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# Class Note for EMSE 388 at GW (4)

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Date Created: 02/07/15

EMSE 388 Quantitative Methods in Cost Engineering CHAPTER 15 MULTIPERIOD CAPITAL BUDGETING Companies often have more worthwhile project under consideration than their financial resources allow them to undertake EXAMPLE Project 1 2 3 4 5 6 7 8 9 Year10uthOWin Millions 1200 5400 600 600 3000 600 4800 3600 1800 Year20utflowin Millions 300 700 600 200 3500 600 400 300 300 NPVin Millions 1400 1700 1700 1500 4000 1200 1400 1000 1200 0 Notice that all projects add a positive NPV to the companies available capital For example project 1 adds 14 Million in terms of Net Present Value Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 178 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 0 Project 1 needs 12 Million dollars in expenditure to keep the project going in the first year and 3 Million Dollars in the Second Year 0 Company s available capital in the first year is 50 Million 0 Company s available capital in the second year is 20 Million OBSERVATIONS 0 Project 2 and Project 5 are not feasible due to these resource constraints 0 Project 7 is feasible but eats up all the money in the first year not leaving any room for other projects Yet project 7 only adds an NPV of 14 Million Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 179 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering 0 Project 3 on the other hand only needs 6 Million in the first year 6 Million in the second year adds an NPV of 17 Million and still allows for other project to be undertaking due to limited demands on available resources PROBLEM DESCRIPTION Determine the combination of project to undertake over multiple years that maximizes the combined NPV while guaranteeing that each year the money spent on project does not exceed the available capital Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 180 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering SOLUTION ASSUMPTIONS 1Assuming we may undertake a fraction of each project how can we maximize our NPV 2 If we cannot undertake a fraction of a project but must undertake all of a project how can we maximize NPV 3 Suppose that if Project 4 is undertaken then Project 5 must be undertaken as well How can we maximize our NPV SOLUTION MAY BE FOUND USING EXCEL SOLVER Note that the problem is a linear optimization problem as objective function is linear function of the changing variables as well as the constraint functions Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 181 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Solution under Assumption 1 Chosen 100 000 100 100 000 097 005 000 100 Project 1 2 3 4 5 6 7 8 9 Year 1 Outflow in Millions 1200 5400 600 600 3000 600 4800 3600 1800 Year 2 Outflow in Millions 300 700 600 200 3500 600 400 300 300 NPV in Millions 1400 1700 1700 1500 4000 1200 1400 1000 1200 Total NPV Observation 7027 All resources have been used Year Used Available 15000lt 5000 22000lt 2000 1As expected project 3 is completely executed Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 182 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering HOW IMPORTANT ARE THE RESOURCE CONSTRAINTS 0 Suppose you had an additional 1 million dollars in Year 1 how much could you improve the bottom line 0 Suppose you had an additional 1 million dollars in Year 2 how much could you improve the bottom line ANSWER CAN BE FOUND BY RERUNNING SOLVER WITH NEW CONSTRAINTS Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 183 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering NPV in Millions NPV in Millions Year 1 Year 2 Available 7027 Difference Available 7027 Difference 45 6833 194 15 6095 932 46 6889 138 16 6282 745 47 6944 083 17 6468 559 48 7000 027 18 6655 373 49 7014 014 19 6841 186 50 7027 000 20 7027 000 51 7041 014 21 7138 111 52 7055 027 22 7235 207 53 7068 041 23 7311 284 54 7082 055 24 7378 351 55 7095 068 25 7444 417 56 7109 082 26 7511 484 57 7123 095 27 7578 551 58 7136 109 28 7644 617 59 7150 123 29 7711 684 60 7164 136 30 7778 751 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 184 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering OBSERVATIONS 0 With 1 additional million dollars in year 1 you are able to improve NPV by 