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Decision Analysis, Finance Basics

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2 Questions

QUESTION #1
LAPTOP SELECTION

Jonna is in market to buy a new laptop. Six different machines are under consideration. All laptops are essentially the same, but they vary in price and reliability. The least expensive model is also the least reliable, the most expensive is the most reliable, and the others are in between. The laptops are described as follows:

A Price $1260 Expected number of days in the shop per year = 5.5
B Price $1750 Expected number of days in the shop per year = 2
C Price $860 Expected number of days in the shop per year = 8
D Price $1575 Expected number of days in the shop per year = 3.5
E Price $1525 Expected number of days in the shop per year = 2.5
F Price $1245 Expected number of days in the shop per year = 4



The laptop will be an important part of Jonna’s livelihood for the next two years. (After two years, the laptop will have a negligible salvage value.) In fact, Jonna can foresee that there will be specific losses if the laptop is in the shop for repairs. The magnitude of the losses are uncertain but are estimated to be approximately $175 per day that the laptop is down.

a. Can you give any advice to Jonna without doing any calculations? (Maximum four line answer, No calculation, No graph required)
b. Use the information given to determine weights KP and KR, where R stands for ‘reliability’ and P stands for ‘price’.
c. Calculate overall utilities for the laptops, What do you conclude?
d. What consideration other than losses might be important in determining the trade off rate between cost and reliability? List at least three of them.
(Please show all the steps)

Question 2:

QUESTION 2
HELP – THE BETTOR (Calculation required 4 decimal places, Objective: Maximization of wealth)

A utility function is called Linear-plus-exponential when it contains both linear and exponential terms.

Brigg, a bettor, has a choice between the following two alternatives:
(For simplicity it is assumed that cost of each alternative is negligible, equivalent to zero)

Alternative # A 5% chances to WIN $11,900
95% chances to WIN $1200

Alternative # B 90% chances to WIN $2100
10% chances to LOSE $2150


If Brigg has $3,000, having utility function U(x) = ln(x) – 0.0005x, where x is total wealth which Alternative he should choose A or B?

If Brigg has $6,000, having utility function U(x) = ln(x) – 0.0005x, where x is total wealth which Alternative he should choose A or B?

If Brigg has $12,000, having utility function U(x) = 0.0015x -12.48e-x/13420, where x is total wealth which Alternative he should choose A or B?

If bettor is not risk neutral and having utility function U(x) = 1.75 - e-x/13420 what will be your recommendation, Alternative A or B. Calculate Risk premium for Alternative A and B independently? Which Alternative will give high certainty value to Brigg? Assume Brigg is risk neutral, what will be your recommendation among the alternatives?

NOTE :
(MUST calculate at least 4 decimal places otherwise you may not choose correct alternative and marks will be deducted.) (It is advisable to use Excel)

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