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# Developing a Forecasting Model

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A regional hospital is considering the expansion of the ER 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 5 and 6 percent per year due to inﬂation (inﬂation rate can change
each year to a value between 5 and 6 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, the hospital estimates that the
mean volume of visits to the ER will increase by 2,000 visits per year during the next 5 years.
This increase will have to be absorbed by the ER expansion, so the mean of the predicted
volume for the expansion during the ﬁrst year of operations is 2,000 visits; in year two it's 4,000
visits, and so on. They also estimate that these annual number of visits are normally distributed
with a standard deviation of 250 visits. You may assume that a particular year's volume is
independent of other years' number of visits. The hospital discounts ﬁiture cash flows at 10
percent per year.

Analyze this problem using @RISK 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 third 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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Hi, please see the attached Excel sheet. The cell formulas in blue use @Risk inputs, and the cells in ...

#### Solution Summary

In this solution, we show how to construct a forecasting model and use it to determine whether a hospital expansion will be profitable.

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