CLV analysis

 
CLV analysis practice question
Suppose Dave is a junior manager of Hollywood Gym at NYC. There are 1000 members to be acquired. Monthly membership fee is $25, monthly variable cost (including retention cost) is $10 and acquisition cost is $30. The membership renewal data for the past several years shows average monthly retention rate is 80%. 
The company executive provides some limited budget for a new marketing campaign. According to Dave’s estimation, it costs $3/month to increase the monthly retention rate by 10% (thus upto 88%) by giving them coupons and gifts.   
Therefore, within the limitation of the marketing budget, he can either A) spend $3 per person per month to increase the retention rate to 88%, or  B) acquire 10% more new members. 
Which would you recommend to Dave between A) and B)? 
1) Use the following formula (annual discount rate=10%). 
???????????? =
((???????????????????????????? −???????????????????????????????? ????????????????) ×(1+???????????????????????????????? ????????????????))/ (1+???????????????????????????????? ???????????????? −???????????????????????????????????? ????????????????)
−???????????????????????????????????????????? ???????????????? 
※ The CLV formula above looks different from that in the lecture slide. Why? 
2) Compute CLV for 1-year horizon (12 months) and compare the result with that in 1). In this case, please use Excel.