I have tried numerous times to solve this and used up all my attempts and still don't have it can you please explain how to solve these four questions from the given info?

Customer Lifetime Value

An important metric that attempts to capture the relationship between customer satisfaction and repeat sales is Customer Lifetime Value (CLV), the present value of the stream of lifetime purchases made by repeat customers. CLV incorporates the joint effects of retention rate (r) and margin per customer ($M) into a single metric. CLV is the present value of the customer relationship developed with that customer. The higher the CLV, the more valuable is a given customer to the firm. The CLV metric requires three pieces of information as inputs for its computation. These three input variables should make sense:

• The dollar contribution per period (can be any defined period, but the period analyzed is usually a month, a quarter, or a year) for retaining a given customer. This contribution is estimated as we have seen before, as the difference between the sales revenue generated by the customer and the variable costs needed to retain that customer.
• The retention rate (r) is the probability that a given customer will be retained for the period analyzed.
• The interest rate used for discounting future cash flows from the customer to their present values.

The formula capturing the relationships between these variables is:

(1) CLV = Customer Lifetime Value $M = Customer cash margin per period r = Customer retention rate per period i = Discount rate per period.

Consider the following example. Consider an internet retailer for shoes and related accessories. The retailer could, for example, be Zappos which is extremely well-known for its exemplary customer service programs and reliance on CLV to monitor the health of this program. The retailer classifies its customers by how much they purchase in a given period, assume the time period is one month. The resulting classification has three categories: Low Yield, Moderate Yield, and High Yield customers. Although the retailer examines the CLVs of all three categories, we illustrate the computations with only the Moderate Yield group. The objective is to determine if it is worthwhile to target the group with an enhanced loyalty program that is estimated to cost approximately $3.50 per customer per month. The retailer currently spends $1.50 per customer per month of retention. This category of customers, on average, spends $75 per month on shoes and accessories. After subtracting off the variable costs of goods (50%), the resulting average contribution is $37.50 per customer per month. Subtracting off the cost of the current loyalty program yields a final margin ($M) of $36.00. The current retention rate is 75%. Management feels that the added cost of the new loyalty program will increase the retention rate to 80% per month. The relevant discount rate is 12% per year or 1% per month. Should the increased investment in the loyalty program be made? The CLV for the current loyalty program is:

(2)

The CLV anticipate based on the revised loyalty program is:

(3)

It, therefore, appears that the increased investment in the customer reward program may be worthwhile. In fact, using a little algebra (or Excel's Goal Seek facility) we can determine a "break-even" retention rate needed to ensure that CLV does not drop below the original CLV of $160. The resulting algebraic equation is:

(4)

This formula, derived from Equation 1, yields the retention rate (r) for a given discount rate (i) and customer contribution ($M) that will achieve a given CLV. For our running example, the retention rate needed to achieve the same original CLV of $138.46 is:

(5)

This means that spending $3.50 per customer for the enhanced loyalty program need only generate an increase in the retention rate of .7644 - .75 = .0144 (1.44%) to yield the same CLV as the old program. Management anticipates that actual retention will go up to r=.8, an increase of .05 substantially exceeding the break-even rate of .7644. Thus, it seems that there exists little risk that the added cost of the new program will end up reducing customer lifetime value rather than increasing it.

So far, our examination of customer lifetime value has focused on how retention rates affect CLV. Most customer loyalty programs are designed to, in part, maintain or improve retention. However, marketers also employ loyalty and rewards programs to encourage customers to buy more of the same or related goods or to upgrade their purchases to higher-priced, higher-margin items. Clearly, these efforts, if successful, will positively impact customer lifetime value. Since such programs are designed to increase the margins generated by customers, the impact on CLV can be projected by increasing the magnitude of $M in Equation (1). For example, assume a customer rewards program that costs $5.00 per customer per month is expected to increase the average margins earned from customers by roughly 5% in addition to increasing retention rate from .75 to .8 per month. Without the program, customer margins average $50 per customer per month. What is the anticipated increase in CLV for the rewards program? Begin by estimating CLV without the rewards program in place (assume i = .01 per month):

(6)

The projected value of $M for the new rewards program is the $50 original $M plus 5% (i.e. $2.50) minus the cost of the program ($5.00): $50.00 + $2.50 - $5.00 = $47.50. CLV for the new program, therefore, is:

(7)

It, therefore, appears that the proposed rewards program will be worthwhile, but only if the retention rate increases as well as $M. If retention rate remains the same (i.e. r = .75), CLV actually declines to $182.69. You should do the calculations to verify this. An interesting question is how much must $M increase to achieve the same projected CLV of $226.19 if retention rate remains r = .75? Solving equation (1) for $M yields:

(8)

This means that sales revenue (and margins) will have to increase by $8.81 ($58.81 - $50.00) to offset no change in the customer retention rate. The decision to move forward with the program may be a tough one. Management will need to evaluate the risks associated with the proposed rewards program's ability to increase sales and/or retention rates.

Another interesting question is what effect will a constant growth in margins per customer have on CLV? Ideally, loyalty and rewards programs will yield continuing increases in the average margins per customer over time. The effect of anticipated constant growth in customer margins on CLV can be estimated with a simple modification to Equation (1) which adds the growth rate to the retention rate in the denominator of the equation:

(9)

For example, in Equation (7) if we assume the rewards program will have the further benefit of increasing customer margins by 1% per month (g = .01), the net effect on CLV is:

(10)

Clearly, a constant growth rate in average customer margins, even as small as 1% per period, can have a significant effect on CLV.

It's Your Turn. Show Us What You Have Learned.

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

Q1:Shannon's brewery currently boasts a customer base of 1,750 customers that frequent the brewhouse on average twice per month and spend$26per visit. Shannon 's current variable cost of goods sold is 50% of sales. The customer retention rate per month is0.82% ,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.

Q2:Assume that Shannon's decides to move forward with its loyalty/rewards program. Estimates for the cost per customer are$3.2per month. Average customer margins, before subtracting off the cost of the loyalty/rewards program, are expected to be$36per customer per month with a boost in retention to82%per month. What is the resulting CLV if the annual interest rate for discounting cash flows remains the same as in Q1? Compute your answer to the nearest dollar.

Q3:Assume that Shannon's current CLV=$142.00. Based on the change in CLV you computed in the last question, should Shannon's implement the rewards program?

Group of answer choices

Yes -- introduce rewards program.

No -- do not introduce rewards program

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

Q4:Assume that Shannon's decides to move forward with its loyalty/rewards program. Estimates for the cost per customer is$5.55per month. Average customer margins,beforesubtracting off the cost of the loyalty/rewards program, are expected to be34.38. 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 is1%per month. (Note: This problem assumes that you employ some algebra to solve the CLV formula forr.) Express your answer to four decimal places e.g. .1234. Do not express in percent form.