#8 (Calculating the expected NPV of a project) Management at the Doctors Bone and Joint Clinic is considering whether to purchase a newly developed MRI machine that they feel will provide the basis for better diagnoses of foot and knee problems. The new machine is quite expensive and will be used for a number of years. The clinics 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). The CFO assigned a 50 percent probability to the medium-demand state, a 30 percent probability to the high state, and the remaining 20 percent to the low state. After making forecasts of the demand for the machine based on the CFOs judgment and past utilization rates for MRI scans, the following NPV estimates were made:

DEMAND STATE PROBABILITY OF STATE NPV ESTIMATE

LOW 20% $(300,000)

MEDIUM 50% $200,000

HIGH 30% $400,000

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 50 percent, calculate the maximum probability you can assign to the low-demand state and still have an expected NPV of zero or higher. (Hint: The sum of the probabilities assigned to all three states must be 100 percent.) How does knowing the maximum probability of realizing the low-demand state help you assess the project (no calculations required)?