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Present Worth Analysis: Formulating and Evaluating Mutually Exclusive and Independent Project Alternatives

Learn how to formulate and evaluate mutually exclusive and independent project alternatives using the present worth analysis method. Understand how to select the best combination of projects based on given criteria and constraints.

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Present Worth Analysis: Formulating and Evaluating Mutually Exclusive and Independent Project Alternatives

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  1. Mc Graw Hill ENGINEERING ECONOMYFifth Edition Blank and Tarquin CHAPTER V PRESENT WORTH ANALYSIS Adopted and modified by Dr. W-.W. Li of UTEP, Fall, 2003 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  2. 5.1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES • Mutually Exclusive set is where a candidate set of alternatives exist (more than one) • Objective: Pick one and only one from the set. • Once selected, the remaining alternatives are excluded. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  3. 5.1 INDEPENDENT PROJECT SET • Given a set of alternatives (more than one) • The objective is to: • Select the best possible combination of projects from the set that will optimize a given criteria. • Subjects to constraints • More difficult problem than the mutually exclusive approach Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  4. 5.1 FORMULATING MUTUALLY EXCLUSIVE ALTERNATIVES • Mutually exclusive alternatives compete with each other. • Independent alternatives may or may not compete with each other • The independent project selection problem deals with constraints and may require a mathematical programming or bundling technique to evaluate. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  5. 5.1 Type of Alternatives • Revenue/Cost – the alternatives consist of cash inflow and cash outflows • Select the alternative with the maximum economic value • Service – the alternatives consist mainly of cost elements • Select the alternative with the minimum economic value (min. cost alternative) Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  6. 5.1 Evaluating Alternatives • In part, the role of the engineer to properly evaluate alternatives from a technical and economic view • Must generate a set of feasible alternatives to solve a specific problem/concern Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  7. Do Nothing Alt. 1 Alt. 2 Alt. m 5.1 Alternatives Analysis Selection Problem Execution Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  8. 5.2 Present Worth Approach A process of obtaining the equivalent worth of future cash flows to some point in time – called the Present Worth At an interest rate usually equal to or greater than the Organization’s established MARR. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  9. 5.2 THE PRESENT WORTH METHOD P(i%) = P( + cash flows) + P( - cash flows) If P(i%) > 0 then the project is deemed acceptable. If P(i%) < 0 – the project is usually rejected If P(i%) = 0 Present worth of costs = Present worth of revenues: Indifferent! Note: If the present worth of a project turns out to = “0,” that means the project earned exactly the discount rate that was used to discount the cash flows! The interest rate that causes a cash flow’s NPV to equal “0” is called the Rate of Return of the cash flow! Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  10. 5.2 PRESENT WORTH: Special Applications • Present Worth of Equal Lived Alternatives • Alternatives with unequal lives: Beware • Capitalized Cost Analysis • Require knowledge of the discount rate before we conduct the analysis Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  11. 5.2 PRESENT WORTH: Equal Lives • Present Worth of Equal Lived Alternatives – straightforward • Compute the Present Worth of each alternative and select the best, i.e., smallest if cost and largest if profit. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  12. 5.2 PRESENT WORTH: Example Consider: Machine AMachine B First Cost $2,500 $3,500 Annual Operating Cost 900 700 Salvage Value 200 350 Life 5 years 5 years i = 10% per year Which alternative should we select? Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  13. F5=$200 F5=$350 MA 0 1 2 3 4 5 0 1 2 3 4 5 A = $900 $2,500 MB A = $700 $3,500 5.2 PRESENT WORTH: Cash Flow Diagram Which alternative should we select? Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  14. 5.2 PRESENT WORTH: Solving • PA =-2,500 - 900 (P|A, .10, 5) + 200 (P|F, .01, 5) • =-2,500 - 900 (3.7908) + 200 (.6209) • = -2,500 - 3,411.72 + 124.18 = -$5,788 • PB = -3,500 - 700 (P|A, .10, 5) + 350 (P|F, .10, 5) • = -3,500 - 2,653.56 + 217.31 = -$5,936 SELECT MACHINE A: Lower PW cost! Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  15. 5.3 PRESENT WORTH: Different Lives Comparison must be made over equal time periods • Compare over the least common multiple, LCM, for their lives Note: if the lives of the alternatives are not equal, one must create or force a study period where the life is the same for all of the alternatives. One cannot effectively compare the PW of one alternative with a study period different from another alternative that does not have the same study period. