You are considering setting up a ﬁrm to produce robots
You are considering setting up a ﬁrm to produce robots
You are considering setting up a ﬁrm to produce robots Corporate FinanceSpring 2016Problem Set 3: Real OptionsDue: Beginning of class, March 31. Inspired by the Arabian Nights, you have had the idea of creating a lock that openswhen a password is said. You have drawn up the blueprints and applied for a patent.Youare 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, andis therefore uncertain. It can be either high or low with equal probability. When thedemand is high expected cash ﬂows a year from today are $66. When the demand islow expected cash ﬂows 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 thelocks will be high or low. The study takes one year to complete. That is, ifyou commission the study you must decide in one year whether to invest. If youinvest then, the cash ﬂows will arrive two years from today. What is the maximumamount you are willing to pay for the study today?2. You are considering setting up a ﬁrm to produce robots which scrub bathtubs clean.Depending on how many homeowners like your robots, the demand for them can behigh, medium, or low with equal probability. The corresponding expected cash ﬂowsare:DemandAnnual expected cash ﬂowHighMediumLow6000600These cash ﬂows 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 cleanersnationwide, which will tell you what the demand for the robots will be. Thesurvey will be comprehensive, and will takes two years to complete. You willdecide whether to invest or not at that time. What is the NPV of the project ifyou commission the survey?(c) Suppose that you can obtain information using a focus group instead. A focusgroup is a study where a small number of users is brought together and askedabout 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 isthat the information from the focus group is less precise than from the survey.1The 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 mediumwith probability 1/3 (and low with probability zero). When the result is negativedemand will be low with probability 2/3 and medium with probability 1/3. Whatis 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. Themodel is still at the design stage. If you decide to buy it, you will have to pay the fullcost, $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. Thecost per mile depends on the fuel eﬃciency of the truck running on gas, which will onlybe known after production and testing, that is, in one year.If the eﬃciency is low, the cost per mile will be $1.5. If the eﬃciency is high, the costper mile will be $0.50. Both possibilities are equally likely. The revenues and the costsof 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 oﬀers you a device that can be attached to thetruck. The device allows the truck to run on either gas or electricity. You willhave to buy the device together with the truck, that is, today. The eﬃciency ofthe truck with respect to electricity is also unknown, and just as before, will beknown once the truck is delivered to you. If you buy the device you can choosebetween the two at the beginning of year 2 (after observing the eﬃciency of thetruck with respect to gas and electricity).â¢ With probability 0.5 the cost of running the truck on gas will be $1.50 permile, and the price of running the truck on electricity will be $1.60 per mile.â¢ With probability 0.5 the cost of running the truck on gas will be $0.50 permile, 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 permile costs are:â¢ With probability 0.5 the cost of running the truck on gas will be $1.50 permile, and the price of running the truck on electricity will be $0.40 per mile.â¢ With probability 0.5 the cost of running the truck on gas will be $0.50 permile, 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

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