Question

QUESTION 2 Assume that Shannon’s decides to move forward with its loyalty / rewards program. Estimates for the cost per customer are $5.81 per month. Average customer margins, before subtracting off the cost of the loyalty / rewards program, are expected to increase to 33.91 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.

Answer 1

where n is number of years

M is cost of retention

GC is gross contribution

d is discount rate

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

the formula would be

sum of infite geometric progreesion is a/1-x

where a is first term and and r is 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 given interest rate is 1% per month so annula interest would be 12%

Hence, total=33.37*12*r/(1.12-r)+5.96*12*1.120.5/(1.12-r)

This should equal to 120

Hence, back calculation gives retention rate, r = 0.1128