Hello,

I would appreciate if anyone can help me as I have a HW due tomorrow at midnight.

Thank you

Spring 2016 - EBF 304W Homework 3 Due: 5:00pm on Friday, 18 March 2016 (via ANGEL) 50 points Instructions: Please answer all questions clearly and completely. Justify and support your conclusions. If you use graphs or tables in your answers, they must be clear enough that I can understand them (this means labeling axes, variables, and so forth). If a question requires you to make calculations, you must show your work. If you make calculations using Excel, please include your spreadsheet output as an appendix. Your homework must be submitted electronically via ANGEL. Homework assignments must be submitted in a single electronic file in pdf file format with all text in 12 point Times New Roman font and 1 inch margins (I should not have to look at your spreadsheet for any answers, only to award partial credit). Do not forget to include your name. Late homework assignments will lose 10% per late day (e.g., late day 1 begins at 5:01pm on the due date and ends at 5:00pm on the following day). Question 1 (5 points): You are evaluating a prospect for oil drilling. You have three options for participation in the field development. You can drill yourself; farmout the drilling to a partner company; or back-in to the field if development is successful. (The back-in option is basically the option to participate that can be exercised after you know whether the field will be productive.) The payoffs of each option differ depending on whether the field is productive or is dry. The table below shows the payoffs for each participation option under each productivity outcome. Drill Field is a Producer Field is Dry $45,000 -$30,000 Farmout $14,500 $0 Back-in $25,000 $0 Let p be the probability that the field is a producer. Plot the Expected Monetary Value of each participation option as a function of p. Under what circumstances should you choose each participation option? Question 2 (5 points): There is an expert who can predict the likelihood of the field being a producer with 100% accuracy. The probability that the field will be a producer for your company's mineral lease is 45%. Construct the decision tree for this problem and calculate the expected value of perfect information (EVPI) for the expert's prediction. Question 3 (10 points): Your own company's team of geologists has a fairly accurate prediction record as well, and the cost of pulling them off of their other projects and making a prediction on this field is minimal. However, they are only accurate 90% of the time when the field is a producer (P(Producer|ExpertPredictsProducer) = 0.90), and 70% of the time when the field is dry (P(Dry|ExpertPredictsDry) = 0.70). The probability of the field being a producer remains the same at 45%. Construct the decision tree for this problem and calculate the expected value of imperfect information (EVII). Page 1 of 3 Scenario for Questions 4-7: Hammond Energy is considering building a 100 MW power plant whose output will be sold into the New York electricity market. The number of hours that the power plant will operate annually and the market price of electricity are both uncertain. Suppose that the power plant either operates at full capacity during a given hour or not at all (i.e., the plant never runs at, say, 50% capacity). The number of hours that the plant will run during a year is uncertain, but is described as a uniform distribution between 0 and 8,760 hours per year. The market price of electricity is uncertain, but is described using a triangular distribution with a mode of $65 per MWh; a maximum of $500 per MWh; and a minimum of $0 per MWh. For the purposes of this scenario, assume that the plant has zero marginal cost (i.e., fuel for the plant is free, and the plant requires no maintenance). Question 4 (10 points): Generate 200 random draws for the number of hours per year that the plant will run, and 200 random draws for the market price of electricity. Plot three cumulative distribution functions (CDFs) showing the number of hours that the plant runs; the market price of electricity; and total annual revenue (remember that for the i-th draw of the number of hours and the market price, the i-th draw for revenue is equal to (# hours)i 100 (market price)i. Please show each CDF on a separate set of axes (so you should have three plots in your response). What is the expected value of annual revenue for the plant? What is the 90% quantile for annual revenue of the plant? Question 5 (10 points): Suppose that the plant had a capital cost of $5 million. Calculate the expected value of IRR for the plant over a ten-year operating horizon as well as the 90% quantile IRR (in other words, use the expected value and 90% quantile of annual revenues from Question 7 when calculating IRR). Assume that the capital cost is incurred in Year 0, while the revenues are enjoyed from Year 1 to Year 10. Questions 6 and 7: One common issue with performing Monte Carlo analysis is determining the number of random draws to use. Generally, you should keep adding random draws until the random distribution that you have generated does not change \"very much.\" In the following two questions we will look at two different ways of defining \"does not change very much.\" Question 6 (5 points): In this question we will use an iterative procedure for determining when you have generated enough random draws. We will use the triangular distribution from the power plant scenario above. Let k and k be the mean and standard deviation of k random draws from that triangular distribution (so 500 would be the mean from 500 random draws from the triangular distribution, for example). Based on the triangular distribution in the power plant scenario, calculate and plot 500 to 10,000 in increments of 500 (so you would calculate 500, 1500, 2000 and so forth). Plot 500 to 10,000 in increments of 500 (so you would calculate 500, 1500, 2000 and so forth). Based on your plots, how many random draws are \"enough\" for the power plant problem? Be sure to justify your answer. Page 2 of 3 Question 7 (5 points): In this question we will use the mean of the triangular distribution itself to determine when you have generated enough random draws. The mean of a triangular distribution with mode c, minimum a, and maximum b is . Calculate the mean of the triangular distribution for the power plant problem directly using this formula. Then, for each k that you calculated in Question 5, calculate the percentage difference between k and the actual mean of the triangular distribution T. We will say that k is \"enough\" draws when the difference between k and T is less than 1%. Based on this method, how many draws from the triangular distribution is \"enough\" for the power plant problem? If you never find that the difference between k and T is less than 1% in magnitude, report your answers and say that more than 10,000 draws are needed. Page 3 of 3