Young screenwriter Carl has just finished his first script. It has action, drama, and humor, and he thinks it will be a blockbuster. He takes the script to every motion picture studio in town and tries to sell it but to no avail. Finally, ACME studio offers to buy the script for either $30,000 today or 1.75 percent of the movie’s profits. There are two decisions the studio have to make. The first is to decide if the script is good or bad; the second is to decide if the movie is good or bad. First, there is a 90 percent chance that the script is bad. If it is bad, the studio does nothing more and throws the script out. If the script is good, it will shoot the movie. After the movie is shot, the studio will review it, and there is a 60 percent chance that the movie is bad. If the movie is bad, the movie will not be promoted and will not make a profit. If the movie is good, the studio will promote it heavily; the average profit for this type of movie is $55 million.

Assume Carl is risk neutral (i.e. not risk averse or risk loving), which one should Carl pick?

Question

Young screenwriter Carl has just finished his first script. It has action, drama, and humor, and he thinks it will be a blockbuster. He takes the script to every motion picture studio in town and tries to sell it but to no avail. Finally, ACME studio offers to buy the script for either $30,000 today or 1.75 percent of the movie’s profits. There are two decisions the studio have to make. The first is to decide if the script is good or bad; the second is to decide if the movie is good or bad. First, there is a 90 percent chance that the script is bad. If it is bad, the studio does nothing more and throws the script out. If the script is good, it will shoot the movie. After the movie is shot, the studio will review it, and there is a 60 percent chance that the movie is bad. If the movie is bad, the movie will not be promoted and will not make a profit. If the movie is good, the studio will promote it heavily; the average profit for this type of movie is $55 million.

Assume Carl is risk neutral (i.e. not risk averse or risk loving), which one should Carl pick?

BlackTom AI · Accepted Answer

We’re asked to evaluate Carl’s two payment options given the earnings structure of the studio project, assuming risk neutrality.
First, restating the scenario in brief: There’s a 90% chance the script is bad, in which case ACME does nothing and pays nothing. If the script is good (10% chance), the movie is made. After production, 60% of such movies are bad, and 40% are good. If the movie is good, the average profit is $55 million. Carl can either take $30,000 today or receive 1.75% of the movie’s profits if the movie is profitable.
Option A: Take $30,000 today. This is a certain payoff with no risk, equal to $30,000.
Option B: Take 1.75% of the movie’s profits. To compute the expected value of this option, multiply the probability of a profitable outcome by 1.75% of the profit whenever that outcome occurs.
Step 1: Determine when a profit occurs. The script must be good (10% chance), and then the movie must be good (40% chance given a good script), resulting in an overall probability of a profitable movie of 0.10 × 0.40 = 0.04, i.e., 4%.
Step 2: Compute the profit amount if profitable. If the movie is good, the average profit is $55,000,000. 1.75% of $55,000,000 equals 0.0175 × 55,000,000 = $962,500.
Step 3: Compute the expected value for the 1.75% option. EV = (probability of profit) × (1.75% of profit) = 0.04 × $962,500 = $38,500.
Now compare the two options:
- Option A yields a sure $30,000.
- Option B yields an expected value of $38,500, based on the probability of a profitable movie and the percent of profits offered.
Thus, in terms of expected monetary value, Option B (1.75% of profits) has a higher EV than taking $30,000 today.
A few potential subtle points to keep in mind:
- If the movie ends up being bad, there is no profit, and the 1.75% share yields $0 for that outcome, which is already reflected in the 4% overall chance of a profitable movie.
- The 60% chance of a bad movie after a good script reduces the overall probability of profit to 4%, so even though the per-success payoff is large, the chance of hitting that payoff is relatively small.
- If Carl were risk-averse, he might favor the sure $30,000, but since the problem states he is risk neutral, we compare expected values rather than risk-adjusted values.
- The calculation assumes the “average profit” of $55 million is the relevant figure for the EV calculation. If the distribution around that average is highly skewed, that could affect risk considerations, but not the given risk-neutral EV comparison here.
- If there were any ambiguity about when profits are realized or how profits are split, that could change the EV, but under the stated assumptions, the 1.75% option yields $962,500 on profitable outcomes and 0 otherwise, leading to $38,500 EV.

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