Question

Management at the? Physicians' Bone and Joint? (PB&J) Clinic is considering whether to purchase a newly developed MRI machine that the manufacturer tells them will provide the basis for better diagnoses of foot and knee problems. The new machine is quite expensive but should last for a number of years. The? clinic's CFO asked an analyst to work up estimates of the NPV of the investment under three different assumptions about the level of demand for its use? (high, medium, and? low). To carry out the? analysis, the CFO assigned a 55 percent probability to the? medium-demand state, a 27 percent probability to the? high-demand state, and the remaining 18 percent to the? low-demand state. After forecasting the demand for the machine based on the? CFO's judgment and past utilization rates for MRI? scans, the analyst made the following NPV? estimates:

Demand State Probability of State NPV Estimate

Low 18% $(290,000)

Medium 55% $196,000

High 27% $406,000

a. What is the expected NPV for the MRI machine based on the above? estimates? How would you interpret the meaning of the expected? NPV? Does this look like a good investment to? you?

b. Assuming that the probability of the? medium-demand state remains 55 percent, calculate the maximum probability you can assign to the? low-demand state and still have an expected NPV of 0 or higher. (Hint?: The sum of the probabilities assigned to all three states must be 100? percent.)

Answer 1

A. The expected NPV should be Probability of the state multiply by the NPV =165,220

B. In order to maximize the low state with constraint of NPV O or positive, it should be ~42% (41.73850575%)

Equation= -2,900X+107,800+182,700-4060X

-2900= -290,000*(X/100)(to be found)
107,800= 55% * 196,000
(406,000)* (45-X)/100= 182,700-4060X-------------------- Probability should be 1=X+0.55+0.45-X

Solving this would get us X.