Project Risk Evaluation and Management. Rules for Group Work No. 2

Transcription

1 Project Risk Evaluation and Management Rules for Group Work No. 2 Content This work consists of solving five exercises, while making use of appropriate software used in the Risk Project Evaluation and Management course. Each group will need to present their solution for one exercise in class, and will need to answer to specific and general questions related with the exercise. So, each group will need to prepare and submit: A word file with the solution of the exercises, presenting clearly the information used to solve the exercise, the assumptions in use, as well as the main outputs produced while using the software to solve the problem; The copy of the software files used to solve the exercises; A short presentation of the exercise to be presented in class. These files will need to be sent electronically to monica.oliveira@ist.utl.pt by the 1 st of June. Exercises to be presented and discussed in class by each group Group Exercise to be Group 1: Daniel da Marça Teixeira; Gil Tomé Henriques Ferreira; Tiago Alexandre Alves Octício Group 2: Luís Filipe Alves Dinis; José Duarte Ferreira Pinto Gaspar; Vera Lobato da Fonseca Saragga Leal Group 3: Pedro Filipe Pereira Furtado; 57324Nuno Miguel Lopes Santana; Diogo Manuel Costa Elias; Sara Raquel Ferreira Tomas Group 4: Ana Moreira; Inês Melo; 55683Joana Lima; Group 5: Leonor Sanches de Sousa Uva; João Bernardo Santos Paiva Leitão Pereira; Luís Fernando Frade Barão Faria da Fonseca Group 6: Diogo Filipe Silveirinha Figueiredo; 64651Luis Miguel Sousa Oliveira; Luis Miguel de Sá Marques Loureiro; João Carlos Varela Lázaro Group 7: Hugo Dias Morais; Jorge Andrade; Alexandra Antonio Group 8: Bárbara Esperança Santiago Virgílio; 57327Susana Isabel Gandum Semedo; Samantha Bulha Lopes Pereira Group 9: Diogo Lamelas; Manuel Laia Valente; André Ricardo Feio Seco Group 10: Luís Prudêncio; Frederico Manuel Marques Goncalves; Juliana Sequeira Pinto Group 11: Adelina Cruz; Bárbara Braguez da Gama Paninho; 56146Leonor Alves Cristóvão Group 12: Bruno Joel de São José Rodrigues; Charles Louis Arthur Xavier discussed in class Mónica Oliveira, RPEM 2008/2009 1

2 Marie de Castro de Carvalho; Margarida Servinho da Silva Maggiolli Group 13: Francisco de Bragança Pinheiro da Silva; Gonçalo Santos; António Orlando de Novais Ramos Henriques de Almeida Group 14: João Pedro Leal dos Ramos; 64419Válter Grego da Cunha; André Lopes Fradinho Group 15: Miguel Ruben Feiteira Marques; Diana D'Elpas Buzaglo; Sofia Pereira Francisco Gameiro Group 16: António Silva; Mário André Rocha Cristóvão Coelho; Luis Manuel Calhau Contente Group 18: Lorenzo Cimarossa; Giulio Lucacci; Filippo Andrea Zampieri; David Ricardo Gonçalves 5 Evaluation criteria Evaluation will be based upon: degree of correction of the solution; level of communication of the word solution report; adequacy of software use; quality of the presentation and discussion. Work 2 is worth 35% of the final grade of the course, and its presentation and discussion is worth 5%. Mónica Oliveira, RPEM 2008/2009 2

