# A regional medical center is considering the expansion

March 13, 2016

Question
A regional medical center is considering the expansion of the emergency room to accommodate an expected increase in patient loads. Fixed (up-front) costs are equally likely to be any value between 1 and 1.5 million \$. For the first year of the project, average variable cost per visit and revenue per visit are expected to be \$55 and \$165 respectively. The chief financial officer estimates that variable costs will increase between 4 and 5 percent per year due to inflation (inflation rate can change each year to a value between 4 and 5 percent. All values within this range are equally likely). However, because of growing regulatory pressure and managed care contracting, average revenue per visit is not expected to increase for the next five years.

Using a forecasting model to study the trend in demand for the ER room, the medical center estimates that the volume of emergency room activity will increase by 1,800 per year, at least during the next 5 years. This increase will have to be absorbed by the ER expansion, so the forecasted mean volume for the expansion during the first year of operations is 1,800 visits, 3,600 visits during the second year, and so on. They also estimate that the forecasting error for each year’s forecast is normally distributed with standard deviation of 200 visits. You may assume that the forecasting errors are independent. The hospital discounts future cash flows at 12 percent per year.

Analyze this problem using Monte Carlo simulation with 5,000 replications and answer the following questions:

a)What is the probability that the ER expansion generates positive net discounted profits at the end of the fourth year of operations?

b)Produce a graph showing the distribution of net discounted profits at the end of the fifth year of operations.

c)Give a 95% confidence interval for the net discounted profits at the end of the fifth year of operations.

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