Reference no: EM132346583

Case Study: Risk and Uncertainty

Address the following case study relating to developing a new automobile.

Note: There is a video of a hand-worked problems to accompany section3 but not the other sections because the questions follow from the reading.

Please submit your work as a single Word document. When I request calculations, you can write them by hand and incorporate a photograph into the document or you can type up the calculations in the document. Similarly, you can create any tables by hand, in Word, or other ways, but your tables should be clear. The document should be approximately 2-4 pages (counting each side of the paper as a page) in length. Please indicate in some way which part of the document responds to each question. The assignment will be graded based on correctness, effort, and presentation.

You are an executive for an automobile manufacturer. You are trying to decide whether to invest the company's money into developing a new SUV (SUV), developing a new hybrid (Hybrid), developing both jointly (Joint), or buying back some bonds (Bonds). The profitability of each development depends upon how high gasoline prices are when the vehicles are released. The analysts at your firm determine that there is a 25% chance of high gas prices, a 50% chance of medium gas prices, and a 25% chance of low gas prices. The payoffs (in billions) to each project in each of the three events are presented in the table below.

Section 1 - Introduction (pages 625-632)

Describe a source of risk associated with developing a new vehicle.

Describe a source of uncertainty associated with developing a new vehicle.

Calculate the expected value of each project in the table above as well as the standard deviation and coefficient of variation.

Section 2 - Decisions Under Risk (pages 632-637)
As much as possible, rank the four projects under each decision rule (you can assume that the assumptions of each rule are met):
(a) Expected value rule
(b) Mean-variance rules
(c) Coefficient of variation rule

Section 3 - Expected Utility (pages 637-645)
a) Suppose you have the utility function:

U(Π) = 10Π

What is your expected utility from pursuing each project? Which project should you choose? Does this utility function suggest that you are risk averse, risk loving, or risk neutral?

Suppose you instead have the utility function:

U(Π) = √(20 + Π)

What is your expected utility from pursuing each project? Which project should you choose? Does this utility function suggest that you are risk averse, risk loving, or risk neutral? (Hint: Convert the square root to a fractional polynomial to take the derivative. And note that fractional polynomials are always positive.)

Section 4 - Decisions Under Uncertainty (pages 645-649)

Assume that your firm no longer has any faith in the probabilities of each level of gas prices and this problem becomes a problem about uncertainty. As much as possible, rank the four projects under each decision rule:

a) Maximax criterion
b) Maximin criterion
c) Minimax regret criterion
d) Equal probability criterion

Attachment:- Risk and Uncertainty Case Study.rar