3 Exercise 1 Steve Sheffler is president, CEO, and majority stockholder of Southern Electronics, a small firm in the town of Silicon Mountain. Steve faces a major decision: two firms, Big Red Business Machines and Banana Computer, are bidding for Southern Electronics. Steve founded Southern 15 years ago, and the company has been extremely successful in delivering progressive computer components. Steve is ready to sell the company (as long as the price is right!) so that he can pursue other interests. Last month, Big Red offered Steve 5 million and shares of Big Red stock (currently trading at 50 per share and not expected to change substantially in the future). Until yesterday, Big Red s offer sounded good to Steve, and he planned on accepting it this week. But a lawyer from Banana computer called last week and indicated that Banana was interested in acquiring Southern Electronics. In discussions this past week, Steve learned that Banana is developing a new computer, code named EYF, that, if successful, will revolutionalize the industry. Southern Electronics could play an important role in the development of the machine. In their discussions, several important points were surfaced. First, Banana has said that it believes the probability that the EYF will succeed is 0.6, and that if it does, the value of Banana s stock in the future will increase from the current value of 30 per share. Although the future price is uncertain, Banana judges that, conditional on the EYF s success, the expected price of the stock is 50 per share. If the EYF is not successful, the price will probably decrease slightly. Banana judges that if the EYF fails, Banana s shares will be between 20 and 30, with an expected price of 25. Yesterday Steve discussed this information with his financial analyst, who is an expert regarding the electronics industry and whose counsel Steve trusts completely. The analyst pointed out that Banana has an incentive to be very optimistic about the EYF project. being realistic, though, said the analyst, the probability that the EYF succeeds is only 0.4, and if it does succeed, the expected price of the stock would be only 40 per share. On the other hand, I agree with Banana s assessment for the share price if the EYF fails. Negotiations today have proceeded to the point where Banana has made a final offer to Steve of 5 million and 150,000 shares of Banana stock. The company s representative has stated clearly that Banana cannot pay any more than this in a straight transaction. Furthermore, the representative claims, it is not clear why Steve will not accept the offer because it appears to be more valuable than the Big Red offer. a) In terms of expected value, what is the least that Steve should accept from Banana? b) Steve has obviously two choices, to accept the Big Red offer or to accept the Banana offer. Draw an influence diagram representing Steve s decision, and solve it using an adequate computer program. c) Draw and solve a complete decision tree representing Steve s decision. d) Why is it that Steve cannot accept the Banana offer as it stands? Mónica Oliveira, RPEM 2008/2009 3

4 Steve is well aware of the difference between his probabilities and Banana s, and realizes that because of this difference, it may be possible to design a contract that benefits both parties. In particular, he is thinking about put options for the stock. A put option gives the owner of the option the right to sell an asset at a specific price (for example, if you own a put option on 100 shares of General Motors (GM) with an exercise price of 75, you could sell 100 shares of GM before the expiration date of the option; this would be useful if the stock price fell below 75). Steve reasons that if he could get Banana to include a put option on the stock with an exercise price of 30, then he would be protected if the EYF failed. Steve proposes the following deal: He will sell Southern Electronics to Banana for plus shares of Banana stock and a put option that will allow him to sell the shares back to banana for 30 per share anytime within the next year (during which time he will become to know whether the EYF succeeds or fails). e) Calculate Steve s expected value for this deal ignore tax effects and the time value of money. f) The cost to Banana of their original offer was simply * 30= Show that the expected cost to Banana of Steve s proposed deal is less than 9.5 million, and hence in Banana s favour. Again, ignore tax effects and the time value of money. Exercise 2 A friend of yours can invest in a multiyear project. The cost is Annual cash flows are estimated to be 5000 per year for six years but could vary between 2500 and Your friend estimates that the cost of capital (interest rate) is 11%, but it could be as low as 9.5% and as high as 12%. The basis of the decision to invest will be whether the project has a positive net present value. Construct a tornado diagram for this problem. On the basis of the tornado diagram, advise your friend regarding either (1) whether to invest or (2) what to do next in the analysis. Indicate which other instruments, other than Tornado diagrams, could be used to inform this investment decision. Exercise 3 MIP is a manufacturing company that performs contract work for a wide variety of firms. It primarily manufactures and assembles metal items, and so most of the equipment is designed for precision machining tasks. The executives of MIP currently are trying to decide between two processes for manufacturing a product. Their main criterion for measuring the value of a manufacturing process is net present value (NPV). The contractor will pay MIP $8 per unit. MIP is using a three year horizon for its evaluation (the current year and the next two years). Process 1 Under the first process, MIP s current machinery is used to make the product. The following inputs are used: Mónica Oliveira, RPEM 2008/2009 4

