Economics of Risk and Uncertainty Applied Problems

Please, complete the following 3 applied problems in a Word or Excel document. Show all your calculations and explain your results. Submit your assignment in the drop box by using the Assignment Submission button.

1. A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump-sum of $10mln, or in parts, where $5.5mln can be provided in year 1, and another $5.5mln can be provided in year 2. Assuming the opportunity interest rate is 6%, what is the present value of the second alternative? Which of the two alternatives should be chosen and why? How would your decision change if the opportunity interest rate was 12%? Please, show all your calculations.

2. Volkswagen is considering opening an Assembly Plant in Chattanooga, Tennessee, for the production of its 2012 Passat, tailored for the US market. The CEO of the company is considering two potential options for the size of the plant: one is a large size with a projected annual production of 150,000 cars, and the other one is a smaller size plant, which is cheaper to build, but can only produce up to 80,000 cars per year. Depending on the expected level of demand for these cars in the US, Volkswagen has to decide which option is more profitable. The discount rate is 6% and for simplicity purposes, the CEO is only evaluating a two-year horizon. The initial factory setup cost, the expected demand scenarios, profit, and probabilities are shows in the below table. Calculate the Net Present Value in each of the two options. Which option should the CEO choose and why? Please, show all your calculations.

Factory Size

Factory setup cost

($m)

Demand

Year 1 Profit ($m)

Probability

Year 2 Profit ($m)

Probability

Large

100

Low

Medium

High

20

80

100

0.4

0.4

0.2

60

90

150

0.3

0.5

0.2

Small

70

Low

Medium

High

30

50

70

0.4

0.4

0.2

70

80

90

0.3

0.5

0.

3. An angel investor is considering investing in one of two start-up businesses and is evaluating the expected returns along with the risk of each option in order to choose the better alternative.

· Business 1 is an innovative protein energy drink, which has ENPV of $100,000 with a standard deviation of $40,000.

· Business 2 is a unique chicken wings dipping sauce with an ENPV of $60,000 and a standard deviation of $25,000.

a) Apply the coefficient-of-variation decision criterion to these alternatives to find out which is preferred by the angel investor, assuming that he/she is risk-averse.

b) Apply the maximin criterion, assuming that the worst outcome in Business 1 is to lose $5,000, whereas the worst outcome in Business 2 is to make only $5,000 in profit.

c) If you were the angel investor, what is your certainty equivalent for these two projects? Are you risk-averse, risk-neutral, or risk-lover?

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