After years of working in management consulting in LONDON, BOB earned a good fortune of money and would like to resign from his job and instead open a gourmet Indian restaurant. Cooking has always been BOBs passion, and he believes the growing LONDON market would truly appreciate fine ITALIAN cuisine. The extensive travel associated with BOBs consulting job has given him the opportunity to study gourmet ITALIAN restaurants in many cities in ENGLAND, and whenever possible, he talked to the managers to better understand the profitability of their operations.

BOB has developed a pro-forma monthly cash flow analysis, which is shown in Exhibit 1 below.

Unfortunately, just about every number in this analysis is uncertain. BOB wants to build a Monte Carlo simulation model to better understand the risks of this venture.

From his conversations with restaurant owners in other cities, BOB estimates probability distributions for the variables as follows:

* Number of customers per month: This is very hard to predict. BOB is optimistic about the demand but recognizes the uncertainty and assigns a lognormal distribution with a mean of 2,400 and a standard deviation of 800 (when the value of the variable is large, which is the case here, it is usually acceptable to treat the variable as continuous, i.e., ignoring the integer constraint).

* Average sales per customer: BOBs prices will be set according to his estimate of what customers will pay. At this point, he is uncertain about the average sales per customer and assigns a normal distribution with a mean of $25.00 per customer and a standard deviation of $4.00 (we can truncate the normal distribution at zero i.e., only keeping the non-negative part but this only has minimal effect on the simulation result because the mean is a large positive relative of the standard deviation. So, for simplicity, no need to truncate the normal distribution here).

* Direct cost of sales: This includes the costs of food served to customers as well as other incidental expenses (e.g., laundry). BOB assigns a normal distribution with a mean of $7.00 per customer and a standard deviation of $1.00 (following the same reasoning above, no need to truncate the normal distribution).

* Payroll costs. BOB assigns a triangular distribution with a most likely value of $24,000 per month and a minimum value of $19,000 and a maximum of $32,000.

Other fixed costs: BOB has identified a location in LONDON and estimates that rent, utilities, and insurance for the location will cost about $8,000 dollars per month. He is quite confident about this and does not feel the need to model it as uncertain.

Some of these uncertainties are correlated. Specifically:

* Food with more expensive ingredients will typically be sold at higher prices. BOB estimates that the average sales per customer and direct costs of sales per customer are positively correlated with a correlation of 0.6.

* The payroll costs will tend to vary with the number of customers: if you have more customers you need more staff members to serve them. BOB estimates that the number of customers and payroll expenses are positively correlated with a correlation of 0.4.

* Build a simulation model of this venture to answer the following questions. Run at least 1,000 trials to answer each question.

d) The most important assumption in BOB's model is the assumption about the mean number of customers: he has assumed that the number of customers is lognormally distributed with a mean of 2,400 and a standard deviation of 800. Assuming BOB is risk-neutral, how does the choice of location change if we vary the mean number of customers away from the assumed value of 2,400? You may assume that the standard deviation and correlations remain the same as this mean changes. Construct a plot showing how the expected values for these three alternatives change as we vary the mean of the number of customers from 1,000 to 4,000 customers per month and estimate the points at which the preferred location changes. (Hint: you can use a data table to vary the mean parameter of the lognormal demand distribution and track the profits in the three locations. Define cells in the data table as forecasts. During the simulation, CB will vary the mean parameter, sample the demand distribution with the mean parameter, and compute the corresponding profit.)

Because of his frequent travel to WALES, BOB became acquainted with BILL, the owner of a fine Indian restaurant there. As it turns out, BILL's son STEVE lives in LONDON, and he has contemplated selling his restaurant in WALES and moving to LONDON to be closer to STEVE and his family. BILL and BOB have discussed forming a partnership to open the restaurant in LONDON. BOB believes that BILL's experience would increase the likelihood that the restaurant will be successful. Specifically, BOB believes that BILL's expertise will increase the mean of the monthly demand distribution (= number of potential customers) from 2,400 to 2,800; the distribution remains lognormally distributed with a standard deviation of 800 and the correlation between the number of customers and payroll costs remains unchanged. All of the other assumptions and correlations also stay the same. In the arrangement they have discussed, BILL would be paid a fixed management fee of $3,000 per month plus a bonus of 50% of the monthly profits (before taxes) above $9,000. For this analysis, assume that the restaurant will be in location A.

Exhibit 1: Pro-forma Cash Flow Analysis Monthly Cash Flows \begin{tabular}{lr} Number of Customers & 2400 \\ Average Sales & $25.00 per customer \\ Direct Cost of Sales & $7.00 per customer \\ Gross Margin & $43,200= (Number of customers) * (Average Sales - Direct Cost) \\ \cline { 2 - 3 } Payroll (including taxes) & $24,000 \\ Other Fixed Costs & $8,000 \\ Total Operating Expenses & $32,000= (Payroll) + (Other Fixed Costs) \\ Profit (before Taxes) & $11,200= (Gross Margin) - (Total Operating Expenses) \end{tabular} \begin{tabular}{ccc} Location & MaximumCapacity(customerspermonth) & FixedCosts($permonth) \\ \hline A & 4,000 & 8,000 \\ B & 2,500 & 5,000 \\ C & 5,000 & 12,500 \end{tabular}