable cost

of goods sold is $50\%$ of sales. The customer retention rate per month is $0\mathrm{.}85,$ based on data

collected from its website and an analysis of credit card receipts. Its current cost of capital for

borrowing and investing is about $12\%$ per year or $1\%$ per month. What is Shannon's approximate

CLV for its average customer? Compute your answer to the nearest penny.

Q$2$: Assume that Shannon's decides to move forward with its loyalty$/$rewards program.

Estimates for the cost per customer are $$3\mathrm{.}2$ per month. Average customer margins, before

subtracting off the cost of the loyalty$/$rewards program, are expected to be $$36$ per customer

per month with a boost in retention to $82\%$ per month. What is the resulting CLV if the annual

interest rate for discounting cash flows remains the same as in Q$1?$ Compute your answer to the

nearest dollar.

Q$3$: Assume that Shannon's current CLV$=$$$142\mathrm{.}00.$ Based on the change in CLV you computed in

the last question, should Shannon's implement the rewards program?

Yes $--$ introduce rewards program.

No $--$ do not introduce rewards program

There is insufficient data to answer "yes" or $"$no$."$

Q$4$: Assume that Shannon's decides to move forward with its loyalty$/$rewards program.

Estimates for the cost per customer is $$6\mathrm{.}44$ per month. Average customer margins, before

subtracting off the cost of the loyalty$/$rewards program, are expected to be $33\mathrm{.}87.$ Assuming that

Shannon's wishes to obtain a minimum CLV of $$120,$ what is the required retention rate that

must be achieved? Assume that the interest rate is $1\%$ per month. $($Note: This problem assumes

that you employ some algebra to solve the CLV formula for $r.)$ Express your answer to four

decimal places e$.$g$.\mathrm{.}1234.$ Do not express in percent form.