Here are the final numerical results for each section of the exam. You can use them to check your work if you do the exam for practice. If you have trouble with the problems, or don't get the answers shown here, stop by during office hours or make and appointment and we can go over them.
NPV of A = $10.5 million; NPV of B = $15.1 million. Plan B is better.
Net EV of remediating without testing: $6 million. Net EV of doing the test and then choosing whether or not to remediate: $8 million. It's better to buy the test.
(a) PV of costs: B = $100 million; S = $101.6 million; C = $86.6 million.
(b) Expected NPV: B = $25.4 million; S = $48.8 million; C = $38.8 million. Policy S is best. Even though it has the lowest probability of success, if it does succeed it produces much larger annual benefits than B and has much lower annual costs than C.
Option A: C0 = $88.9k; C1 = $133.3k; saving = $11.1k.
Option B: Expected utility of A = 316; Expected utility of B = 338. Plan B is better. It has a CE of $114,373.
Q = 45; P = $55; profit = 0.
Q = 28; P = $122; annual profit = $3,136.
EV = -$1,321. The firm should not undertake the project.
(a) Annual CS during patent = $1,568; Annual CS after patent = $6,272; Total PV of CS from patents = $22,672. Expected CS = 0.4*$22,672 = $9,069.
(b) Firm's new EV with the prize = $679. It would now be willing to undertake the project. For efficiency, it was OK to calculate the expected net value of either the CS or SS produced by the test. For the former: $9,069-0.4*($5,000) = $7,069; for the latter: $9,069 + $680 - 0.4*($5,000) = $7,748. Note that the expected cost of the prize is only $2,000 because the government does not pay the $5,000 unless the FDA approves the test.