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Comparing Mutually Exclusive Alternatives & Capital Budgetting

Comparing Mutually Exclusive Alternatives & Capital Budgetting. Ref: Chapter 5 & section 10.4. Capital Budgeting. Trying to get the the most with what you’ve got. Look at all possible combinations of projects to create a capital plan

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Comparing Mutually Exclusive Alternatives & Capital Budgetting

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  1. Comparing Mutually Exclusive Alternatives&Capital Budgetting Ref: Chapter 5 & section 10.4

  2. Capital Budgeting • Trying to get the the most with what you’ve got. • Look at all possible combinations of projects to create a capital plan • Analyze each mutually exclusive alternative using one of the analysis methods

  3. Why Capital Budgeting • Capital Budgeting is critical in business and all organizations that have limited resources. • Defence budget and discretionary spending - whose money is it anyway? • Treasury board, the govt’s board of directors.

  4. Evaluation of Multiple Investment Alternatives • Basic Question: Should a project be included in the capital budget? • For DND - APC’s, Submarines or Helicopters ?

  5. Definitions • PROJECT - a single engineering proposal being considered • INVESTMENT ALTERNATIVE - a decision option. Therefore one project represents two investment alternatives: accept or reject.

  6. Definitions Continued • INDEPENDENT PROJECT - can be accepted or rejected without influencing the accept/reject decision of another project. • DEPENDENT PROJECTS - projects are related in such a way that the acceptance of one of them will influence the acceptance of others.

  7. Types of Dependent Projects • Mutually Exclusive - can only accept one alternative from the set. • Contingent - acceptance of one requires the acceptance of another. • Note - a fixed budget adds an external dependency if the cost of all projects exceeds the funds available.

  8. Check Mutually Exclusive alternatives are: a. Independent b. Dependent

  9. Formulating Mutually Exclusive Alternatives • Necessary to enumerate all feasible combinations of projects that could make up the capital project. • Can then apply budget or other constraints and decision criteria to select the best capital project.

  10. Approach 1 - Enumeration Method • Create a matrix of all possible alternatives. • For 2 independent projects, 4 alternatives - do nothing, P1 only, P2 only, or P1 and P2. • A = 2n, where A = the number of alternatives and n = the number of projects.

  11. Example • Consider five investment projects A to E Suppose projects A and B are mutually exclusive. Project C is independent, but D is contingent on C. Also E is contingent on B. • 25 = 32 Alternatives to consider

  12. EXAMPLE - Formulating Mutually Exclusive Alternatives Project A -100 Project B -200 Project C -100 Project D -300 Project E -200 Consider five investment projects with cash flows initial costs estimated above. Suppose projects A and B are mutually exclusive. Project C is independent, but D is contingent on C. Also E is contingent on B. Formulate the total number of feasible investment alternatives and tabulate their Cash Flows.

  13. 1 0 0 0 0 0 5 1 0 1 0 0 Graphical Interpretation B E A C D Alternative A B C D E 2 1 0 0 0 0 3 0 1 0 0 0 4 0 0 1 0 0 6 0 1 1 0 0 7 0 1 0 0 1 9 0 0 1 1 0 10 1 0 1 1 0 11 0 1 1 0 1 12 1 0 1 1 0 13 0 1 1 1 1

  14. Total Number of Mutually Exclusive Alternatives Alternative Projects 1 - 2 A 3 C 4 B 5 A,C 6 B,C 7 B,E 8 C,D 9 A,C,D 10 B,C,E 11 B,C,D 12 B,C,D,E

  15. Elements of Decision Criteria • Basic problem: How do we select the best mutually exclusive alternative? • Solution: depends on how you define best - your decision criteria

  16. Three Important Factors • Differences between alternatives • The MARR • The do nothing alternative

  17. Differences Between Alternatives Fundamental Rule • When comparing mutually exclusive alternatives, it is the difference between them that is relevant for determining the economic desirability of one over the other.

  18. Fundamental Rule – General Process • Step 1 - Put the mutually exclusive alternatives in order of increasing initial cost (investment at t = 0) • Step 2 - The cheapest option becomes the defender • Step 3 - The next cheapest becomes the challenger. • Step 4 - Apply the appropriate decision criteria to the difference between the two options.

  19. Fundamental Rule – General Process Cont’d • If the increase in investment is economically desirable, the challenger becomes the defender otherwise, reject the challenger • Step 5 - Continue until all alternatives are evaluated • The last defender is the best choice

  20. Minimum Acceptable Rate of Return (MARR) • Decision criteria have as their objective the maximization of equivalent profit, given that all investment alternatives must yield a return that exceeds some MARR. • MARR represents management’s cut-off rate - a policy decision.

  21. The Do Nothing Alternative • Does not mean the money is buried in the back yard. • Means do nothing about the alternatives being considered. • Money is still invested and expected to yield at least the MARR • Therefore, for the do nothing alternative: - PE (MARR) = 0 - AE (MARR) = 0 - FE (MARR) = 0

  22. Decision Criterion - Analysis Methods • PE/FE/AE on total investment • PE on incremental investment • IRR on incremental investment

  23. Multiple-Alternative Comparison Based on Total Investment • Step 1 - Remove non-profitable projects. • Step 2 - Generate mutually exclusive alternatives. • Step 3 - Order alternatives by increasing order of investment. • Step 4 - Remove alternatives that exceed budget.

