MSING014B DECISION & RISK ANALYSIS ─ 2012/2013 FINAL EXAM
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MSING014B
DECISION & RISK ANALYSIS - 2012/2013
FINAL EXAM
CleanFuelTechTM
CleanFuelTechTM is a company affiliated with UCL scientists and engineers. It is one of several pioneering companies that produce fuel cell engines for automobiles. Instead of traditional combustion engines which require gasoline and emit carbon dioxide, the fuel cell engines require hydrogen and emit water. In addition to being environmentally friendly, because the supply of hydrogen in the atmosphere and ocean is virtually limitless, fuel cell engines are seen as a solution to future gasoline shortage. Many civic organizations promote the usage of such engines, and as a result, many major cities around the world operate buses that run on such fuel cells (e.g. currently in London you can spot fuel cell buses operating).
Until recently, manufacturing cars using fuel cell engines were economically infeasible by automakers due to the high cost of fuel cell engines, which results in high selling prices for the consumers. However, the cost to produce fuel cell engines have declined significantly over the last decade and due to the rise in gasoline prices and rising environmental awareness among consumers, automakers are finding that there will be sufficient demand for fuel cell cars, despite its higher price. The major automakers from US, Germany, Japan, and South Korea have stated their intention to commercialize fuel cell cars by 2015, and are investigating its feasibility.
Part I: Simulation
CleanFuelTech is aiming to build a large scale production facility (costing £50M) to be able to accommodate the potential demands of fuel cell engines to those automakers. Before undergoing the large investment, they would first like to get a good sense of the annual profit they would earn (i.e. sales and variable costs).
Currently, they estimate that there are anywhere between 2 to 4 automakers that would be interested in their engine. The demands from each of these automakers are expected to be of similar scale as the automakers would be initially cautious about such new products. If the automakers buy the fuel cell engines, they expect the automakers to adopt the engines for 1~3 car models (lines). Each line will produce between 2000 to 4000 cars, with 3000 cars being the most likely estimate. The price they will charge will depend on negotiations and the particular engine specifications, but they are sure that the price per engine would fall anywhere between £3,000 and £4,500 with £3,500 being the most likely. The variable production cost of each engine, after the production facility is set up, is to range anywhere between £2,000 and £3,500, with £3,000 being most likely.
CleanFuelTech expects to employ about 10 knowledgeable professional sales associates with sufficient industry ties to help them approach and sell to the automakers. They have sent many offers and the number they eventually end up hiring will be anywhere between 8 and 12. Each of their annual salary for these sales staff would be anywhere between £150,000 and £250,000 depending on their qualifications and experience.
Question 1. Scenario Analysis
(i) Using the key uncertainties (risk factors) presented in Table 1, determine the equation for the annual profit before investment (i.e. total sales - variable cost).
(ii) Based on the stated equation, what are the best-case scenario and the worst-case scenario?
Question 2. Simulation Analysis - Distributions
To perform a simulation analysis, we need to identify an appropriate probability distribution to model each of the risk factors.
(i) Define (loosely) what a probability distribution is and discuss its role in simulation.
(ii) Determine an appropriate distribution and their parameters for each of the risk factors.
Question 3. Simulation Analysis - Average
You have used the distributions specified above to perform a simulation analysis (1,000 iterations) using @Risk and produced the following output.
(i) What is the average annual profit for this venture, and carefully explain its meaning. Would this value change significantly if the number of iterations were increased from 1,000 to 10,000?
(ii) If the investment for the production facility is £50M, what is the chance that CleanFuelTech recover its investment after one year?
(iii) What is the realistic downside (Value at Risk) in terms of the annual profit level after the £50M investment? What is the realistic upside? Would these values change significantly if the number of iterations were increased from 1,000 to 10,000?
Question 4. Managing Risk – Tornado Diagram
Examine the tornado diagram found from @Risk.
(i) What does this tornado diagram tell you?
(ii) How does the variable production cost compare to the price per engine? Why?
Part 2: Resource Allocation
UniversalMotors (UM) is an automaker based in the US, who is interested in entering the fuel- cell automobile market. They are keen to purchase fuel cell engines to put into their cars from an outside vendor (e.g. CleanFuelTech), as they lack the in-house capability.
