International Pictures is trying to decide how to distribute its new movie ‘Claws’. ‘Claws’ is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie’s controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a ‘limited first-run release’ at a few selected theaters, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for ‘Claws’:

PROFITS (Millions of $)
Level of
success Probability Limited General
release distribution
Smash .3 22 12
Modest .4 9 8
Bomb .3 –10 –2

International can run sneak previews of ‘Claws’ to get a better idea of the movies’ ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at $1m.

What is the opportunity loss for a General Distribution for a Smash level of success?

What would the optimal action be for International before running the sneak preview?

1) Run a limited release with an expected payoff of $7.20m

2) Run a limited release with an expected payoff of $6.20m

3) Run a general distribution with an expected payoff of $7.20m

4)Run a general distribution with an expected payoff of $6.20m

What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies’ level of success?

1) $9.6 m
2) $7.2 m
3) $6.2 m
4) $2.4 m

What would be the joint probability for a ‘bomb success’ and excellent preview given that in the past, it was found that 40% of all bomb successes were rated excellent?

What is the posterior probability of a bomb given the sneak preview indicates good?

What is the maximum amount that should be paid for the sneak preview [i.e. what would be the expected value of sample information (EVSI)]?

1) $1.04 million
2) $2.58 million
3) $7.20 million
4) $8.24 million

To calculate the opportunity loss for a General Distribution for a Smash level of success, we need to compare the potential profits for a General Distribution with the highest possible profits for a Smash level of success, which is $22 million.

Opportunity loss for a General Distribution = Highest possible profits for Smash - Profits for General Distribution
= $22 million - $12 million
= $10 million

Therefore, the opportunity loss for a General Distribution for a Smash level of success is $10 million.

Before running the sneak preview, we need to calculate the expected payoffs for both a limited release and a general distribution.

The expected payoff for a limited release is calculated by multiplying the probability of each level of success with their respective profits and summing them up.

Expected payoff for limited release = (Probability of Smash * Profit for Limited Release) + (Probability of Modest * Profit for Limited Release) + (Probability of Bomb * Profit for Limited Release)
= (.3 * 9) + (.4 * 9) + (.3 * -10)
= $2.7 + $3.6 - $3
= $3.3 million

The expected payoff for a general distribution is calculated in the same way.

Expected payoff for general distribution = (Probability of Smash * Profit for General Distribution) + (Probability of Modest * Profit for General Distribution) + (Probability of Bomb * Profit for General Distribution)
= (.3 * 12) + (.4 * 8) + (.3 * -2)
= $3.6 + $3.2 - $0.6
= $6.2 million

The optimal action for International before running the sneak preview would be to run a general distribution with an expected payoff of $6.2 million. So the correct option would be 4) Run a general distribution with an expected payoff of $6.20m.

The maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movie's level of success is the difference between the expected payoffs for a limited release and a general distribution.

Maximum amount to pay for reliable forecast = Expected payoff for limited release - Expected payoff for general distribution
= $3.3 million - $6.2 million
= -$2.9 million

Since the maximum amount to pay for a reliable forecast is negative, it means that International would not be prepared to pay anything for an absolutely reliable forecast.

The joint probability for a 'bomb success' and excellent preview can be calculated using conditional probability.

Joint probability = Probability of bomb success * Probability of excellent preview given bomb success
= 0.3 * 0.4
= 0.12

Therefore, the joint probability for a 'bomb success' and excellent preview is 0.12.

To calculate the posterior probability of a bomb given the sneak preview indicates good, we need to use Bayes' theorem.

Posterior probability of a bomb given good preview = (Probability of bomb * Probability of good preview given bomb) / Probability of good preview
= (0.3 * 0.6) / (0.1 * 0.1 + 0.4 * 0.25 + 0.3 * 0.6)
= 0.18 / (0.01 + 0.1 + 0.18)
≈ 0.18 / 0.29
≈ 0.621

Therefore, the posterior probability of a bomb given the sneak preview indicates good is approximately 0.621.

To calculate the expected value of sample information (EVSI), we need to compare the expected payoffs with and without the sneak preview.

Expected payoff without sneak preview = (Probability of limited release * Expected payoff for limited release) + (Probability of general distribution * Expected payoff for general distribution)
= (0.5 * 3.3) + (0.5 * 6.2)
= 1.65 + 3.1
= $4.75 million

Expected payoff with sneak preview = (Probability of excellent preview * Probability of bomb * Profit for General Distribution) + (Probability of excellent preview * Probability of modest success * Profit for General Distribution) + (Probability of excellent preview * Probability of smash success * Profit for General Distribution) +
(Probability of good preview * Probability of bomb * Profit for General Distribution) + (Probability of good preview * Probability of modest success * Profit for General Distribution) + (Probability of good preview * Probability of smash success * Profit for General Distribution)

EVSI = Expected payoff with sneak preview - Expected payoff without sneak preview
= 7.2 - 4.75
= $2.45 million

Therefore, the maximum amount that should be paid for the sneak preview (i.e., the expected value of sample information) is $2.45 million. So the correct option would be 2) $2.58 million.