Question

Shannon’s currently boasts a customer base of 1,750 customers that frequent the brewhouse on average twice per month and spend $29 per visit. Shannon ‘s current variable cost of goods sold is 50% of sales. The customer base is growing at the rate of 3% per month with a customer retention rate of 0.73%, based on data collected from its website and an analysis of credit card receipts. It’s current cost of capital for borrowing and investing is about 12% per year. What is Shannon’s approximate CLV for its average customer? Compute your answer to the nearest penny.

Question 2

Assume that Shannon’s decides to move forward with its loyalty / rewards program. Estimates for the cost per customer are $5.28 per month. Average customer margins, before subtracting off the cost of the loyalty / rewards program, are expected to increase to 34.72 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 Q1 (i.e. 12%)? Round your answer to the nearest penny.

Assume that Shannon’s decides to move forward with its loyalty / rewards program. Estimates for the cost per customer are $6.03 per month. Average customer margins, before subtracting off the cost of the loyalty / rewards program, are expected to be 34.36. 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. Compute your answer to the nearest 1/100 of a percent e.g. 50.13%. However, do not include the % symbol.

ALL PARTS PLEASE

Answer 1

First:

CLV can be calculated as

CLV = m ( r / (1 + i - r) )

where

m = Avg gross margin per customer

= 50% of spending

= 50% of $29

= $14.5 per visit.

There are 24 visit in a year = 24 * 14.5 = $348

r = retention rate = 0.73%

i = discount rate = cost of capital = 12%

CLV = 348 ( 0.73 / (1 + 0.12 - 0.73)) = $1,320.6 (Ans is multiplied by 2)

Question 2:

Net present customer lifetime value is given by

= cash flows from the program / ( 1 + ratio) ³

ratio = 12 % / 12 = 1%    (since it is per month)

No. of months for Q₁ = 3

Cash flow from the program = 34.72 - 5.28 = $ 29.44

Substituting value in the formula

= 29.33 / (1 + 0.01) ³

= 28.5741

= $ 28.57

Therefore, Net present customer lifetime value (CLV) is $ 28.57

Last part:

where n is the number of years

M is the cost of retention

GC is a gross contribution

d is the discount rate

Now, if we are to calculate for perpetuity, i.e., infinite series

the formula would be

the sum of infinite geometric progression is a / 1-x

where a is the first term and r is a common ratio

in our case, a = GC * r / (1+d)

x = r / (1+d)

First-term would be : (GC * r / (1+d)) / (1-r / 1+d) = GC * r / (1+d-r)

Similarly, second term would be M / (1+d)^0.5 / (1 - r / (1+d) = M * (1+d)^0.5 / (1 + d -r)

As the given interest rate is 1% per month so annual interest would be 12%

Hence, total = 34.36 * 12 * r / (1.12 - r ) + 6.03 * 12 * 1.12^0.5 / (1.12 - r)

This should equal to 120.

or,

120 = 412.32 r + 76.578 / (1.12 - r)

or,

134.4 - 120 r = 412.32 r + 76.578

or,

532.32 r = 57.82

or,

r = 57.82 / 532.32 = 0.1086

Hence, back-calculation gives retention rate, r = 0.1086 or 0.11 (Ans)