Homework - Sensitivity Analysis & Basic Probability

Homework Questions:

Part A -

1) Questions

a. What is a sensitivity study? Why does one perform them?

b. What are the three types of sensitivity studies that should be performed on which one should perform Sensitivity Studies?

c. In what order should they be conducted? Why?

2) Suppose one has $1000 to invest for 1 year. One can invest in a CD that will make between 4% and 6% (expected value of 5%). One can invest in Stock. If one invests in stock, one can expect the brokerage fee to be between $50 and $100 (expected value of $75). One can expect that the return on the stock will be between -15% and +40% (expected value of +12.5%).

a. Develop an "Input Variable Range Table".

b. What is the "Base" Net Investment Profit (NIP) for each investment?

c. Perform a 1-Sided Sensitivity study for the effect of each variable on the NIP. (Note there are two cases CD case and Stock Case).

d. Develop a Tornado Diagram from this study.

e. For which variables does it make sense to model as an uncertain event? Why?

3) Consider problem 2) above. Suppose you believe that the probability that the market will go up is somewhere between 20% and 30% (expected value is 25%). Assuming expected values for CD rate and brokerage fee,

a. Develop a decision tree model for this.

b. What is the expectation value for the buy stock decision? How does it compare to the CD decision option? Which decision option would you recommend? Why?

c. Perform a probability sensitivity analysis. How is your decision recommendation affected by this result? Why?

4) Clemen 1st and 2nd Edition: Read the "Facilities Investment and Expansion Case Study"

or

Clemen 3rd Edition: Read the Strenlar Case Study (Ch. 4, pp. 171-172) and Strenlar Part II (Ch. 5, pp. 229). a. Create Tornado diagrams for each decision options using the variables suggested to analyze the sensitivity.

b. Based on your analysis, discuss your results and the implications for Fred's decision model. If he were to refine his model, what refinements should he make?

In order to do a good job with the analysis, a number of assumptions must be made. Assume the following:

• $8 million in profits is the present value of all profits to be realized over time.
• $35 million in sales is also the present value of all future sales.
• Fred Wallace's interest rate is 7.5% per year.
• Fred's time frame is 10 years. We will use 10 years to evaluate the job offer and the lump sum.
• If Fred goes to court, he continues to be liable for the $500,000 he owes. The $8 million in profits is net after repaying the $500,000. As indicated in the case, If Fred and PI reach an agreement, then PI repays the debt.
• If Fred accepts the lump sum and options, and if the manufacturing process works, then the options pay 70,000 × $12 at a point 18 months in the future. Thus, the present value of the options is 12×70,000/1.03753= $752,168. That is, we figure three periods at 3.75% per period. The purpose of this is simply to put a value on the options.
• The options are non-transferable. Thus, there is no need to figure out the "market value" of the options.

Facilities Investment and Expansion Case Study

a. Develop a Tornado Diagram for the top 10 variables.

Part B -

1) Questions:

a. Identify and briefly describe the three major types of Probability?

b. Identify and briefly describe the two major types of Random Variable?

c. Identify and briefly describe the two major types of probability distributions?

d. How does the type of distribution determine how one calculates the mean or variance of a distribution or data set? Provide equations.

Some Other Potential Test Questions:

1) What is a Type III Error?

2) What is a Type I Error? A Type II Error?

3) What is a one-way sensitivity study?

4) What is a two-way sensitivity study?

5) What is a tornado diagram? What does it permit you to do?

6) How does one construct a tornado diagram?

7) Given the American Eagle Example done in class, perform a High/Low r analysis.

a. Determine the Base, High and Low r value EV for the purchase decision

b. Does the range in r or the range cause a greater variance in the EV for the purchase decision? Explain.

8) What are the four Axioms of Probability Theory?

9) What are the four Fundamental Theorems?

10) What does it mean for two events to be independent?

11) What does it mean for two events to be mutually exclusive?

12) What is the difference between a Probability Mass Function (PMF) and a Probability Density Function (PDF)?

13) Is a PDF a probability? Explain why or why not.

14) What is a Cumulative Distribution Function? How is it related to the PMF and PDF?

15) What is an "expectation value" of a distribution or data set?

16) What is a "Random Variable" (RV)?

17) How is the Variance of a RV related to the mean of the RV and the expectation value of the square of the RV?

18) How does one calculate the standard deviation for a distribution or data set?

19) What does the mean tell you about a distribution/data set? What does the standard deviation tell you?

20) What is the covariance of two variables? What does it measure?