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ENGM 661

ENGM 661. Multiple Investment Alternatives Sensitivity Analysis . Learning Objectives for tonight:. Given two or more investment alternatives, be able to identify the mutually exclusive alternatives.

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ENGM 661

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  1. ENGM 661 Multiple Investment Alternatives Sensitivity Analysis

  2. Learning Objectives for tonight: • Given two or more investment alternatives, be able to identify the mutually exclusive alternatives. • Given two or more mutually exclusive investment alternatives, be able to determine the best alternative by • the present worth method • the annual worth method • the incremental rate-of-return • Given a problem description, be able the breakeven point between two or more investment alternatives. • Given a cash flow, be able to perform a sensitivity analysis on one or two parameters of the cash flow.

  3. Summary • NPW > 0 Good Investment • EUAW > 0 Good Investment • IRR > MARR Good Investment Note: If NPW > 0 EUAW > 0 IRR > MARR

  4. Multiple Investments • NPWA > NPWB Choose A • Must use same planning horizon • EUAWA > EUAWB Choose A • Same Planning Horizon implicit in computation • IRRA > IRRB Choose A • Must use Incremental Rate-of-Return IRRB-A < MARRChoose A

  5. Example Suppose we have two projects, A & B A B Initial cost $50,000 $80,000 Annual maintenance 1,000 3,000 Increased productivity 10,000 15,000 Life 10 10 Salvage 10,000 20,000

  6. 10 9 9 . . . 0 1 2 3 10 50 Present Worth A A NPW(10) = -50 + 9(P/A,10,10) + 10(P/F,10,10)

  7. 20 12 12 . . . 0 1 2 3 10 Present Worth B B 80 NPW(10) = -80 + 12(P/A,10,10) + 20(P/F,10,10)

  8. Conclusion NPWA > NPWB Choose A

  9. 10 9 9 . . . 0 1 2 3 10 50 Equivalent Worth A EUAW(10) = -50(A/P,10,10) + 9 + 10(A/F,10,10)

  10. 20 12 12 . . . 0 1 2 3 10 Equivalent Worth B EUAW(10) = -80(A/P,10,10) + 12 + 20(A/F,10,10)

  11. Conclusion EUAWA > EUAWB Choose A

  12. 30 115 1 2 3 4 5 100 100 Different Planning Horizons Example: Suppose MARR is 10%. Suppose also that we can invest in T-bill @15% or we can invest in a 5 year automation plan. A B NPW = 30(P/A,10,5) - 100 = $13,724 NPW = 115(1.1)-1 - 100 = $4,545 B

  13. Problem But this ignores reinvestment of T-bills for full 5-year period. 201,135 0 5 100 NPW = 201.135(P/F,10,5) - 100 = $24,889 A

  14. Conclusion Projects must be compared using same Planning Horizon

  15. 4,500 3,500 3 4,000 Example; NPW A NPW = -4 + 3.5(P/A, 10,3) + 4.5(P/F,10,3) = -4 + 3.5(2.4869) + 4.5(.7513) = 8.085 = $8,085

  16. Example: NPW 5,000 3,000 B 3 6 NPW = -5 + 3(P/A,10,6) + 5(P/F,10,6) 5,000

  17. Example: NPW 5,000 3,000 B 3 6 NPW = -5 + 3(P/A,10,6) + 5(P/F,10,6) = -5 + 3(4.3553) + 5(.5645) 5,000

  18. Example: NPW 5,000 3,000 B 3 6 NPW = -5 + 3(P/A,10,6) + 5(P/F,10,6) = -5 + 3(4.3553) + 5(.5645) = 10.888 = $10,888 5,000

  19. Planning Horizons • Least Common Multiple • Shortest Life • Longest Life • Standard Planning Horizon

  20. 4,500 4,500 3,500 3 6 4,000 4,000 Example; NPW A NPW = -4 -4(P/F,10,3) + 3.5(P/A,10,6) + 4.5(P/F,10,3) + 4.5(P/F,10,6)

  21. Example: NPW 5,000 3,000 B 3 6 NPW = -5 + 3(P/A,10,6) + 5(P/F,10,6) 5,000

  22. Conclusion NPWA > NPWB Choose A

  23. 4,500 3,500 3 4,000 EUAW A EUAW = -4(A/P,10,3) + 3.5 + 4.5(A/F,10,3) = -4(.4021) + 3.5 + 4.5(.3021) = 3.251 = $3,251 Note: NPW = 3,251(P/A,10,6) = 3,251(4.3553) = $14,159

  24. EUAW 5,000 3,000 B 3 6 EUAW = -5(A/P,10,6) + 3 + 5(A/F,10,6) = -5(.2296) + 3 + 5(.1296) = 2.500 = $2,500 Note: NPW = 2,500(P/A,10,6) = $10,888 5,000

  25. EUAW Equivalent Uniform Annual Worth method implicitly assumes that you are comparing alternatives on a least common multiple planning horizon

  26. Class Problem Two alternatives for a recreational facility are being considered. Their cash flow profiles are as follows. Using a MARR of 10%, select the preferred alternative.

