Chapter 6 Rate of Return Analysis: Multiple Alternatives 6-1

Transcription

1 Chapter 6 Rate of Return Analysis: Multiple Alternatives 6-1

2 LEARNING OBJECTIVES Work with mutually exclusive alternatives based upon ROR analysis 1. Why Incremental Analysis? 2. Incremental Cash Flows 3. Interpretation 4. Incremental ROR by PW 5. Incremental ROR by AW 6. Multiple alternatives 6-2

3 Sct 6.1 Why Incremental Analysis is N Necessary Assume we have two or more mutually exclusive alternative Objective: Which, if any of the alternatives is preferred? Prior Chapters: Use the PW or AW approach This chapter: We apply the ROR approach Present Worth: Equal service lives must apply When using the ROR method to select from among alternatives one must always use the incremental cash flow approach. 6-3

4 Ranking Inconsistency For some problems, PW and ROR may rank the same problems differently. Why? PW assumes reinvestment at the MARR or discount rate. ROR assumes reinvestment at the i* or i rate Two different reinvestment rate assumptions apply 6-4

5 Review of Problem Types INDEPENDENT AND MUTUALLY EXCLUSIVE ALTERNATIVES INDEPENDENT - Selection of one alternative does not effect the selection of others. Example: select all projects with a ROR> 20% MUTUALLY EXCLUSIVE - Selection on one alternative precludes the selection of others. Example: select the project with the highest ROR. 6-5

6 Sct 6.2 ROR for Mutual Exclusive Projects Given Two or more alternatives Rank the investments based upon their initial time t = 0 investment requirements Rank from low to high Summarize the investments in a tabular format 6-6

7 Tabular Format t Alt. A Alt. B Lowest Highest 0 $ $ B - A 1 $ $ 2 $ $ Find the ROR of this investment which is (B A) N $ $ 6-7

8 Example Two Investments: A and B A costs $30,000 at time t = 0 B costs $50,000 at time t = 0 MARR = 10% Life is 4 years 6-8

9 Example: A and B For this problem, A is superior to B based on PW and on ROR! A is ranked first B is ranked second 6-9

10 Form the Difference (B A) For mutually exclusive alternatives One should focus on the differences between the alternatives Differences are illustrated best by forming what is called the incremental investment (B-A) 6-10

11 Incremental Investment A B (B-A) Lowest First Cost investment Next Highest first Cost investment = The Incremental investment Find the ROR of this investment The investment (B-A) measures the difference between investment B and investment A The decision maker will go with A at first. If the extra investment in moving from A to B is worth it, then the decision maker will go with B. If the extra investment is not worth it then B is rejected and one would stay with A 6-11

12 Example for Two Alternatives A and B Computed 18% shows that B has the lowest PW cost and would be preferred to A Note: No ROR exists these are pure cost type problems 6-12

13 Focus on the Incremental Cash Flow (B-A) -$50,000 15,000 15,000 50,000 15,000 15,000 Question? Is it worth spending an additional $50,000 in the automatic machine in order to receive the incremental savings shown to the left? Compute the ROR of the incremental cash flows The incremental cash flows have a mixture of (+) and (-) signs As such, an i* value may indeed exist 6 21,

14 Incremental ROR = % Using the Excel IRR function, we observe that the i* value for the incremental investment is 35.95%. This exceeds the firm's MARR, so the higher cost alternative is worth the incremental investment 6-14

15 NPV Plot of A and B A is equivalent to B at incremental ROR rate of 35.95% NPV(i%) NPV PLOT-INC. C.F Note: The two PW plots intersect at 35.95% Disc. Rates 6-15

16 i* (B-A) = % The incremental i* (B-A) is greater than the firm s discount rate of 18% Since i* (B-A) > MARR, accept the increment and go with Alternative B This is the same decision if PW at 18% is found B is clearly the winner! 6-16

17 Sct 6.3 Interpretation of Rate of return on the Extra Investment The i* incremental is the ROR of the additional or incremental investment required to move from one project to the next most costly project If the i* incremental value is < MARR the increment is not worth it. Go with the lower investment cash flow 6-17

18 Multiple Alternatives If Cost-Revenue Problem Calculate the computed i* s for each alternative in the set Discard those alternatives whose i* value is less than the MARR they would lose anyway! Remember: If the calculated rate of return earned on an incremental investment is MARR, the alternative associated with the higher investment is preferred 6-18

19 Independent Projects If dealing with independent projects, one does not compute incremental investments among the candidate projects Rule: Accept all projects whose calculated ROR > MARR and stay within any budget limitations 6-19

20 Observation About the i* (B-A) value Given two mutually exclusive alternatives, A and B. The i* (B-A) value also represents the interest rate at which the two alternatives are economically equivalent. 6-20

21 Sct 6.4 Rate of Return Evaluation Using PW: Incremental and Breakeven The PW approach based on the development in Chapter 5 for ME (mutually exclusive) alternatives is: Given multiple alternatives If unequal lives, either Apply the LCM of life approach Or, establish a common project life (study period) 6-21

22 PW Approach for ME Alternatives Order (rank) the alternatives by their initial investment cost at time t = 0 The smaller investment alternative is A. The next highest investment cost is called B Compute the incremental investment (B-A) and cash flows Calculate the PW at i% of the incremental cash flows. Usually i% = MARR 6-22

