Telecom

Ms$.$ Grey works for Umbrella Cellular. She has been conducting a customer acquisition

program whereby Umbrella provides a free smartphone to all new customers. She wants to

know if this is worthwhile. She assumes the following:

A newly acquired customer generates $$100$ in revenues in the first quarter.

Customer revenues grow at a rate of $10\%$ per quarter.

Profit margins are $60\%$ of revenues.

The quarterly retention rate is $50\%.$

Umbrella uses a $14\%$ annual discount rate.

a$.$ What is the lifetime value of a customer?

b$.$ Currently, marketing costs incurred to acquire a customer are $$100$ per acquired

customer. In addition, Umbrella must pay the smartphone manufacturer $$75$ per phone that

it provides to the acquired customer for free. Can Umbrella afford this customer

acquisition program?