ME 443

1. ME 443 COMPARISON OF ALTERNATIVES Prof. Dr. Mustafa Gökler

2. INTRODUCTION A systematic approach that can be used in comparing the economic worths of engineering investment alternatives is summarized as follows: 1. Define the set of feasible, mutually exclusive alternatives to be compared. (Mutually exclusive means that no more than one alternative can be chosen)

3. INTRODUCTION 2. Define the planning horizon to be used in the comparison. 3. Develop the cash flow profiles for each alternative. 4. Specify the MARR to be used. 5. Compare the alternatives using a specified measure of worth. 6. Perform supplementary analyses. 7. Select the preferred alternative.

4. DEFINING INVESTMENT ALTERNATIVES An individual investment alternative selected from a set of alternatives can be made up of several investment proposals. Investment proposals are distinguished from investment alternatives by noting that investment alternatives are decision options; investment proposals are single projects or undertakings that are being considered as investment possibilities.

5. PROPOSAL-ALTERNATIVE Developing Investment Alternatives from Investment Proposals Proposals Alternative xA xB xC Explanation 1 0 0 0 Do nothing 2 0 0 1 Accept proposal C only 3 0 1 0 Accept proposal B only 4 0 1 1 Accept proposal B and C only 5 1 0 0 Accept proposal A only 6 1 0 1 Accept proposal A and C only 7 1 1 0 Accept proposal A and B only 8 1 1 1 Accept all three proposal

6. PROPOSAL-ALTERNATIVE Among the alternatives formed, some might not be feasible, depending on the restrictions or constraints placed on the problem. To illustrate, there might be a budget limitation that precludes the possibility of combining all three proposals; thus, Alternative 8 would be eliminated.

7. PROPOSAL-ALTERNATIVE Additionally, some of the proposals might be mutually exclusive proposals. For example, Proposals A and B might be alternative computer configurations, and only one is to be selected; in this case Alternative 7 would be eliminated from consideration.

8. PROPOSAL-ALTERNATIVE Other proposals might be contingent proposalssothat one proposal cannot be selected unless another proposal is also selected. As an illustration of a contingent proposal, Proposal C might involve the procurement of output device, which require the selection of the computer configuration associated with Proposal B.

9. PROPOSAL-ALTERNATIVE In such a situation, Alternatives 2 and 6 would be infeasible. Feasible Alternatives : 1,3,4,5

10. EXAMPLE(5.5) Suppose a planning horizon of 5 years is used and there are three investment proposals. Cash flow profiles for the proposals are given in Table 5.4. A budget limitation of $50,000 is available for investment among the proposals. Proposal B is contingent on proposal A, and Proposals A and C are mutually exclusive

11. EXAMPLE

12. EXAMPLE(5.5) Based on the restrictions associated with the combinations of proposals, only four investment alternatives are to be considered. These are developed in Table 5.5. Alternative 0 is the “do-nothing” alternative; Alternative 1 involves Proposal C alone; Alternative 2 involves Proposal A alone; and Alternative 3 involves a combination of Proposals A and B alone. The cash flow profiles for the four alternatives are given in Table 5.6.

13. EXAMPLE

14. EXAMPLE

15. DEFINING THE PLANNING HORIZON In comparing engineering investment alternatives, it is important to compare them over a common period of time. We define that period of time to be the planning horizon.

16. DEFINING THE PLANNING HORIZON Some commonly used methods for determining the planning horizon to use in economy studies include: 1. Least common multiple of lives for the set of feasible alternatives, denoted T. 2. Shortest life among alternatives, denoted Ts. 3. Longest life among alternatives, denoted Tl 4. Some other period of time. ^

17. EXAMPLE Alternative A - 3 years, B - 6 years, C – 5 years 1. Least common multiple of lives for the set of feasible alternatives, denoted T = 30 years 2. Shortest life among alternatives, denoted Ts = 3 years 3. Longest life among alternatives, denoted Tl =6 years 4. Some other period of time. T=5, T=10, T=2 etc. ^

18. DEVELOPING CASH FLOW PROFILES Specially desiged forms are often provided for aiding the analist in developing cash flow profiles and conducting the analysis. Some examples are shown in the text book.

19. SPECIFYING MARR -minimum attractive rate of return (MARR), required rate of return, return on investment, discount rate. -The discount rate that is specified, establishes the firm’s MARR in order to for the investment to be justified. - The interest paid for the use of money is a cost of money.

