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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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