Problem $7-21$ Decision Trees

Young screenwriter Carl Draper 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 studios offers to buy the script for either $$10,000$ today or $2$ percent of the movie's profits. There are two decisions the studio will have to make. The first is to decide if the script is good or bad; the second is to decide if the movie is good or bad. First, there is a $85$ percent chance that the script is bad. If it is bad, the studio does nothing more and throws the script out. If the script is good, it will shoot the movie. After the movie is shot, the studio will review it$,$ and there is a $55$ percent chance that the movie is bad. If the movie is bad, the movie will not be promoted and will not turn a profit. If the movie is good, the studio will promote heavily; the average profit for this type of movie is $$14\mathrm{.}9$ million. Carl rejects the $$10,000$ and says he wants the $2$ percent of profits. What is value of accepting $2$ percent of the profits? $($Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.)$

Payment to screenwriter

Which payment option should Carl accept?

Upfront offer

Percentage of the profit