20. SPECIFYING MARR MARR is generally taken as the bank interest rate. Some other approaches used to establish the MARR include the following: 1. Add a fixed percentage to the firm's cost of capital. 2. Average rate of return over the past 5 years is used as this year's MARR.

21. SPECIFYING MARR 3. Use different MARR for different planning horizons. 4. Use different MARR for different magnitudes of initial investment. 5. Use different MARR for new ventures than for cost-improvement projects.

22. SPECIFYING MARR 6. Use as a management tool to stimulate or discourage capital investments, depending on the overall economic condition of the firm. 7. Use the average stockholder's return on investment for all companies in the same industry group.

23. COMPARING ALTERNATIVES • There are two types of approach • Ranking Approach • Incremental Approach

24. COMPARING ALTERNATIVES 1. Ranking Approach: Computing the PW (or AW or FW) of each alternative and recommending the one having the greatest PW (or AW or FW)

25. COMPARING ALTERNATIVES 2.Incremental Approach : Computing the PW of each increment of investment and select or reject increments dependimg upon whether or not they have positive or negative worth.

26. COMPARING ALTERNATIVES In Incremental approach, the particular increment is justified if PW > 0 FW > 0 AW > 0 IRR > MARR ERR > MARR SIR > 1

27. COMPARING ALTERNATIVES The Philosophy about incremental apprach leads the following guideline principles 1. Each increment of investment capital must justify itself (by sufficient rate of return on that investment)

28. COMPARING ALTERNATIVES 2. Compare a higher investment alternative against a lower investment alternative only if that lower investment alternative is justified.

29. COMPARING ALTERNATIVES 3. Choose the alternative project that requires the highest investment for which each increment of additional capital is justified. The justified alternative that requires the least investment capital is considered as the BASE Alternative

30. EXAMPLE

31. EXAMPLE

32. EXAMPLE (PW) 1. a) PW (Ranking Approach) The present worth of Alternative 0, the do nothing alternative, is zero. PW0(15%) =0 PW1(15%) = $4500(P|A 15,5) = $4500(3.3522)= $15,085 PW2(15%) = = -$50,000 + $20,000(P|A 15,5) = -$50,000 + $20,000(3.3522) = $17,044 PW3(15%) = -$75,000 + $20,000(P|A 15,5) + $5000(P|G 15,5) = -$75,000 + $20,000(3.3522) + $5000(5.7751) = $20,920 Since Alternative 3 has the greatest present worth, it would be recommended. PW0 <PW1 <PW2 <PW3

33. EXAMPLE (PW) 1. b) PW (Incremental Approach) Using an incremental approach, since no other alternative requires a smaller initial investment than Alternative 0, it will be used as the base for incremental comparison. Based on a rank ordering of alternatives by the size of the initial investment required, the first incremental comparison will be between Alternatives 0 and 1.

34. EXAMPLE (PW) If the present worth of the incremental difference is positive, then Alternative 1 will be preferred to Alternative 0, and it will become the new base for incremental comparison; if the present worth of the incremental difference is negative, then Alternative 0 will remain the base, and Alternative 1 will be discarded from further consideration.

35. EXAMPLE (PW) PW0(15%) =0 PW1- 0 (15%) = $4500(P|A 15,5) = $4500(3.3522)= $15,085 PW1- 0 > 0, Alternative 1 is preferred to Alternative 0. Next, we look at the increment of investment required to go from Alternative 1 to Alternative 2. The present worth of the incremental investment will be PW2-1 (15%) = - $50,000 + $15,500(P|A 15,5) = $1959 PW2-1 > 0Alternative 2 is preferred to Alternative 1.

36. EXAMPLE (PW) Next, we look at the incremental investment needed to go to Alternative 3 from Alternative 2. The incremental present worth will be PW3-2 (15%) = -$25,000 + $5000(P|G 15,5)= $3876 Since PW3-2 > 0, Alternative 3 is preferred to Alternative 2. Since no additional alternatives are available, we conclude that Alternative 3 is the most economic choice.

37. EXAMPLE (AW) 2.a) AW (Ranking Approach) AW0(15%) =0 AW1(15%) = $4500 AW2(15%) =-$50,000(A|P 15,5) + $20,000 = -$50,000(0.2983) + $20,000 = $5085/year AW3(15%) = - $75,000(A|P 15,5) + $20,000 + $5000(A|G 15,5) = -$75,000(0.2983) + $20,000 + $5000(1.7228) = $6242/year Alternative 3 is recommended since it has the greatest annual worth.

