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CHAPTER 12

M c. Graw. Hill. ENGINEERING ECONOMY Fifth Edition. Blank and Tarquin. CHAPTER 12. Selection from Independent Projects Under Budget Limitation. M c. Graw. Hill. ENGINEERING ECONOMY Fifth Edition. Blank and Tarquin. CHAPTER 12. Learning Objectives. Learning Objectives.

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CHAPTER 12

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  1. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 Selection from Independent Projects Under Budget Limitation Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  2. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 Learning Objectives Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  3. Learning Objectives • Capital Rationing rationale; • Use of PW analysis in capital rationing among independent projects; • Use of PW to select from several unequal-life independent projects; • Application of Linear Programming to the solution of capital budgeting problems. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  4. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 12.1 An Overview of Capital Rationing Among Projects Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  5. 12.1 Capital Budgeting Overview • Investment capital represents a scarce resource; • Some projects may be funded and some may not! • We have, then, the “independent project selection” problem. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  6. 12.1 Projects • Project: • An investment opportunity for the firm; • Generally been evaluated and found to be acceptable given that funds are or will be available to fund (execute) the project. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  7. 12.1 Independent Projects • Independent Projects: • The cash flows of one project do not in anyway impact the cash flows of any other project in the set. • Selection of one project to accept or reject does not impact any other project in the set. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  8. 12.1 Project Bundles • A “bundle” is a collection of independent projects. • Independent-type projects tend to be quite different from each other. • Not all projects can be selected – budget constraints may exist. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  9. 12.1 Capital Budgeting – Characteristics • Identify independent projects and their estimated cash flows; • Each project is selected entirely, or it is not selected at all; • Objective: maximize the return on investment Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  10. 12.1 Selection Guidelines • Accept projects with the best PW values determined at the MARR; • Provided the investment capital limit is not exceeded. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  11. (A) $$ Cash Flow Profile $$ Budget (B) $$ Cash Flow Profile (C) $$ Cash Flow Profile 12.1 The Capital Budgeting Problem Objective: Max. PW of the selected bundles Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  12. 12.1 Max Present Worth • Previous Assumption of equal Life for the alternatives is no longer valid for capital budgeting; • No life cycle beyond the estimated life of each bundle; • PW is over the respective life of each independent project. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  13. 12.1 Reinvestment Assumption • The following is assumed for the capital budgeting problem All positive net cash flows of a project (bundle) are reinvested at the MARR from the time they are realized until the END of the LONGEST-LIVED project! With this assumption, projects (bundles) with unequal lives can be accommodated in the analysis. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  14. 12.1 Flexibility Issue • Given a budget of, say, $b: • This constraint may marginally disallow an acceptable project that is next in line for acceptance! • How is this situation handled in practice? Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  15. 12.1 Marginally Exceeding the Budget • Assume project A has a PW(i%) > 0. • If the addition of A to the selected set will cause the budget to be overspent by, say, $1,000 – should A be included? • Mathematically – NO! • In practice – A might be added and the budget limit “b” slightly readjusted to accommodate A’s addition. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  16. 12.1 Suggested Objective Function • ROR can be used to select projects; but must apply the incremental ROR method; • It is suggested that PV be used as the criteria in the associated objective function. • It is easier to apply PV at the MARR to all of the projects. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  17. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 12.2. Capital Rationing Using PW Analysis of Equal-Life Projects Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  18. 12.2 Rationing for Equal-Life Projects • Given a set of candidate projects whose lives are all equal; • Calculate the PV(MARR) for each project; • Formulate all of the mutually exclusive bundles from the set; Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  19. 12.2 Mutually Exclusive Bundles • Assume you have 4 projects having equal lives; • Candidate set = { A, B, C, D}; • The Do-Nothing (DN) alternative is also an option: Set = { DN, A, B, C, D }; • Given 4 projects, how many mutually exclusive bundles can be formed? Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  20. 12.2 Number of Bundles • Given “m” projects (independent), how many possible bundles are there? • Rule: Total no. of bundles = 2m; • 2m – 1 bundles if you cut out the DN option; • If m = 4 then 24 – 1 = 15 bundles (excluding the DN option). Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  21. 12.2 Number of Bundles • Manual approaches are not well suited for “large” numbers of candidate projects. • If m = 30 then 230 bundles to evaluate; Equal 1,073,741,824 bundles! • Require a more sophisticated approach other than a manual analysis. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  22. 12.2 Example of Bundling: m =4 Assume: ProjectInvestment $ A $10,000 B 5,000 C 8,000 D 15,000 $38,000 Total Assume b = $25,000 (The budget max.) What, then, is the optimal combination of projects? Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  23. 