problem 1 (5 points) The Museum of "El Encierro" (Pamplona, Spain) offers a membership which costs $80 a year. Members to the Museum have free access to all exhibitions, receive invitations for special events, and get a 15% discount in all purchases made in the museum gift store. The average margin for the membership program is 75%. There are currently 5,000 active members and the average retention rate is 80% (which has been stable over the last few years).

(a) What is the value of the current base of members? (Assume an infinite horizon and a 10% discount rate.) (1 point)
(b) Carlos Mondragon, director of marketing, has proposed a one-time expenditure of $60,000 to run an ad campaign aimed to acquire new members. How many members would they need to acquire to make this investment pay off (breakeven) in the long term? (1 point)
(c) Carlos also wants to find out the maximum amount of money they should spend to increase the retention rate of current customers from 80% to 85%. (1 point)
(d) Do you have any other suggestions of how the museum could leverage the value of its customer base? What type of behavioral data would you recommend Carlos to collect? (2 point)