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You are presented with two investment opportunities.

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1.;You are presented with two investment opportunities.;I. The cost is $30,000 to be paid today. In each of the coming three years, you will obtain $19,000;with 60% chance and $4,000 with 40% chance, beginning from a year from today.;II. The cost is $30,000 to be paid today. With probability p, you will obtain $10,000 in each of the;coming 4 years, and with probability (1-p), you will obtain $10,000 in each of the coming 5 years.;a) If the market rate is 10%, and if your choice depends only on the expected value of either option;(you do not base your decision on the riskiness of either option),what should p be for you to be;indifferent between two options?;b) Suppose that p=0.2 and you pick option II. How much would you be willing to pay now to get paid;exactly 5 years? (That is, how much would you pay to avoid the uncertainty?);2.;Uber is a ridesharing service headquartered in San Francisco, which operates in multiple;international cities. Currently Uber has $20 million and has the following pattern of potential cash flow;with its planned investment in a new fleet of cars, minivans, and pickups to be used by its customers.;If the company can borrow and lend at 10%, should it invest on a big fleet or small fleet today?;(Answer by drawing and solving a decision tree. Identify each decision and chance node properly);Here are the specifics of each option;Big fleet: costs $200 million today. The investment results in success with probability 0.60 and in;failure with probability 0.40. If the system is successful, it will produce $120 million per year for the;following 5 years beginning a year from today, and $20 million per year otherwise.;Small Fleet: costs $20 million today. The investment results in success with probability 0.60 and in;failure with probability 0.40. If the system is successful, it will produce $10 million per year for the;following 5 years ($0 otherwise).;One year after the investment (after the first cash flow is realized and uncertainty about;success/failure is resolved), Uber may choose to expand and invest $320 million on a bigger fleet;whose projected cash flow is as described above.;3.;Remember that, for this problem, we assumed no;time value of money. Assume also that you are not required by law to buy car insurance. That is, buying car insurance is a;purely economic decision.;You are considering buying car insurance for the coming year. Whether or not you buy insurance, you;have the following probability distribution over the car accident damages.;with 90% chance you will have no accident;with 7% chance you will have a small accident with $300 worth of damage;with 3% chance, you will have a big accident with $13,000 worth of damage.;The terms of the insurance: Your deductible is $500.;Extension: Assume that if you do not buy insurance and have a big accident, there is a a 60% chance;that your father will pay the damages for you (that is, your payment is $0).;What is the risk of being self-insured (measured by standard deviation,?)?;Additional Requirements;Level of Detail: Show all work

 

Paper#15367 | Written in 18-Jul-2015

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