5 Demand: Demand for each of the three years is unknown. These three quantities are modelled as discrete random variables denoted D 0,D 1 and D 2 with the following probability distributions: D 0 P(D 0 ) D 1 P(D 1 ) D 2 P(D 2 ) 11 k k k k k k k k k 0.4 Variable Cost: Variable cost per unit changes each year, depending on the cost for material and labor. Let V 0, V 1 and V 2 represent the tree variable costs. The uncertainty surrounding each variable is represented by a normal distribution with mean $4 and standard deviation $0.40. Machine failure: Each year, MIP s machines fail occasionally, but obviously it is impossible to predict when or how many failures will occur during the year. Each time machine fails, it costs the firm $8000. Let Z 0, Z 1 and Z 2 represent the number of machines failures in each of the three years, and assume that each is a Poisson random variable with parameter λ=4. Fixed Cost: Each year a fixed cost of $12,000 is incurred. Process 2 The second process involves scrapping the current equipment (it has no salvage value) and purchasing new equipment to make the product at a cost of $60,000. Assume that the firm pays cash fir the new machine, and ignore tax effects. Demand: Because of the new machine the final product is slightly altered and improved, and consequently the demands are likely to be higher than before, although more uncertain. The new demand distributions are: D 0 P(D 0 ) D 1 P(D 1 ) D 2 P(D 2 ) 14 k k k k k k k k k 0.5 Variable cost: Variable costs still changes each year, but this time V 0, V 1 and V 2 are each judged to be normal with mean $3.50 and standard deviation $1.00. Machine failures: Equipment failures are less likely with the new equipment, occurring each year according to a Poisson distribution with parameters λ=3. They also tend to be less serious, costing only $6,000. Fixed cost: The fixed cost of $12,000 is unchanged. Mónica Oliveira, RPEM 2008/2009 5

6 Questions 1. Draw an influence diagram for this decision problem. Do you think it would be feasible to solve this problem with an influence diagram? Explain. 2. Write out the formula for the NPV for both processes described above. Use the variables names as specified, and assume a 10% interest rate. 3. For process 1, construct a model and perform 1000 simulation trials. Estimate the mean and the standard deviation of NPV for this process. Print a histogram of the results, and estimate the probability of a negative NPV occurring. 4. Repeat Question 3 for Process Compare the distribution of NPV for each of the two alternatives. Which process would be better for MIP? Why? Exercise 4 Don Newcomb was perplexed. It has bee five years since he has founded Interplants INC., a research and development firm that developed genetically engineered plants for interplanetary space flight. During those five years, he and his scientists had made dramatic advances in developing special plants that could be used for food and air purification systems in space stations and transports. In fact, he mused, their scientific success had been quite rosy. Everyone had been optimistic. Indeed, he was one of many investors who had jumped at the chance to be involved in the development of such technology. But now, after five tumultuous years, the prospects were less exciting. First, there had been the disappointing realization that none of the superpowers had made substantial progress on an ion engine to power space vehicles. Such an engine was absolutely crucial to the success of the interplanetary space flight, because theoretically, at least it would make travel 10 times as fast as conventionally powered ships. When the importance of such an engine became obvious, the superpowers had generously funded a huge multinational research project. The project had made substantial progress, but many hurdles remained. Don s risk assessors estimated that there was still a 15% chance that the ion engine would prove an infeasible power source. If this were to happen, of course, Don and the many other investors in space travel technology would lose out. Then there was the problem with the settlement policy. The superpowers could not agree on a joint policy for the settlement of interplanetary space, including the deployment of space stations as well as settlements on planets and their satellites. The United American Alliance urged discretion and long range planning in this matter, suggesting that a multinational commission be established to approve individual settlement projects. Pacificasia and Allied Slavic Economic Community were demanding that space be divided now. By immediately establishing property Mónica Oliveira, RPEM 2008/2009 6

