1 / 64

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.

elie
Download Presentation

CHAPTER 12

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. • Chapter Summary 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; • Generally more projects for funding consideration than there are funds available to fund. • 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: • A set of projects ( two or more) are independent if: • 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 in the set does not impact to accept or reject 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. • The candidate set of projects is all projects under consideration for funding from a given budget amount. • 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; • Partial projects are not permitted; • A given budget constraint restricts the total amount available for investment; • Objective: maximize the return on investment using a measure of worth. 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; • Over the project life; • 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: • Equal Life for the alternatives; • No longer valid for capital budgeting; • No life cycle beyond the estimated life of each bundle; • PW over the respective life of each independent project; • Implicit Reinvestment Assumption is in place. 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 Use of ROR – To Select • ROR can be used to select projects; • However – must apply the incremental ROR method (cumbersome); • Recall, ROR and NPV may not rank (select) projects the same; • Different reinvestment assumptions within the two methods; • Use incremental ROR to select! Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  17. 12.1 Suggested Objective Function • It is suggested that PV be used as the criteria in the associated objective function as opposed to ROR. • Probably best to not use the incremental ROR ranking; • 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

  18. 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

  19. 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

  20. 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

  21. 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

  22. 12.2 Number of Bundles • Manual approaches are not well suited for “large” numbers of candidate projects. • If m = 6 then 26 = 64 bundles to evaluate; • 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

  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.) One cannot have all 4 projects because of the budget limitation. What, then, is the optimal combination of projects? Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  24. 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.) From the 15 possible combinations, which one bundle of projects will maximize the present worth of the selected bundle? Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  25. 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

  26. 12.2 Steps for a Manual Analysis • Identify the investments and cash flows for all feasible combinations of the projects where each combination represents an economically mutually exclusive bundle. Consider all possible combinations by taking the projects one at a time, two at a time, etc., and listing. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  27. 12.2 Possible Combinations Where m = 4 1. Do Nothing; 14. BCD 2. A 15. CD 3. B 16. ACD 4. C 5. D 6. AB 7. AC 8. AD 9. ABC 10. ABCD 11. BC 12. BD 13. ABD TOTAL ENUMERATION OF ALL 16 POSSIBLE MUTUALLY EXCLUSIVE COMBINATIONS Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 12.2 Example 1 • 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

  36. 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

  37. 12.2 Example 1: Feasible Bundles Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  38. 12.2 • 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

  39. 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

  40. 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

  41. 12.3 Example 2: Unequal Lives 24 = 16 Bundles to evaluate: 8 are feasible! Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  42. 12.3 Example 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

  43. 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 A and B have the same net cash flow each time period. Blank & Tarquin: 5th edition. Ch.12 Authored by Dr. Don Smith, Texas A&M University

  44. 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

  45. 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

  46. 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

  47. 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

  48. 12.3 C and D in Example 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

  49. 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

  50. 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

More Related