38. EXAMPLE (AW) 2.b) AW (Incremental Approach) AW0(15%) =0 AW1- 0 (15%) = $4500 Since AW1- 0 > 0, Alternative 1 is justified. AW2-1 (15%) = - $50,000(A|P 15,5) + $15,500 = $585/year > O (Prefer Alternative 2 to 1) AW3-2 (15%) = -$25,000(A|P 15,5) + $5000(A|G 15,5) = $1157/year > O (Prefer Alternative 3 to 2) Alternative 3 is the most economic choice.

39. EXAMPLE (FW) 3.a) AW (Ranking Approach) FW0(15%) =0 FW1(15%) = $4500(F|A 15,5) = $30,341 FW2(15%) = - $50,000(F|P 15,5) + $20,000(F|A 15,5) = $34,278 FW3(15%) = - $75,000(F|P 15,5) + $20,000(F|A 15,5) + $5000(P|G 15,5)(F|P 15,5) = $42,073 We prefer Alternative 3 since it has the greatest future worth.

40. EXAMPLE (FW) 3.b) FW (Incremental Approach) FW0(15%) =0 FW1- 0 (15%) = $4500(F|A 15,5) = $30,341 > O (Prefer Alternative 1 to 0) FW2-1 (15%) = - $50,000(F|P 15,5) + $15,500(F|A 15,5) = $3937 > O (Prefer Alternative 2 to 1) FW3-2 (15%) = -$25,000(F|P 15,5) + $5000(P|G 15,5) (F|P 15,5)= $7795 > O (Prefer Alternative 3 to 2) Alternative 3 is the most economic choice.

41. EXAMPLE (IRR) Computing the IRR for each individual alternatives and choose one having the greatest rate is WRONG. In this case, the fact is ignored that any remaining fund will earn only the MARR. In other words, ranking approach for IRR is WRONG.

42. EXAMPLE (IRR) Although it is recommended to use an incremental cash flow approach in applying the IRR method, an alternative approach is possible; it is referred to as the AGGREATE (TOTAL) CASH FLOW APPROACH

43. EXAMPLE (IRR) AGGREATE (TOTAL) CASH FLOW APPROACH The philosophy underlying the aggregate cash flow approach is to maximize the aggregate (or total) return obtained by investing in one of the investment alternatives and the "reserve account."The reserve account consists of the uninvested funds, which are assumed to be earning a return at a rate equal to the MARR.

44. EXAMPLE (IRR) Suppose two investment alternatives, A and B, are being considered: A requires an investment of $10,000, and B requires an investment of $50,000. Suppose A will return $2000/year forever; hence, an IRR of 20% is obtained. Suppose B will return $8000/year forever; in this case, an IRR of 16% is obtained. Now, suppose the MARR is 12%.

45. EXAMPLE (IRR) The aggregate cash flow approach proceeds in the following way. For B to be a feasible investment alternative, $50,000 must be available for investment. Investing in A means that $10,000 will return $2000/year and the reserve account will return 12% of the difference in the amount invested and the amount available for investment (i.e., (0.12)($40,000) or $4800/year).

46. EXAMPLE (IRR) By investing in A, the aggregate return will be $6800/year from an aggregate investment of $50,000. The aggregate rate of return will be 13.6%. By investing the full amount in B, the aggregate rate of return will be 16%. In this case, B is preferred because it has the greatest aggregate rate of return.

47. EXAMPLE (IRR) Using an incremental cash flow approach, we begin with the alternative requiring the smallest initial investment, A, IRR = 20% > MARR; so, A is an acceptable base. An incremental investment of $40,000 is required to step up to B from A; the incremental returns resulting from the incremental investment will be $6000/year; thus, the incremental IRR will be 15%, which is greater than the MARR of 12%. Hence, B is preferred to A.

48. EXAMPLE

49. EXAMPLE (IRR) IRR by INCREMENTAL APPROACH Between Alternatives 1 and 0, there is no incremental investment, but there are incremental returns of $4500 in each of years 1 to 5. The incremental IRR is therefore IRR1-0= (Prefer 1 over 0). Between Alternatives 2 and 1, FW2-1(i) = $0 = -$50,000(F|P i,5) + $15,500(F|A i,5) Trial-and-error,IRR2-1= 16.51% > MARR of 15% (Prefer 2 over 1).

50. EXAMPLE (IRR) Between Alternatives 3 and 2. FW(i)=$0 =-$25,000(F|P i,5)+ $5,000(P|G i,5)(F|P i,5) IRR3-2= 19.35% > 15% MARR (Prefer 3 over 2). Alternative 3 is the most economic choice.