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  16. 5.3 PRESENT WORTH: Lowest Common Multiple of Lives • If the alternatives have different study periods, you find the lowest common life for all of the alternatives in question. • Example: {3,4, and 6} years. The lowest common life is 12 years. • Evaluate all over 12 years for a PW analysis. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  17. 5.3 PRESENT WORTH: Example Unequal Lives • EXAMPLE Machine A Machine B First Cost $11,000 $18,000 Annual Operating Cost 3,500 3,100 Salvage Value 1,000 2,000 Life 6 years9 years i = 15% per year Note: Where costs dominate a problem it is customary to assign a positive value to cost and negative to inflows Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  18. Machine A F6=$1,000 0 1 2 3 4 5 6 A 1-6 =$3,500 F6=$2,000 $11,000 0 1 2 3 4 5 6 7 8 9 A 1-9 =$3,100 Machine B $18,000 5.3 PRESENT WORTH: Unequal Lives i = 15% per year LCM(6,9) = 18 year study period will apply for present worth Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  19. 6 years 6 years 6 years Cycle 1 for A Cycle 2 for A Cycle 3 for A Cycle 1 for B Cycle 2 for B 9 years 9 years 18 years 5.3 Unequal Lives: 2 Alternatives Machine A Machine B i = 15% per year LCM(6,9) = 18 year study period will apply for present worth Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  20. 5.3 Example: Unequal Lives Solving • LCM = 18 years • Calculate the present worth of a 6-year cycle for A PA = -11,000 - 3,500 (P|A, .15, 6) + 1,000 (P|F, .15, 6) = -1,000 - 3,500 (3.7845) + 1,000 (.4323) = -$23,813, which occurs at time 0, 6 and 12 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  21. 0 6 12 18 $23,813 $23,813 $23,813 5.3 Example: Unequal Lives Machine A PA= -23,813-23,813 (P|F, .15, 6)- 23,813 (P|F, .15, 12) = -23,813 - 10,294 - 4,451 = -$38,558 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  22. F6=$2,000 0 1 2 3 4 5 6 7 8 9 A 1-9 =$3,100 $18,000 5.3 Unequal Lives Example: Machine B • Calculate the Present Worth of a 9-year cycle for B Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  23. 5.3 9-Year Cycle for B Calculate the Present Worth of a 9-year cycle for B PB = -18,000-3,100(P|A, .15, 9) + 2,000(P|F, .15, 9) = -18,000 - 3,100(4.7716) + 2,000(.2843) = -$33,359 which occurs at time 0 and 9 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  24. $32,508 $32,508 0 9 18 5.3 AlternativeB – 2 Cycles Machine A: PW =$38,558 PB = -32,508 - 32,508 (P|F, .15, 9) = -32,508 - 32,508(.2843) PB = -$41,750 Choose Machine A Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  25. 5.3 Unequal Lives – Assumed Study Period • Study Period Approach • Assume alternative: 1 with a 5-year life • Alternative: 2 with a 7-year life Alt-1: N = 5 yrs LCM = 35 yrs Alt-2: N= 7 yrs Could assume a study period of, say, 5 years. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  26. 5.3 Unequal Lives – Assumed Study Period • Assume a 5-yr. Study period • Estimate a salvage value for the 7-year project at the end of t = 5 • Truncate the 7-yr project to 5 years Alt-1: N = 5 yrs Now, evaluate both over 5 years using the PW method! Alt-2: N= 7 yrs Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  27. 5.4 FUTURE WORTH APPROACH • FW(i%) is an extension of the present worth method • Compound all cash flows forward in time to some specified time period using (F/P), (F/A),… factors or, • Given P, the F = P(1+i)N Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  28. 5.4 Applications of Future Worth • Projects that do not come on line until the end of the investment period • Commercial Buildings • Marine Vessels • Power Generation Facilities • Public Works Projects • Key – long time periods involving construction activities Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  29. 5.4 Future Worth Example (Figure 5.3) • See Example 5.3 • Calculate the Future Worth of determining the selling price in order to earn exactly 25% on the investment • Draw the cash-flow diagram!! Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  30. 5.5 CAPITALIZED COST • CAPITALIZED COST- the present worth of a project that lasts forever. • Government Projects • Roads, Dams, Bridges (projects that possess perpetual life) • Infinite analysis period Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  31. 5.5 Derivation for Capitalized Cost • Start with the closed form for the P/A factor • Next, let N approach infinity Or, CC(i%) = A/i Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  32. ………………….. 1 2 3 4 5 .. N=inf. A=$50/yr P = ? 5.5 CAPITALIZED COST Assume you are called on to maintain a cemetery site forever if the interest rate = 4% and $50/year is required to maintain the site. Find the PW of an infinite annuity flow Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  33. ………………….. 1 2 3 4 5 .. N=inf. A=$50/yr Find the PW of an infinite annuity flow P = ? 5.5 CAPITALIZED COST P0 = A[P/A,i%,N] P0=A(1/i) Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  34. 