Planet Fitness, Inc, is a franchisor and operator of fitnexs centers in 50 states, the District of Columbia, Puerto Rico, Canada, the Dominican Republic, Panama and Mexico. The company is well-known for its $10 basic membership fee, although customers can also sign up for a more expensive 522.99 PF Black Card membership that comes with additional perks, including additional in-store amenities such as hydro-massage beds and affinity partnerships for discounts and promotions. According to the company's Securities and Exchange Commission 10K filings, as of December 31, 2021. Planet Fitness had 15.2 million members. The company reports that about 60% of its customers are PF Black Card members and the remaining 40% hold basic membership. Planet Fitness's average weighted cost of eapital (i.e. its discount rate) is estimated to be about 7%, according to Giurn Facus. Assume that the company has a customer retention rate of 87% and incurs a variable cost of $4.50 per customer with basic membership and $7.20 per PF Black Card customer. a) What is the customer lifetime value (CLV) of each customer with a PF Black Card membership? (3) points) b) What is the Cl. V of each customer with a basic membership' (3 points) c) What was the CLV of the company's total customer portfolio (i.e. all basic and PF Black members combined) as at December 30,2021 ? (4 points) d) What would be the CLV of a customer with basic membership if the monthly retention rate were 8 I percent? (2 points) e) What would be the CLV of a customer with basic membership if the monthly retention rate were 95 percent? (2 points) f) Taken together what do the results in (b), (d), and (e) tell you about the impact of customer retention on customer lifetime value? (1 point)