The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. (Due to budgeting constraints, only one new picture can be undertaken at this time.)She feels that script 1 has a 70 percent chance of earning about $10,000,000 over the long run, but a 30 percent chance of losing $2,000,000. If this movie is successful, then a sequel could also be produced, with an 80 percent chance of earning $5,000,000, but a 20 percent chance of losing $1,000,000. On the other hand, she feels that script 2 has a 60 percent chance of earning $12,000,000, but a 40 percent chance of losing $3,000,000. If successful, its sequel would have a 50 percent chance of earning $8,000,000, but a 50 percent chance of losing $4,000,000. Of course, in either case, if the original movie were a flop, then no sequel would be produced.
What is the expected value for the optimum decision alternative?
A)$15,000,000
B)$9,060,000
C)$8,400,000
D)$7,200,000
E)$6,000,000

Question

Quizplus · Accepted Answer

To find the expected value for each option, we calculate the expected value of each movie and its potential sequel, considering the probabilities of their respective outcomes.For Script 1:- Expected value of the first movie = (0.7 * $10,000,000) + (0.3 * -$2,000,000) = $7,000,000 - $600,000 = $6,400,000.- Expected value of the sequel (only happens if the first movie is successful, hence multiplied by the success probability of the first movie) = 0.7 * [(0.8 * $5,000,000) + (0.2 * -$1,000,000)] = 0.7 * ($4,000,000 - $200,000) = 0.7 * $3,800,000 = $2,660,000.- Total expected value for Script 1 = $6,400,000 + $2,660,000 = $9,060,000.For Script 2:- Expected value of the first movie = (0.6 * $12,000,000) + (0.4 * -$3,000,000) = $7,200,000 - $1,200,000 = $6,000,000.- Expected value of the sequel (only happens if the first movie is successful, hence multiplied by the success probability of the first movie) = 0.6 * [(0.5 * $8,000,000) + (0.5 * -$4,000,000)] = 0.6 * ($4,000,000 - $2,000,000) = 0.6 * $2,000,000 = $1,200,000.- Total expected value for Script 2 = $6,000,000 + $1,200,000 = $7,200,000.Therefore, the expected value for the optimum decision alternative is $9,060,000, which corresponds to choosing Script 1.

The Head of Operations for a Movie Studio Wants to Determine