UM has recently decided to adopt the fuel cell engine into two of their car lines – Axion and Neptune. The total number of cars UM can produce from the Axion line and the Neptune line are, irrespective of the engine being fuel-cell-based or gasoline-based, 18,000 cars and 6,000 cars respectively. Adopting the fuel-cell car in each production line is practically costless as it involves minor switches in installing a different engine. There are two engine sizes: small and large. Axion is a compact car which can operate with any engine size; Neptune is a midsize car which requires the large engine.
UM has recently purchased 5,000 small fuel-cell engines and 2,000 large fuel-cell engines from CleanFuelTech for a special discounted price of £11,000 and £16,000 respectively.
The current selling prices for a gasoline-based Axion and a gasoline-based Neptune are £15,000 and £25,000 respectively. Based on the recent market research conducted, UM decided on the prices of a fuel-cell-based Axion and a fuel-cell-based Neptune to be £25,000 and £42,000 respectively. At these prices, all of the Axions and the Neptunes produced will be sold regardless of the engine type or size. UM is trying to figure out how many of fuel-cell cars to produce from each of the two car lines (Axion and Neptune) to maximize its revenue. They have come to you for advice.
Question 5. Resource Allocation Model
(i) Using the numbers from UM, define the objective, decision variables, and constraints.
(ii) Formulate the resource allocation problem.
Question 6. Optimal Allocation
(i) How many fuel-cell Axions and fuel-cell Neptunes should UM produce? What is the resulting revenue? (hint: for this problem, you do not need to rely on Excel Solver to find the optimal allocation.)
(ii) How can you be sure that your solution is optimal?
Question 7. Shadow Prices
(i)What is the value of a marginal increase in the Axion line capacity (i.e. from 18,000 to 18,001)? Clearly state your reasoning.
(ii) What is the value of a marginal increase in the number of large fuel-cell engine (i.e. from 2,000 to 2,001)? Clearly state your reasoning.
Part III: Decision Analysis
One year later: After investing £50M to build the production plant, CleanFuelTech has been quite successful, earning the revenue of £25M in its first year. Encouraged by this performance, CleanFuelTech is drawing attention from many different investors. According to market researchers, the long-term outlook looks healthy as the demand for various eco-friendly cars is expected to rise in the next several years.
In particular, they conjecture that the demand will significantly increase in the future, translating into a present value revenue of £250M. However, they also believe that increase in demand will lead to increased number of competitors in the market. In particular, they believe that there is a 90% chance that the market will be segmented, in which case CleanFuelTech will become only one of several market players and capture 20% of the revenue (0.2*£250M). They believe that there is a 10% chance that the market remains relatively unexplored and CleanFuelTech becomes the dominant player in the market, in which case CleanFuelTech can capture 80% of the total revenue (.80*£250M).
To shield off their potential competitors, CleanFuelTech is currently contemplating an additional investment of £100M in the company (e.g. improve production capacity, sales and marketing). They believe that doing so will prevent competition from entering the market in the future. In particular, CleanFuelTech believes it will capture capture 80% of the total revenue (.80*£250M) with 70% chance, and 20% of the total revenue (0.2*£250M) with 30% chance. CleanFuelTech is trying to decide whether or not to go for the additional investment.
Question 8. Decision Tree
(i) Construct the decision tree, filling in the appropriate numbers for each branch/node.
(ii) Determine the average payoffs, and recommend a decision based on the average.
Question 9. Value of Information
As CleanFuelTech is contemplating the additional investment decision, they are approached by a trustworthy and esteemed industry insider who suggests that CleanFuelTech should delay the decision to make the investment. In particular, he believes that investing after realizing the market is segmented is not too late because investing then will reduce the likelihood of competition in the same manner. In other words, the timing of investment does not impact the competitive landscape.
(i) Construct a new decision tree and compute the expected value.
(ii) What is the value of delaying the decision after learning about the market (as opposed to before learning about the market)?
(iii) Clearly state the strategy that CleanFuelTech should follow.
Question 10. Risk Profile
(i) State the risk profiles of the delayed investment (Q9) and early investment (Q8).
(ii) What is the probability of losing money in early investment? In delayed investment? If CleanFuelTech considers losing over £20M as an unacceptable risk, which type of investment would you recommend?
2023-08-11