We are all aware of the fierce competition by mobile phone service companies to get our business. For example, AT&T is always trying to attract Verizon’s customers, and vice versa. Some even give away...

We are all aware of the fierce competition by mobile phone service companies to get our business. For example, AT&T is always trying to attract Verizon’s customers, and vice versa. Some even give away prizes to entice us to sign up for a guaranteed length of time. This example is based on one such offer. We assume that a mobile provider named Syncit is willing to give a customer a free laptop computer, at a cost of $300 to Syncit, if the customer signs up for a guaranteed two years of service. During that time, the cost of service to the customer is a constant $60 per month, or $720 annually. After two years, we assume the cost of service increases by 2% annually. We assume that in any year after the guaranteed two years, the probability is 0.7 that the customer will stay with Syncit. This probability is the retention rate. We also assume that if a customer has switched to another mobile service, there is always a probability of 0.1 that the customer will (without any free laptop offer) willingly rejoin Syncit. The company wants to see whether this offer makes financial sense in terms of NPV, using a 10% discount rate. It also wants to see how the NPV varies with the retention rate. Simulate a 15-year time horizon, both with and without the free offer, to estimate the difference. (For the situation without the free offer, assume the customer has probability 0.5 of signing up with Syncit during year 1.)