Planet Fitness, Inc. is a franchisor and operator of fitnesscenters in 50 states, the District of Columbia, Puerto Rico,Canada, the Dominican Republic, Panama and Mexico. The company iswell-known for its $10 basic membership fee, although customers canalso sign up for a more expensive $22.99 PF Black Card membershipthat comes with additional perks, including additional in-storeamenities such as hydro-massage beds and affinity partnerships fordiscounts and promotions. According to the company’s Securities andExchange Commission 10K filings, as of December 31, 2021, PlanetFitness had 15.2 million members. The company reports that about60% of its customers are PF Black Card members and the remaining40% hold basic membership. Planet Fitness’s average weighted costof capital (i.e. its discount rate) is estimated to be about 7%,according to Guru Focus. Assume that the company has a customerretention rate of 87% and incurs a variable cost of $4.50 percustomer with basic membership and $7.20 per PF Black Cardcustomer.

a) What is the customer lifetime value (CLV) of each customerwith a PF Black Card membership? (3 points)

b) What is the CLV of each customer with a basic membership? (3points)

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 ifthe monthly retention rate were 81 percent? (2 points)

e) What would be the CLV of a customer with basic membership ifthe monthly retention rate were 95 percent? (2 points)

f) Taken together what do the results in (b), (d), and (e) tellyou about the impact of customer retention on customer lifetimevalue?