As before, suppose the firm only offers the subscription plan consisting of NBC, CBS and ESPN. Suppose also that it prices this plan at the rate you computed in question 5. Using other existing field data on consumers who have already adopted the service, you know that an existing customer has a 70% chance of cancelling her service in any given month when you charge the price computed in question 5. Assume that those who cancel their service will never re-activate (i.e., cancellation of service is a terminal state). Your marketing team has determined that the size of your total potential customer market is 500,000 individuals, out of which 150,000 individuals are already existing customers. From accounting, you also know that the cost of providing service to a customer (existing or prospective) is $8 per month1. Moreover, the cost of contacting a prospective customer with an offer to sign up for the service is roughly $5. This "initial marketing contact" cost does not apply to existing customers (i.e., it is free to contact existing customers as this can be automated with software). Finally, the firm's monthly borrowing cost of capital used to discount future cash flows from a customer is 5%. For a visualization, refer to Figure 1 below.

Build a LTV model and calculate the net present value of a prospective and an existing customer respectively. A prospective customer is contacted once per month until they get converted. Assume that once customers sign up, they all have the same probability of renewing their service (i.e., converted subscribers have homogeneous tastes for the service). Show your work. [Hint: use the following LTV model:

new customer formula as NC = -cost + Prob(no response | NC)(NC) + Prob(subscribe | NC)( +C)

existing customer formula as C = Prob(terminate |C)(0)+Prob(renew|C)(m+C)

promo sent to prospective customer cost $5. Unsure how many of these will subscribe.

subscriber marginal cost = $8

28% of subscribers renew

72% of subscribers cancel