Consider again the Sport Hotel example and Example 9.1. Suppose that if the franchise is accepted the value of the hotel is not $8 million but instead $8.75. Everything else, including first year expenses, is the same as shown in the example. Incorporating the real option, what probability of the franchise being granted would represent a "fair investment?" (that is, a probability such that any higher value would create a positive expected value) % Place your answer in percentage form with at least 2 decimal places. For example, and answer of fifteen point four three percent would be entered 15.43. EXAMPLE 9. 1 Let's start with a simplified but practical example of the type of decisions that corporations often face in the presence of uncertainty. Your firm is deciding whether to build a hotel next to a stadium that is trying to obtain a franchise for a major sports team. Your firm wants to be the "official hotel" of the stadium. The sports league will announce their decision in exactly one year. If the franchise is granted, the games will begin two years later (a total of three years from now). To be the official hotel, the hotel must be finished when the games begin. It takes three years to build the hotel. Therefore, you must make the decision today. Let's assume the following costs to getting the hotel opened. First Year: Purchase of the Right to be the Official Hotel $50,000 Purchase of Land $750,000 Purchases of Plans and Permits $200,000 SUBTOTAL $1,000,000 Second Year: Construction of the Building Shell $2,000,000 Third Year: Construction of Building Interior and Furnishings $2,000,000 TOTAL $5,000,000 Now let's assume for simplicity that if the sports franchise is successful the hotel would be a terrific investment and would be worth $8,000,000 when it opened after the third year. However, if the sports franchise is denied, then the hotel will struggle to attract guests and would only be worth $2,000,000. You have been asked to perform a financial analysis of whether the project makes sense. To start the analysis, assume that there is a 50% chance that the franchise will be received whereby the hotel will be worth $8,000,000 and a 50% chance that the hotel will only be worth $2,000,000. Using these probabilities of the franchise's success, the expected value of the benefits of owning the hotel will be halfway between the hotel's value in the good state of nature and the hotel's value in the bad state of nature, or $5,000,000. Note that the two probabilities need not be set equal to each other, but they must sum to 100%. In order to make the problem as easy as possible to follow let's assume that interest rates are 0%. This assumption removes the time value of money so that we can ignore having to discount the cash flows and can simply directly compare cash flows at different points in time. Finally, and again to make the problem simple to follow, let's ignore all other risks such as possible increases in building costs or falling revenues. Since we are ignoring discounting, if there is a 50% chance of the hotel being successful, the expected benefits of building the hotel ($5,000,000) appear to exactly match the costs of building the hotel ($5,000,000). In other words, the project would have a zero expected value. In this case investors should be willing to invest as long as the probability that the franchise is offered is more than 50%