Discussion of the problem
Sanjay Thomas, a second-year MBA student at M.I.T. Sloan School of Management has three choices after he graduates. The first one is an excellent job offer that he received from a top-flight management consulting firm.
The second option is to open an upscale restaurant that will serve Indian gourmet cuisine. The third option is to open the restaurant with his aunt. Each option has positive and negative aspects, but when Sanjay compares them only the financial benefits are relevant.
If Sanjay takes the job offered by the management consulting firm he would earn a salary of $80,000 a year. If he decides to open the restaurant, he would face a different scenario. To figure out Sanjay’s salary he would have to take into account three variables: number of meals sold, revenue per meal, and labor cost.
If Sanjay opens the restaurant in partnership with his aunt, she would guarantee him a salary of at least $3,500 a month, and in return she would get 90% of all monthly earnings in excess of $9,000.
Sanjay estimated the following statistics for the variables that affect the expected salary at the restaurant. First, the number of meals obeys a normal distribution with a mean of 3,000 and a standard deviation of 1,000. Second, the revenue per meals is $20.00 with a probability of 25%, $18.50 with a probability of 35%, $16.
50 with a probability of 30%, and $15.00 with a probability of 10%. Third, the labor cost follows a continuous uniform distribution between $5,040 and $6,860. He also estimates that there are two fixed costs. One is the fixed cost per meal of $11 and the other one is non labor cost of $3,995.
All these variables and fixed costs were used in a simulation software package to forecast the expected salary on the restaurant for the two situations: one running the restaurant by alone, and the other one, running it with his aunt.
Each simulation consisted of 10,000 trials.
The result of Sanjay running the restaurant alone is represented in Graph A. With a mean of $10,845 and standard deviation of $8,568 (Table 1), this option shows that the expected salary would be higher than the $6,666 monthly salary that he would earn in the consulting firm ($80,000/ 12). At the same time, the standard deviation projects a high variability on the expected salary, which means that there is the potential of earning more money than at the firm and of losing money running the business.
As seen in Graph B, The cumulative chart for the first simulation, the probability that Sanjay would earn more than $5,000, the amount he considers acceptable, is around 28%. This value shows the high risk that he has by running the restaurant.
This graph also shows that the probability that he would earn more than $6,666 is 65%. This should sound attractive to Sanjay because he has an opportunity to earn more than $6,666, an opportunity that he would not have at the consulting company. The graph also shows that he has an interesting opportunity of making more than $10,000 with a probability of 50%. Running the restaurant alone has its advantages and disadvantages as seen on the simulation results.
Another simulation was run considering the aunt’s proposal. For this simulation the conditions that the aunt gave Sanjay were included as “if “statements in the program.
The results for this simulation are shown in Graph C. This simulation presented a mean of $7,653 and a standard deviation of $2,700. Even though the mean is lower, the standard deviation is considerably lower which means that the expected salary would be more stable.
Graph D depicts the cumulative distribution for this simulation. The probability that the salary is lower than $5,000 is 28%. There is no change in this result because the changes that the salaries would have with the partnership are not affected if they are between $3,500 and $9,000.
The positive feature in this option is that he will never lose money, and even better, he will guarantee $3,500 a month. At this stage this one looks like the best option that he has. The problem is that it would be very difficult to make more than .