1. Imagine that your company makes wall calendars with photos of cats on them. Each year, your company earns $10 from any calendar that is purchased and it costs $5 to produce each calendar. Unfortunately, due to the abundance of cat photos online, your company is not acquiring new customers for its cat calendars. However, your existing customers appear fairly loyal with 70% of those who bought in a given year returning to purchase another calendar in the next year. Currently, your company plans to offer these cat calendars for another five years and then discontinue the product line. Your company uses an internal discount rate of 10%.
   1. What are gross profits from cat calendars each year per customer?
   2. What is the churn rate for cat calendars each year?
   3. In today's dollars, how much does your company value $1 received in one year?
   4. Calculate the customer lifetime value for customers buying cat calendars.
2. One of your colleagues proposes that retention could be improved from 70% to 75% by including with each calendar a bonus poster of a kitten reading a book. These posters cost $0.25 to produce, each. What are the gross profits under this proposal? What is the CLV under this proposal?