23 PW Approach Mutually Exclusive Case Decision Rule: If PW(MARR) of (B-A) is > 0; Else, accept the increment go with the higher investment cost alternative. reject the increment and go with the lower investment cost option 6-23

24 ROR Case for Unique i* (B-A) For ME alternatives, using the incremental ROR approach, the steps are: Determine incremental cash flows Examine the cash flows for sign changes and apply the cumulative cash flow (CCF) or Norstrom s test from Chapter 7 If a unique i* (B-A) is indicated, solve for it and compare it to MARR If i* (B-A) > MARR, accept the increment, else reject 6-24

25 Incremental ROR: Example year project (merger) New equipment is required Two vendors (A and B) MARR = 15% Which vendor should be selected? Cost /Service Problem 6-25

26 Setup: B vs. A Note: Cannot determine the i* for A or B since there are no + cash flows involved. PW at 15% of A is less than the PW at 15% of B. Based upon computed PW, A is the least costly alternative. Select A! 6-26

27 Conclusion to PW Analysis; Moving to ROR Analysis We could stop now, because the PW at 15% has signaled that A is the winner! Lowest PW cost To proceed with a ROR analysis, the incremental ROR must be determined on the incremental investment (B-A) 6-27

28 Incremental Cash Flow Focus on (B-A) cash flow series 6-28

29 Incr. Cash Flow Results The PW at 15% of incremental cash flow is negative. Result: Reject the increment reject B in favor of A i* (B-A) is less than the MARR of 18%. Reject increment and go with A! Consistent Decision! 6-29

30 The Breakeven ROR The incremental i* (B-A) is the interest rate at which the two alternatives are economically equivalent. This special interest rate is called: Breakeven Interest Rate or, Fisherian Intersection Rate 6-30

31 Breakeven Rate Illustrated For Example 8.3 the NPV Plot is: NPV PLOT-INC. C.F NPV(i%) i*(b-a) rate; Alternatives are identical at this rate Disc. Rates 6-31

32 Conclusions i* (B-A) = % Given: The MARR = 15% For MARR < 12.65% extra investment is justified. Go with B For MARR > 12.65%, the extra investment is not justified: Go with A If MARR = 12.65%, both options are economically equivalent. 6-32

33 Sct 6.5 Rate of return Evaluation Using AW ROR approach requires comparison over an equal-service life When the lives are equal or unequal set up the AW relationship for the cash flows of each alternative Then solve 0 = AW B AW A for the i* value 6-33

34 Sct 6.6 Incremental ROR Analysis of Multiple Mutually Exclusive Alternatives Given N mutually exclusive alternatives Using the incremental ROR method Select the one alternative that Requires the largest investment, and at the same time Indicates that the extra investment over another acceptable investment is justified 6-34

35 Ranking Rules - Ordering 1. Order the alternatives from smallest to largest initial investment 2. Compute the cash flows for each alternative (assume or create equal lives) 3. If the alternatives are revenue-cost alternatives do the following Next slide 6-35

36 Revenue-Cost Alternatives 4. Compute the i* value for all alternatives in the considered set. If any alternative has an i* < MARR drop it from further consideration The candidate set will be those alternatives with computed i* values > MARR. Call this the FEASIBLE set 6-36

37 Revenue-Cost Alternatives Approach - continued Calculate i* for the first alternative The first alternative is called the DEFENDER The second (next higher investment cost) alternative is called the CHALLENGER Compute the incremental cash flow as (Challenger Defender) 6-37

38 Revenue-Cost Approach - continued 4. Compute i* Challenger Defender If i* Challenger Defender > MARR drop the defender and the challenger wins the current round. 5. If i* Challenger Defender < MARR, drop the challenger and the defender moves on to the next comparison round 6-38

39 Revenue-Cost - continued At each round, a winner is determined Either the current Defender or the current Challenger The winner of a given round moves to the next round and becomes the current DEFENDER and is compared to the next challenger 6-39

40 Revenue-Cost - continued 6. This process continues until there are no more challengers remaining. The alternative that remains after all alternatives have been evaluated is the final winner. 6-40

41 Costs Only (Service) Problems ROR Approach Remember Cost problems do not have computed RoR s since there are more cost amounts that revenue amounts (salvage values may exist) Thus there are no feasible i* s for each alternative 6-41

42 Costs Only Problems - Rules Rank the alternatives according to their investment requirements (low to high) For the first round compare: Challenger Defender Cash Flow Compute i* Challenger Defender If i* Challenger Defender > MARR, Challenger wins; else Defender wins 6-42

43 Costs Only Problems -continued The current winner now becomes the defender for the next round. Compare the current defender to the next challenger and compute i* Challenger Defender The winner becomes the current champion and moves to the next round as the defender Repeat until all alternatives have been compared. 6-43

44 Sct 6.7 Spreadsheet Application PW, AW, and ROR Analysis all in one Use the E-solve software for a PW, AW or ROR Analysis Create your own spreadsheet from scratch and employ the built in financial functions. Formatting is most important 6-44

45 Chapter Summary PW and AW methods are preferred methods for evaluating alternatives ROR can be used, but care must be taken If ROR, must perform an incremental analysis Two at a time (paired comparison of alternatives) is required 6-45