014 Million 140000 0 With 1 additional million dollars in year 2 your able to improve NPV by 111 Million DO YOU THINK THAT YOU WOULD BE ABLE TO ENTICE AN OUTSIDE INVESTOR PROMISING A 50 RETURN ON HIS INVESTMENT OF 1 MILLION DOLLARS Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 185 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Solution under Assumption 2 If we cannot undertake a fraction of a project but must undertake all of a project how can we maximize NPV Chosen 1 0 1 1 0 1 0 0 1 Project 1 2 3 4 5 6 7 8 9 Year1 Outflow in Millions 1200 5400 600 600 3000 600 4800 3600 1800 Year20utflowin Millions 300 700 600 200 3500 600 400 300 300 NPV in Millions 1400 1700 1700 1500 4000 1200 1400 1000 1200 Total NPV 7000 Not All resources have been used Year Used Available 1 4800 lt 5000 22000lt 2000 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 186 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Observation 1As expected project 3 is completely executed 2 Forbidding fractional projects only cost very little money HOW IMPORTANT ARE THE RESOURCE CONSTRAINTS 0 Suppose you had an additional 1 million dollars in Year 1 how much could you improve the bottom line 0 Suppose you had an additional 1 million dollars in Year 2 how much could you improve the bottom line Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 187 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering NPV in Millions NPV in Millions Year 1 Available 7000 Difference Year 2 Available 7000 Difference 45 5800 1200 15 5800 1200 46 5800 1200 16 5800 1200 47 5800 1200 17 5800 1200 48 7000 000 18 5800 1200 49 7000 000 19 5800 1200 50 7000 000 20 7000 000 51 7000 000 21 7000 000 52 7000 000 22 7000 000 53 7000 000 23 7000 000 54 7000 000 24 7000 000 55 7000 000 25 7000 000 56 7000 000 26 7000 000 57 7000 000 27 7000 000 58 7000 000 28 7000 000 59 7000 000 29 7000 000 60 7000 000 30 7000 000 Lecture Notes by Instructor Dr J Rene van Dorp Source Financial Models Using Simulation and Optimization by Wayne Winston Chapter 15 Page 188 EMSE 388 Quantitative Methods in Cost Engineering OBSERVATION 0 Due to the integer constraints we cannot improve our bottom line 0 Even with an additional 10 Million in year 1 and in year 2 we cannot improve on our NPV of 70 Million Solution under Assumption 3 Suppose that if Project 4 is undertaken then Project 5 must be undertaken as well How can we maximize our NPV How can we add a constraint that forces the above assumption to be realized Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 189 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Introduce 0 Project 4 is not chosen 0 Project Sis not chosen 4 1 Project 4 is chosen 5 1 Project Sis chosen ADD THE CONSTRAINT x5 2 x4 Conclusions 1 If Project 4 is chosen x41 Project 5 is chosen x51 2 If Project 5 is chosen x51 Project 4 does not have to be chosen x41 Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 190 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Chosen 1 O 1 O O 1 O O 1 Project 1 2 3 4 5 6 7 8 9 Year 1 Outflow in Millions 1200 5400 600 600 3000 600 4800 3600 1800 Year20utflowin Millions 300 700 600 200 3500 600 400 300 300 NPV in Millions 1400 1700 1700 1500 4000 1200 1400 1000 1200 Total NPV 5500 Observation 1As expected project 3 is completely executed 2 Additional constraint cost us 15 Million We cannot select project 4 anymore Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 191 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering Not all resources have been used Year Used Available 1 4200lt 6000 2 1800lt 3000 Project 4 Project 5 Olt O Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 192 Source Financial Models Using Simulation and Optimization by Wayne Winston EMSE 388 Quantitative Methods in Cost Engineering GENERAL OBSERVATION 0 When additional constraints are imposed the maximum solution decreases in value when original problem is a maximization problem 0 When additional constraints are imposed the minimum solution increases in value when original problem is a minimization problem THIS IS TRUE IN GENERAL MAX fx 3 MAX fx when 9 g o 1 er xe MIN fx 2 MIN fx whenQ g e 2 er xe Lecture Notes by Instructor Dr J Rene van Dorp Chapter 15 Page 193 Source Financial Models Using Simulation and Optimization by Wayne Winston

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