12.2 Example of Bundling: m =4 Assume: ProjectInvestment $ A $10,000 B 5,000 C 8,000 D 15,000 $38,000 Total Assume a b = $25,000 (The budget max.) Feasible bundles must have Positive PV and a total Budget that does not Exceed $25,000/ Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  24. 12.2 Possible Combinations Where m = 4 1. Do Nothing; 13. ABD 2. A 14. BCD 3. B 15. CD 4. C 16. ACD 5. D 6. AB 7. AC 8. AD 9. ABC 10. ABCD 11. BC 12. BD TOTAL ENUMERATION OF ALL 16 POSSIBLE MUTUALLY EXCLUSIVE COMBINATIONS Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  25. 12.2 Ordering the Combinations • Order the bundles from low to high based upon the total budget requirement of the combination. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  26. 12.2 Rank-Ordered Bundles: Total Investment Eliminate Those Mutually Exclusive Bundles That Exceed the $25,000 Budget Limitation. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  27. 12.2 Reduced Budget – Feasible Set Four bundles are infeasible: they exceed the budget amt. dropped from further consideration. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  28. 12.1 The Feasible Set The feasible set of mutually exclusive bundles. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  29. 12.2 Bundle Selection • The previous slide shows the feasible set; • None of the combinations exceed the budget limitation; • If one has the PV of each bundle, then pick the bundle with the maximum present value. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  30. 12.2 General Solution Technique • Develop all mutually exclusive bundles. • Eliminate those bundles whose total investment requirement exceeds the budget amount. • Within each bundle, sum the NCF’s for all projects in that bundle and compute the PV of the bundle at the MARR. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  31. 12.2 General Solution Technique • Let “j” equal the bundle number; • PWj = PW of bundles net cash flows – the initial investment. • Select the bundle with the largest PWj value. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  32. 12.2 Example 12.1 (P407) • Assume “b” = 20 million; • Number of candidate projects = 5 • Set = {DN, A,B,C,D,E} • No. of bundles = 25 = 32 possible combinations. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  33. 12.2 Example for “m” = 5 Projects Amounts are in units of $1,000. 25 Possible Bundles:”E” is removed $21 Million > 20 Million Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  34. 12.2 Example 12.1: Feasible Bundles Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  35. 12.2 Example 12.1 • Max Bundle is { CD }; • Left over budget = 6 million – assumed to be invested at the MARR Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  36. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 12.3 Capital Rationing Using PW Analysis of Unequal-Life Projects Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  37. 12.3 Unequal-Life Projects • It is assumed that reinvestment of positive net cash flows occurs at the MARR from the time they are realized until the end of the longest-lived project. • Use of the LCM of lives is not necessary for the capital budgeting model. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  38. 12.3 Example 12.2: Unequal Lives (P409) 24 = 16 Bundles to evaluate: 8 are feasible! Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  39. 12.3 Example 12.2: PV Summary Select { AC } for $16,000: $4,000 assumed invested at the MARR Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  40. 12.3 Two Independent Bundles A and B • Assume two independent projects, A and B; • Life of A = nA; • Life of B = nB; • A B (unequal lives). • Assume both A and B have uniform series. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  41. 12.3 Notation for Unequal Life Problem • nL = life of the longer lived project; • nj = life of the shorter lived project; • nA = Life of A • nB = Life of B • Diagram the two cash flows on the next slide. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  42. FWB PWB FWA PWA FW nL Investment For A 12.3 Unequal-Life Projects; A and B nB = nL B Longer life Project: i = MARR Investment For B Period of reinvestment @ MARR A nA Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  43. FWA PWA FW nL Investment For A 12.3 Shorter Project: A with Reinvestment A Period of reinvestment @ MARR nA • Compute the FW from nA out to nL of A. • Assumed to be reinvested at the MARR rate! • Yield FWA given reinvestment at the MARR rate. • Then, find PWA from FWA at the MARR rate. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  44. 12.3 Bundling A and B: Unequal Lives • Now A and B have unequal lives; • If reinvestment at the MARR is assumed for the shorter-life project out to the life of the longer life project, then: • One can create a bundle of A and B by computing; • PWBundle = PWA + PWB Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  45. 12.3 C and D in Example 12.2 • Find the PW of the bundle { C,D }. • Unequal life situation. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  46. 0 1 2 3 4 5 6 7 8 9 12.3 Bundle { C, D }. Over 9 years FW = $57,111 • Bundle Cash Flow: $2,540/yr (D) $2,680 (C) • FW(C,D, @ 15%) of + CF’s = +$57,111. • PW(C,D @ 15%) = -$16,000 + 57,111(P/F,15%,9) • = +$235.00 -$16,000 Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  47. 12.3 Bundle Analysis Summary • Given the life of the longest project; • Find the PW(MARR) given reinvestment where required for all bundles; • Throw out any bundles with negative PW’s unless other constraints require their presence. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  48. 12.3 Setting Up to Solve Complex Problems • Solution of complex or large numbers of bundles is best approached by applying linear programming formulations; • The next section describes a 0-1 Linear Programming formulation to the capital budgeting problem. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  49. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER 12 12.4 Capital Budgeting Problem Formulation Using Linear Programming Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  50. 12.4 Application of Integer LP • Formulate as an Integer LP model; • Decision variable is a { 0, 1 } variable; • Let x  {0,1}; • Means: Can have all of a project or none of the project. Partial funding is not permitted! • Objective Function: • Max {Present worth of the selected bundles} • Subject to budget and other constraints. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

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