References to answer : Expected Value

https://youtu.be/amGLWN4hmY0

1. Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.6 probability that the textbook will be successful. If successful, a profit of $300,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $52,000 will occur. Before making the decision to accept or reject the manuscript, the editor is considering sending the manuscript out for review. A review process provides either a favorable (F) or unfavorable (U) evaluation of the manuscript. The past experiences with the review process suggest that probabilities P(F)=0.7 and P(U)=0.3 apply. Lets1=the textbook is successful, ands2=the textbook is unsuccessful. The editor's initial probabilities ofs1ands2will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows:

P(s1|F)=0.8 P(s1|U)=0.35

P(s2|F)=0.2 P(s2|U)=0.65

a. Construct a decision tree assuming the company will first make the decision of whether to send the manuscript out for review and then make the decision to accept or reject the manuscript.

b. Analyze the decision tree to determine the optimal decision strategy for the publishing company.

c. If the manuscript review costs $10000, what is your recommendation? (Hint: Compare it to the expected value of the research study)

d. What is the expected value of perfect information? What does this EVPI suggest for the company? (Hint: This only concerns the don't do branch)

2. A real estate investor can purchase a piece of land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table:

Decision alternatives	States of Nature
Rezoning approved	Rezoning not approved
S1	S2
Purchase, d1	110	-65
Do not purchase, d2	0	0

a. If the probability that the rezoning will be approved is 0.35, what decision is recommended? What is the expected profit? (4 marks)

b. The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows:

LetH_High resistance to rezoning

L_Low resistance to rezoning

P(H) = 0.6 P(S1 | H) = 0.25 P(S2 | H) = 0.75

P (L) = 0.4 P(S1 | L) = 0.85 P(S2 | L) = 0.15

What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision? (8 marks)

c. If the option will cost the investor an additional $8,000, should the investor purchase the option? Why or why not? What is the maximum value that the investor should be willing to pay for the option?