ESD 71 / 1.146 / etc 2005 Final Exam de Neufville 1 ENGINEERING SYSTEMS ANALYSIS FOR DESIGN D R A F T Final Examination, 2005 Points Item Possible Achieved Your Name 2 1 Cost Function 18 2 Engrg Economy Valuation 26 3 Decision Analysis 18 4 Value of Information 15 5 Lattice Development 27 6 Value at Risk 18 7 Option Evaluation 56 TOTAL POSSIBLE 180 TOTAL ACHIEVED GRADE ON 100% (TOTAL/1.80) Structure of the Exam The questions all tie to the design and justification of a proposed project. They take you through the material of the course from the beginning to the end. The technological part is deliberately simple, to reduce the complexity of the calculations and focus on the concepts of the course. Grading The concepts are the focus of the exam. You will earn most of your points by demonstrating that you know what the correct procedures are, and how to use them. You will do this by “running the numbers’. However, in this case the numbers themselves are not too important – points will be deducted for mistakes, but neither the course nor the exam is focused on arithmetic. Because the focus is on the concepts, you should clearly indicate how you going about each part of the exam so that we can give you the credit you deserve. Project You are designing a logistics sorting center. As project manager, you need to be able to justify the design to the decision-making board that can authorize the project. I have completed this test fairly, without copying from others, a book, or the web. Please sign your name legibly ______________________________________ (2points)ESD 71 / 1.146 / etc 2005 Final Exam de Neufville 2 1. Cost Function (18 points) Your design engineers have come up with a plan for the sorting center project. They have sized it in the traditional way, that is, to provide the maximum capacity projected over its life. This maximum capacity has been projected at 8 million packages/year, based on an estimated initial load of 2 million packages/year, that would double every 8 years (that is, would grow at about 9% / year compounded). As you wonder whether if it might be better to roll out the capacity in a couple stages, your staff provides you with their formula for estimating project costs: Cost of building line = Cost of building + Cost of Equipment = 2 + 0.6 (Capacity) 2/3 The cost is expressed in terms of millions of dollars; the capacity in terms of millions of packages per year. a) Define the concept of the “cost function” and its connection to the production function. (4 pts) b) Does this cost function define a convex feasible region? Explain your answer. (3 pts) c) Define “economies of scale”. How is this different from “increasing returns to scale” ? (4 pts) d) It you knew that the cost function did NOT have economies of scale, how would it affect your thoughts about developing the project in stages? (4 pts) e) Does this cost function exhibit economies of scale? Explain your answer. (3 pts)ESD 71 / 1.146 / etc 2005 Final Exam de Neufville 3 2 Engineering Economy Valuation (26 pts) Being pressed for time, you decide to see if you can justify the “base case” project proposed by your design staff. Therefore you do some traditional calculations. USE ONLY TWO-DECIMAL PLACE ACCURACY FOR THIS AND OTHER CALCULATIONS As previously, you assume that the • design is for Capacity = 8 million packages/year = maximum projected demand • cost formula is: Cost = 2 + 0.6 (Capacity) 2/3 -- in millions of dollars • initial demand = 2 million packages/year • growth rate ~ 9 % /year (doubling every 8 years, that is by √2 every 4 years) • life of project = 16 years Assume that • revenues in any 4-year period = 4 x (demand at end of the period) x ($0.4 per 1000 packages) • revenues are paid in at the end of each period • the company normally uses a discount rate ~ 20%, which is its estimated WACC Not having a spreadsheet available, you will do your analysis by filling in the table below. For simplicity, and in keeping with 2 decimal point accuracy, you can assume: (1 +0.2) exp(4) =2; and √2 = 1.4 Base Case Project Years 0 1-4 5-8 9-12 13-16 Demand at period end (millions 2 Revenue for 4 years (millions) Cost Net Cash Flow Discounting Factor at 20% Discounted Cash Flow Net Present Value a) What is your estimate of the project NPV? (15 pts) b) Define pay-back period. Estimate it for the project. (4 pts) c) Define internal rate of return. By looking at the table, what would you estimate it to be? (3 pts) d) One of your engineers asks you to justify the apparently high discount rate. You therefore explain that the WACC is….. (4 pts)ESD 71 / 1.146 / etc 2005 Final Exam de Neufville 4 3 Decision Analysis (18 pts) Wondering about the desirability of an alternate design that would roll out the project in 2 phases, you decide to do a simple decision analysis to test the following alternatives: • Base Case: build full 8 million capacity now • Phased Case: build 4 million at start, add 4 million at end of the second period (year 8) The cost of construction is as before: 2 + 0.6 (Capacity) 2/3 As an experienced professional, you estimate that there is a 10% probability that your company will not be able to obtain the permits to build the second phase in year 8, so that revenues for the “phased case” would be capped for the last 2 periods (years 9-16) The tables below indicate where new data needs to be inserted (compared to previous table). Phased Project (with second phase built) Years 0 1-4 5-8 9-12 13-16 Demand at period end (millions 2 Revenue for 4 years (millions) Cost Net Cash Flow Discounted Cash Flow Net Present Value Phased Project (with second phase NOT built, revenues capped) Years 0 1-4 5-8 9-12 13-16 Sales at period end (millions) 2 Revenue for 4 years (millions) Cost Net Cash Flow Discounted Cash Flow Net Present Value a) Draw the decision tree. Fill in all relevant data. (15 pts) b) Which is the better choice? The full project from start or the phased project? (3 pts)ESD 71 / 1.146 / etc 2005 Final Exam de Neufville 5 4 Value of Information ( 15 pts) Thinking about the possibility that the phased alternative is attractive, you decide to estimate whether if would be