1 Introduction You are working as a business analyst for a popular cafe chain that is planning to expand its operations. Your manager has asked you to design a Monte Carlo simulation model using R program to evaluate different expansion strategies and determine the optimal one. You need to consider factors such as location, estimated revenue, initial investment, and operating costs.

2 Objective The objective of this assignment is to use Monte Carlo simulation to assess the risks and rewards associated with various expansion strategies for the cafe chain. You will evaluate the performance of different strategies and determine the best one based on net present value (NPV), payback period, and return on investment (ROI).

3 Data You have been provided with the following data:

1. A list of potential locations, each with the following information:

(a) Estimated initial investment (construction, equipment, etc.)

(b) Estimated monthly operating costs (rent, utilities, wages, etc.)

(c) Estimated monthly foot traffic (number of potential customers)

(d) Estimated average spend per customer

2. The cafe chain's required rate of return (discount rate)

3. The company's target payback period

4 Probability Distributions

The following probability distributions will be used to model the uncertainty in the data:

1. Initial investment: Triangular distribution with min, max, and most likely values provided for each location

2. Monthly operating costs: Normal distribution with mean and standard deviation provided for each location

3. Monthly foot traffic: Poisson distribution with mean provided for each location

4. Average spend per customer: Lognormal distribution with mean and standard deviation provided for each location.

problem 1. develop a Monte Carlo simulation model for each potential location, considering the provided data and probability distributions. Calculate the monthly revenue and net cash flow for each location. the calculate the Net Present Value (NPV) for each location using the cafe chain's required rate of return and finally analyze the results of your simulations, considering NPV (discount rate 0.1). Identify the optimal location for expansion based on your analysis.

Location	Initial Investment (min)	Initial Investment (most likely)	Initial Investment (max)	Monthly Operating Cost (mean)	Monthly Operating Cost (std)	Monthly Foot Traffic (mean)	Average Spend per Customer (mean)	Average Spend per Customer (std)
A	150000	175000	200000	15000	1000	4500	8	1.5
B	120000	140000	160000	12000	800	3500	10	2
C	180000	210000	240000	18000	1200	6000	9	1.7
D	100000	120000	140000	10000	700	2800	11	2.2