Problem 1 - The manager of Fort Motors is considering developing one of two proposed new car models, A and B. For Model A, it is estimated that a one-time investment of $1000,000 will be required by product design at the beginning of the first year. For model B, a one-time investment of $500,000 to product design is needed at the beginning of the first year. The introduction of either model to the market depends on the result of market survey that will be conducted after the concept car is designed. The period required from design to beginning production of either car model is expected to be 2 years. If the model is not introduced, the investment to the product design can not be recovered. Based on the initial analysis, the probability for model A not introduced to marker is estimated to be 0.4. The probability for model B not introduced to marker is estimated to be 0.3.

If the car model A is introduced to market, it will need a one-time investment of $3000,000 to modify the existing production line at the end of year 2. The market demand for this car model can either be High, Medium, or Low. The probability is estimated to be P (high)=0.3, P (medium)=0.4 P (Low)=0.3. Depending on the market demand the net annual revenue is estimated to be $2500,000 for high demand, $2,000,000 for medium demand, and $1,500,000 for low demand. The production of Model A will be continued for 5 years.

If the car model B is introduced to market, it will need a one-time investment of $500,000 to modify the existing production line at the end of year 2. The market demand for this car model can also be either High, Medium, or Low, with P (high)=0.5, P(medium)=0.3, P(Low)=0.2. Depending on the market demand, the net annual revenue is estimated to be $1,000,000 for high demand, $600,000 for medium demand, and $400,000 for low demand. The production of Model B will be continued for 5 years.

(a) Suppose Fort Motor's design team can only afford to design one car model, structure this problem with a decision tree, draw the cash flow diagram for each decision path, find the present worth for each decision path.

(b) Suppose the MARR of Fort Motor is 10%, solve the decision problem for Fort Motor's manager using EMV based on present worth.

(c) Draw the risk file and the cumulative risk profile for the selected strategy. What conclusion can you draw from looking at the profiles?

Problem 2 - As a manager of a small business, you are considering to introduce a new product. The production requires a new machine. You figure out that you could buy it for $190,000, but the price could be in between $180,000 and $200,000. Because of the budget limitation you can only pay 60% of the machine price with your own saving. You will borrow the other 40% with an interest rate around 9% per year (but subject to change in between 8.5% and 10%).

The demand of this product is predicted to be 15,000 per year and but could be in between 14800 and 15500. The unit price could be in between $2 and $3, and now you believe that $2.5 is a reasonable price right now. The raw material cost is estimated to be $0.9 but could be in between $0.5 and $1.2. The operation cost of the equipment is around $0.2 for one product but could be in between $0.1 and $0.25. The maintenance cost for this equipment is estimated to be $2000 per year but could be in between $1500 and $2300.

Suppose you could always invest your cash in the money market that give a return at 8% per year for sure.

Please do following analysis:

a) Construct the Influence Diagram for this decision problem and identify the inputs and mathematic models that relate these inputs (decision variables) to the decision problem.

b) Construct the Tornado Diagram

c) Based on Tornado Diagram, identify two most sensitive variables, and do two-way sensitivity analysis based on these two variables. Illustrate your result in two-way sensitivity graph

d) Can you decide whether to invest after these analyses? If not, what to do next?