  27. 5 4 3 2 1 1 2 3 4 5 11 4 3 2 1 2 3 5 Critical Thinking A Use Net Present Worth and least common multiple of lives to compare alternatives A & B. B

  28. 5 4 3 2 1 1 2 3 4 5 11 4 3 2 1 2 3 5 Critical Thinking A Use Net Present Worth and least common multiple of lives to compare alternatives A & B. NPWA = 288(P/A,10,15) = 288(7.6061) = $2,191 NPWB = 926(P/A,10,15) = 926(7.6061) = $7,043 B

  29. Spreadsheet

  30. 226 A B 110 1 1 100 200 IRRA = 10% IRRB = 13% Incremental Analysis Suppose we have two investment alternatives

  31. 226 A B 110 1 1 100 200 IRRA = 10% IRRB = 13% Incremental Analysis Suppose we have two investment alternatives IRRB > IRRA Choose B

  32. Correction Investment alternative B costs $200. If we forego B for $100 invested in A, we have an extra $100 which can be invested at MARR. If MARR = 20%,

  33. 230 A 110 120 + = 1 1 1 100 100 200 IRRA = 15% Correction Investment alternative B costs $200. If we forego B for $100 invested in A, we have an extra $100 which can be invested at MARR. If MARR = 20%,

  34. 230 226 A B 1 1 200 200 IRRA = 15% IRRB = 13% Correction IRRA > IRRB Choose A

  35. 106,200 A B 60,000 1 1 50,000 90,000 IRRA = 20% IRRB = 18% Example 2 • Suppose we have $100,000 to spend and we have two mutually exclusive investment alternatives both of which yield returns greater than MARR = 15%.

  36. 106,200 A B 60,000 1 1 50,000 90,000 IRRA = 20% IRRB = 18% Example 2 IRRA > IRRB Choose A

  37. Example 2 106,200 A B 60,000 1 1 50,000 90,000 NPWA = -50 + 60(1.15)-1 = $2,170 NPWB = -90 + 106.2(1.15)-1 = $2,350 NPWB > NPWA Choose B

  38. Example 2 Remember, we have $100,000 available in funds so we could spend an additional $50,000 above alternative A or an additional $10,000 above alternative B. If we assume we can make MARR or 15% return on our money, then

  39. A 60,000 57,500 117,500 + = 1 1 1 50,000 50,000 100,000 i = 20% i = 15% ic = 17.5% Example 2 if we invest in A, we have an extra $50,000 which can be invested at MARR (15%).

  40. B 106,200 11,500 117,700 + = 1 1 1 90,000 10,000 100,000 i = 18% i = 15% ic = 17.7% Example 2 If we invest in B, we have an extra $10,000 which can be invested at MARR (15%).

  41. 117,500 117,700 A B 1 1 100,000 100,000 IRRA = 17.5% IRRB = 17.7% Example 2 IRRcB > IRRcA Choose B

  42. Incremental Analysis

  43. Differing Planning Horizons

  44. Differing Planning Horizons

  45. ENGM 661Engineering Economics forManagers Break Even & Sensitivity

  46. Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. Your boss asks you to figure out if it should be done.

  47. 25,000 1 2 3 4 5 100,000 Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. i = 15%

  48. 25,000 1 2 3 4 5 100,000 Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. i = 15% NPW = -100 + 25(P/A,15,5) = -16,196

  49. 25,000 1 2 3 4 5 100,000 Motivation Suppose that by investing in a new information system, management believes they can reduce inventory costs. After talking with software vendors and company accountants you arrive at the following cash flow diagram. i = 15% NPW = -100 + 25(P/A,15,5) = -16,196

  50. 40,000 1 2 3 4 5 100,000 Motivation Boss indicates $25,000 per year savings is too low & is based on current depressed market. Suggests that perhaps $40,000 is more appropriate based on a more aggressive market.

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