1. (20 points) a) Suppose that fixed cost for the production of a medical device are expected to be random...

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1. (20 points) a) Suppose that fixed cost for the production of a medical device are expected to be random between $50,000 and $90,000. Use the Excel function RANDBETWEEN(50000,90000) to generate a random number between these limits. Denote your random number by F and write in the number here F = _______________.

b) Suppose that the product will sell for $3,000 with variable cost of $1,000. The sales manager believes that sales will be normally distributed with an average of 75 annually, with a standard deviation of 15. Use the value for F from part a) for the following questions. What is the breakeven point? BEP = ____________________.

c) What is the probability of a loss? Show all work and relevant calculations.

d) What is the profit/loss when 100 units are sold?

e) How many units must be sold to earn a profit of $50,000?

f) What is the probability of a profit of $50,000 or more?

2. (20 points) Consider the three portfolios given below. Suppose that they are based on a $10,000 investment. Portfolio 1 was developed using the principles discussed in the Black Swan: The Impact of the Highly Improbable. Portfolio 2 was developed Peter Lynch II. Portfolio 3 was developed using Vector Vest.

a) Let p be obtained using the Excel function RAND(). This should give you a random number between 0 and 1. Round it off to 3 decimal places and write is here, p = _______.

Portfolio 1 Payoff 500 4,000 20,000

Probability .70 .20 .10

Portfolio 2 Payoff -2,000 -1,000 1,000 5,000

Probability .05 .10 .45 .40

Portfolio 3 Payoff 1,000 10,000

Probability p 1 − p

b) Find the expected payoff for each portfolio. Based on an expected payoff criterion, which portfolio is best?

c) Find the MAD for each portfolio. Show all calculations

d) Which portfolio do you consider to carry the most risk? Explain why using criteria discussed in Chapter 1&2 of the course textbook.

3. (20 points) a) A company is trying to decide on an alternative to grow their production capacity. Payoffs for A₁ and A₂ (in thousands) are uncertain and ranges have been estimated. Payoffs for A₃ are constant. For each alternative/demand level lower and upper bounds are given below in the form (lower, upper). Use the RANDBETWEEN(a, b) Excel function to obtain a random number representing demand, then write (type) in your random numbers in the table below.

Demand

Low Poor Good Excellent

A₁ (-10, 0) (0, 10) (11, 25) (30, 50)

Alternatives A₂ (-30, -5) (-5, 20) (20, 50) (50, 100)

A₃ 25 25 25 25

Probability .30 .35 .20 .15

Demand

Low Poor Good Excellent

A₁

Alternatives A₂

A₃ 25 25 25 25

Probability .30 .35 .20 .15

Now fill in the following What’s Best Table. Be sure to give a conclusion in terms of an alternative (i.e., A₁, A₂, or A₃).

What’s Best Table

(b) (c) (d) (e) (f)

Expected Standard

Maximax Maximin Maximean Payoff Deviation

A₁

A₂

A₃

Best Alternative

4. (10 points) Suppose that you the director of the Human Resources department of a large Fortune 500 company. Your job is to hire an assistant director for HR. Create a process map for this task. Be sure to include at least one decision point. Neatness counts on this problem. Try to construct the process map using drawing tools either in Word, Excel or some other software.

5. (10 points) Using the internet, Yahoo Finance in particular, find a company whose stock satisfies the following criteria:

a) It has a market of over 100 billion

b) It has a beta of less than 0.90

c) It has a P/E ratio under 20

Discuss the risk associated with your stock compared to other similar stocks in the S&P 500.

6. (20 points) An investor is considering two different asset allocations. Portfolio I invests $25,000 in a real estate trust fund and $5,000 into a Gold ETF. Portfolio II invests $15,000 in the real estate trust fund and $15,000 into a Gold ETF. Over the investment period (one year) the real estate trust fund can either increase by 10%, or decrease by 5% with probabilities .7 and .3 respectively. The Gold ETF will either increase by 5% or decrease by 2% with probability .5 and .5 respectively.

a) Fill in the payoff table below for the investment decision. Note that there should be 4 states to consider.

b) Determine the probabilities. Assume that the performance of the real estate trust fund and gold are independent.

Portfolio I

Portfolio II

Probability

7. (20 Points) A construction company is being sued as the result of an accident suffered by an employee. The plaintiff was working on a balcony railing when it gave way and he suffered serious injuries as a result. In his suit, he charged the company with negligence and asked for an award of $3 million. The company was advised by its lawyers that there is a 70% chance that the construction company will be found negligent. However, even with a negative verdict, there is only a 20% chance that the jury will award the full $2 million. There is a 50% chance that the award will be for only $1 million, a 20% chance it will be for $100,000, and a 10% chance the award will be $10,000. The lawyers also indicated that they could settle before the trial using an arbitrator. The lawyers believe that with an arbitrator there is a 60% that the plaintiff will be awarded $1,000,000, and a 40% chance that the plaintiff will be awarded $500,000. If they go to trial and are found negligent, they could settle for $1.75 million before the jury determines the award. There is also a third possibility of settling without a trial and without an arbitrator. In this alternative the cost to the construction company would be $900,000.

a) Construct a decision tree that represents this situation.

b) Determine what course of action the construction should take in order to minimize its expected cost.

c) Identify the best and worst case for the course of action given in part b)