Hi, I don't know how to calculate the NPV if future cash flow is uncertain.

Corporate Finance Spring 2016 Problem Set 3: Real Options Due: Beginning of class, March 3 1. Inspired by the Arabian Nights, you have had the idea of creating a lock that opens when a password is said. You have drawn up the blueprints and applied for a patent.You are considering setting up a factory to produce these locks. The cost of the project is $30 today. The demand for the locks depends on how much people like your idea, and is therefore uncertain. It can be either high or low with equal probability. When the demand is high expected cash ows a year from today are $66. When the demand is low expected cash ows a year from today are $34. The discount rate is 10%. (a) What is the NPV of the project? (b) Suppose you can commission a study that tells you whether the demand for the locks will be high or low. The study takes one year to complete. That is, if you commission the study you must decide in one year whether to invest. If you invest then, the cash ows will arrive two years from today. What is the maximum amount you are willing to pay for the study today? 2. You are considering setting up a rm to produce robots which scrub bathtubs clean. Depending on how many homeowners like your robots, the demand for them can be high, medium, or low with equal probability. The corresponding expected cash ows are: Demand Annual expected cash ow High Medium Low 600 0 -600 These cash ows will begin one year after the investment is made and continue forever. The cost of the project is $300 today. The discount rate is 50% (yes, thats not a typo). (a) What is the NPV of the project? (b) Suppose you can commission a survey of homeowners and professional cleaners nationwide, which will tell you what the demand for the robots will be. The survey will be comprehensive, and will takes two years to complete. You will decide whether to invest or not at that time. What is the NPV of the project if you commission the survey? (c) Suppose that you can obtain information using a focus group instead. A focus group is a study where a small number of users is brought together and asked about their reaction to the robots. This will take only one year to complete (again, you will decide whether or not to invest at that time). The catch is that the information from the focus group is less precise than from the survey. 1 The result of the study will be either positive or negative with equal probability. When the result is positive demand will be high with probability 2/3 and medium with probability 1/3 (and low with probability zero). When the result is negative demand will be low with probability 2/3 and medium with probability 1/3. What is the NPV of the project if you commission the focus group? (d) Which type of study, if any, should you commission? 3. You are considering buying a new model of truck for your shipping operation. The model is still at the design stage. If you decide to buy it, you will have to pay the full cost, $40,000, today, and the truck will be delivered to you in one year. The truck will be run for one year, for 50,000 miles. Expected revenue is $2/mile. The cost per mile depends on the fuel eciency of the truck running on gas, which will only be known after production and testing, that is, in one year. If the eciency is low, the cost per mile will be $1.5. If the eciency is high, the cost per mile will be $0.50. Both possibilities are equally likely. The revenues and the costs of fuel in the second year accrue at the end of that year. The discount rate is 10%. (a) What is the NPV of buying the truck? (b) The manufacturer of the truck oers you a device that can be attached to the truck. The device allows the truck to run on either gas or electricity. You will have to buy the device together with the truck, that is, today. The eciency of the truck with respect to electricity is also unknown, and just as before, will be known once the truck is delivered to you. If you buy the device you can choose between the two at the beginning of year 2 (after observing the eciency of the truck with respect to gas and electricity). With probability 0.5 the cost of running the truck on gas will be $1.50 per mile, and the price of running the truck on electricity will be $1.60 per mile. With probability 0.5 the cost of running the truck on gas will be $0.50 per mile, and the price of running the truck on electricity will be $0.40 per mile. What is the most you should pay for the device? (c) Suppose now instead that the per-mile costs are: With probability 0.5 the cost of running the truck on gas will be $1.50 per mile, and the price of running the truck on electricity will be $0.40 per mile. With probability 0.5 the cost of running the truck on gas will be $0.50 per mile, and the price of running the truck on electricity will be $1.60 per mile. How much would you be willing to pay for the device now? 2