5.5 CAPITALIZED COST • P0 = $50[1/0.04] • P0 = $50[25] = $1,250.00 • Invest $1,250 into an account that earns 4% per year will yield $50 of interest forever if the fund is not touched and the i-rate stays constant. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  35. 5.5 CAPITALIZED COST: Endowments • Assume a wealthy donor wants to endow a chair in an engineering department. • The fund should supply the department with $200,000 per year for a deserving faculty member. • How much will the donor have to come up with to fund this chair if the interest rate = 8%/yr. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  36. 5.5 CAPITALIZED COST: Endowed Chair The department needs $200,000 per year. P = $200,000/0.08 = $2,500,000 If $2,500,000 is invested at 8% then the interest per year = $200,000 The $200,000 is transferred to the department, but the principal sum stays in the investment to continue to generate the required $200,000 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  37. 5.5 Capitalized Cost Example • EXAMPLE Calculate the Capitalized Cost of a project that has an initial cost of $150,000. The annual operating cost is $8,000 for the first 4 years and $5000 thereafter. There is an recurring $15,000 maintenance cost each 15 years. Interest is 15% per year. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  38. $4,000 $8,000 $15,000 $15,000 $15,000 $15,000 0 1 2 3 4 5 6 7 15 30 ……… $150,000 5.5 Cash Flow Diagram “i”=15%/YR N= How much $$ at t = 0 is required to fund this project? The capitalized cost is the total amount of $ at t = 0, when invested at the interest rate, will provide annual interest that covers the future needs of the project. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  39. 5.5 CAPITALIZED COST - Example Continued • 1. Consider $4,000 of the $8,000 cost for the first four years to be a one-time cost, leaving a $4,000 annual operating cost forever. • P0= 150,000 + 4,000 (P|A, .15, 4) = $161,420 2.855 Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  40. 0 15 30 45 60 …….. ……. 5.5 CAPITALIZED COST - Continued • Recurring annual cost is $4,000 plus the equivalent annual of the 15,000 end-of-cycle cost. Take any 15-year period and find the equivalent annuity for that period using the F/A factor. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  41. ……. 0 15 30 45 60 …….. $15,000 A for a 15-year period 5.5 CAPITALIZED COST: One Cycle Take any 15-year period and find the equivalent annuity for that period using the F/A factor Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  42. 5.5 CAPITALIZED COST • 2. Recurring annual cost is $4,000 plus the equivalent annual of the 15,000 end-of-cycle cost. • A= -4,000 - 15,000 (A|F, .15, 15) = -4,000 - 15000 (.0210) = -$4,315 • Recurring costs = -$4,315/i = -4,315/0.15 =-$28,767/yr Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  43. 5.5 CAPITALIZED COST • Capitalized Cost = 161,420 + 5315/.15 = $196,853 • Thus, if one invests $196,853 at time t = 0, then the interest at 15% will supply the end-of-year cash flow to fund the project so long as the principal sum is not reduced or the interest rate changes (drops). Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  44. 5.6 Payback Period Analysis • Two forms for this method • Discounted Payback Period (uses an interest rate) • Conventional Payback Period (does not use an interest rate) • Payback is the period of time it takes for the cash flows to recover the initial investment. Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  45. 5.6 Payback Period Analysis • Discounted Payback Approach • Find the value of np such that: Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  46. 5.6 Payback for Example 5.8 • Discounted • Machine A: 6.57 years • Machine B: 9.52 years • Undiscounted • Machine A: 4.0 years • Machine B: 6.0 years • Go with Machine A – lower time period payback to recover the original investment Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  47. 5.6 Payback Method Summarized • Payback is only a rough estimator of desirability • Use as an initial screening method • Avoid using this method as a primary analysis technique for selection projects • Totally avoid the no-return payback period Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  48. 5.7 Life Cycle Costs (LCC) • Extension of the Present Worth method • Used for projects over their entire life span where cost estimates are employed • Used for: • Military/Defense Projects • New Product Lines • Large construction projects Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  49. 5.7 Life Cycle Defined – Detailed Phases • Needs Assessment Phase • Conceptual Design Phase • Detailed Design Phase • Production/Construction Phase • Operation – (upgrading to extend) Phase • Retirement/Disposal Phase The life can be for years into the future Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

  50. Cost-$ TIME 5.7 Life Cycle: Two General Phases Cumulative Life Cycle Costs Acquisition Phase Operation Phase Blank & Tarquin: 5th Edition. Ch. 5 Authored By: Dr. Don Smith, Texas A&M University.

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