Hale\'s TV Productions is considering producing a pilot for a comedy series in t
ID: 2748039 • Letter: H
Question
Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $200,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows:
The probabilities for the states of nature are P(S1) = 0.20, P(S2) = 0.30, and P(S3) = 0.50. For a consulting fee of $50,000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant:
Choose the correct decision tree for this problem.
Graph (ii)
What is the recommended decision if the agency opinion is not used? What is the expected value? Enter your answer in thousands of dollars.
Recommended decision Produce
Expected Value = $ thousands.
What is the expected value of perfect information? Enter your answer in thousands of dollars.
EVPI = $ thousands.
What is Hale's optimal decision strategy assuming the agency's information is used?
If Favorable Produce
If Unfavorable Sell
What is the expected value of the agency's information? Round your answer to two decimal places. Enter your answer in thousands of dollars.
EVSI = $ thousands.
Is the agency's information worth the $50,000 fee? What is the maximum that Hale should be willing to pay for the information?
Decision Yes
Hale should pay no more than $ thousands. Round your answer to two decimal places. Enter your answer in thousands of dollars.
Explanation / Answer
There are two Decision nodes. At the first stage/level the choice is about either to enagage agency or no agency and second stage/level is to produce pilot or sell the rights to competitor for $200,000. In case the decision is to produce pilot then there are three possibilities: 1 rejection (loss of $100,000) or 2. sell the rights for 1 year (profit of $50,000) or 3. sell the rights for 2years (profit of $450,000).
Outcomes of agency recommendations may be favourable or unfavourable, each one followed by stage2 decision making about conducting pilot or selling the rights.
Correct decision tree is (ii)
The expected value in the absence of option of agency is maximum of the two options : $220,000
Selling rights to competitor for $200,000 or Do Pilot for expected value $220,000 (-100*.2 + 50*.3 + 450*.5)
In order to evaluate the options with respect to agency and the expected value of perfect information, we are required to rework the probabilities of states in the light of agency's recommendations based on baye's theorem of conditional probabilities.
At node (6) expected value is $305,000 (-100*.06+50*.28+450*.66) whereas value at node(7) is $200,000, therefore value of $305,000 passed to node (3) with the choice of d1
At node (8) expected value is $45 (-100*.47+50*.36+450*.17) whereas value of node (9) is $200,000, therefore value of $200,000 passed to node (4) with the choice of d2
Therefore expected gain at node(2) is $270,350 (305000*.67+200000*.33) As the agency charges $50,000
Hence the expected value at node(2) is $220,350
In case perfect information is known with respect to states, the maximum expected value is $325,000 [(200*.2+200*.3+450*.5),000]
Therefore the EVPI =$105,000 (325000-220000)
Without using agency, the expected value calculated is $220,000
whereas using agency the expected value ( without fee to the agency) is calculated as $270,350
Therefore expected value of agency is $50,350
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