7 rights, they claimed, the superpowers would be able to develop the optimum space economy in which the superpowers could establish their own economic policies within their colonies as well as determine trade policies with the other superpowers. Europe favoured the idea of a commission, but also was eager to explore other available economic possibilities. The discussion among the superpowers had been going on since long before the founding of Interplants. Five years ago, progress was being made, and it appeared that an agreement was imminent. But 18 mouths ago the process stalled. The participants in the negotiations had established positions from which they would not budge. Don has followed the discussion closely and had even provided expert advice to the negotiators regarding the potential for interplanetary agricultural developments. He guessed that there was only a 68% chance that the superpowers would eventually arrive at an agreement. Naturally, until an agreement was reached there would be little demand for space travelling plants. Aside from these external matters, Don still faced the difficulty issue of developing a full scale production process for his plants. He and his engineers has some ideas about the costs of the process, but at this point, all they could do was come up with a probability distribution for the costs. In thinking about the distribution, don had decides to approximate it with a three point discrete distribution. Thus, he characterized the three branches as inexpensive, moderate and costly, with probabilities 0.185, 0.63 and respectively. Of course, his eventual profit (or loss) depended on the costs of the final process. Don also had thought long and hard about the profits that he could anticipate under each of the various scenarios. Essentially he thought about the uncertainty in two stages. First was de determination of costs, and second was the outcome of the external factors (the ion engine research and the negotiations regarding settlement policy). If costs turned out to be inexpensive hen, in the event that the superpowers agreed and the ion engine was successful, he could expect a profit of 125 billion credits. He would lose 15 billion credits if either the engine or the negotiations failed. Likewise, if costs were moderate, he could anticipate either a profit of 100 billion credits if both of the external factors resulted in a positive outcome, or a loss of 18 billion if either of the external factors were negative. Finally, the corresponding figures in the case of a costly production process were profits of 75 billion credits or a loss of 23 billion. This is so confusing, complained Don to Paul Fiester, his chief engineer. I really never expected to be in this position. Five years ago none of these risks were apparent to me, and I guess I just don t tolerate risk well. After a pause, Paul quietly suggested well, maybe you should sell the business. Don considered that. Well, that s a possibility. I have no idea how many crazy people out there would want it. Mónica Oliveira, RPEM 2008/2009 7

8 Some of the other engineers and I might be crazy enough, Paul replied. Depending on the price, of course. At least we d be going in with our eyes open. We know what the business is about and what the risks are. Don gave the matter a lot of thought that night. What should I sell the company for? I hate to give up the possibility of earning up to 125 billion credits. But I don t like the possibility of losing 23 billion either no one would! As he lay awake, he finally decided that he would let the business go with all risks for 20 billion credits. If he could get that much for it, he d sell. If not, he d just as soon stick with it, in spite of his frustrations with the risks. Questions 1. Draw a decision tree for Don Newcomb s problem. 2. What is the significance of his statements that he would sell the business for 20 billion credits? 3. Suppose that Don s risk attitude can be modelled with an exponential utility function. If his certainty equivalent were 15 billion credits, find his risk tolerance. What would his tolerance be if his certainty equivalent were 20 billion? Exercise 5 A scientist collected the following weights (in grams) of laboratory animals: 9.79; 9.23; 9.11; 9.62; 8.73; 11.93; 10.39; 8.68; 9.76; 9.59; 11.49; 9.86; 11.41; 9.6; 7.24 a) Use these data to create a data based CDF for the distribution of weights for lab animals. Estimate the probability that an animal s weight will be less than 9.5 grams. b) Fit a normal distribution to these data on the basis of the sample mean and sample variance. Use this normal distribution to estimate the probability that an animal s weight will be less than 9.5 grams. c) Do you think the normal distribution used in part b is a good choice for a theoretical distribution to fit these data? Why or why not? Mónica Oliveira, RPEM 2008/2009 8