  24. Multiple-Alternative Comparison Based on Total Investment Cont... • Step 5 - Remove dominated alternatives. • Step 6 - Calculate PE for remaining alternatives. • Step 7 - Select alternative with highest PE. Note: Step 6 can be replaced by FE or AE - same result

  25. Multiple-Alternative Comparison Based on Total Investment - Example Cash Flow Project A B C D E 0 -100 -200 -100 -300 -200 1 50 50 30 100 100 2 50 100 80 100 100 3 50 200 120 100 150

  26. Example - Steps 1-4 Alternatives Projects 0 1 2 3 1 - 0 0 0 0 2 A -100 50 50 50 3 C -100 30 80 120 4 B -200 50 100 200 5 AC -200 80 130 170 6 B,C -300 80 180 320 7 B,E -400 150 200 350 8 C,D -400 130 180 220 9 A,C,D -500 180 230 270 10 B,C,E -500 180 280 470 11 B,C,D -600 180 280 420 12 B,C,D,E -800 280 380 570

  27. Example - Steps 5 and 6 Alternatives Projects 0 1 2 3 PE(10%) 1 - 0 0 0 50 0 2 A -100 50 50 50 24.34 3 C -100 30 80 120 83.54 4 B -200 50 100 200 78.36 5 AC -200 80 130 170 107.88 6 B,C -300 80 180 320 161.9 7 B,E -400 150 200 350 164.61 8 C,D -400 130 180 220 32.23 9 A,C,D -500 180 230 270 56.57 10 B,C,E -500 180 280 470 248.15 11 B,C,D -600 180 280 420 110.59 12 B,C,D,E -800 280 380 570 196.84

  28. Present Worth on Incremental Investment Criteria • Step 1 - Put the mutually exclusive options in increasing order of initial cost. • Step 2 - Designate cheapest option as the first defender • Step 3 - The next cheapest option becomes the challenger and calculate the present equivalent of the cash flow resulting from challenger - defender.

  29. Present Worth on Incremental Investment Criteria Cont... • Step 4 - If the result from step 3 is positive, challenger becomes new defender and continue, otherwise challenger is replaced with the next cheapest option and continue. • Step 5 - Continue until all options are evaluated - the last defender is the best option. (i.e., it is the largest possible investment that makes at least MARR. In other words, it is the option with the highest NPW that earns at least MARR.)

  30. Example - PW on Incremental Investment Consider the following projects: Yr 0 1 2 3 Project 1 -1000 550 550 550 Project 2 -2000 875 875 875 Project 3 -3000 1400 1400 1400 Project 4 -4000 1665 1665 1665 Additional data: - Fixed budget of $5,000 - Projects 1 and 2 are mutually exclusive - meet the same requirement - Project 4 is contingent on project 1 Problem - Select the best capital program using both PE on total investment and IRR on incremental investment, MARR = 15%.

  31. Solution • A = 2n = 16 alternatives, where n = 4 projects. • All projects appear profitable, none to remove. • Generate mutually exclusive alternatives. • Put options in increasing order of initial investment.

  32. Solution Cont... • Remove any options that exceed budget. • Remove dominated proposals. • Designate cheapest option as the defender and next cheapest as the challenger and apply decision criteria to the difference between their respective cash flows. • The last defender is the best option.

  33. Alt 1 2 3 4 5 6 7 8 Projects - 1 2 3 1,3 1,4 2,3 1,3,4 Yr 0 0 -1000 -2000 -3000 -4000 -5000 -5000 -8000 Yr 1 0 550 875 1400 1950 2215 2275 3615 Yr 3 0 550 875 1400 1950 2215 2275 3615 Yr 2 0 550 875 1400 1950 2215 2275 3615 Alternative Cash Flows

  34. Calculations - Present Worth on Incremental Investment • Defender 1 Challenger 2 : Cash flow on difference: - 1000 550 550 550 PE (15%) = 255.8 > 0 therefore reject 1. • Defender 2 Challenger 3 : Cash flow on the difference: -1000 325 325 325 PE (15%) = -258 < 0 therefore reject option 3. • Defender 2 Challenger 4 : -2000 850 850 850 PE(15%) = -59 < 0 therefore reject option 4.

  35. Calculations - Present Worth on Incremental Investment Cont... • Defender 2 Challenger 5: -3000 1400 1400 1400 PE(15%) = 196.5 >0 therefore reject 2. • Defender 5 Challenger 7: -1000 325 325 325 PE(15%) = -258 < 0 therefore option 5 is best • Conclusion: invest in plan 1 and 3. The remaining $1000 to be invested at a min of MARR elsewhere.

  36. Multiple-Alternative Comparison by IRR on Incremental Investment • Step 1 - Order alternatives by increasing order of initial investment • Step 2 - Compute cash flow difference between pairs and calculate IRR on the increment of investment: if greater than MARR accept the larger investment and continue. If less than MARR, reject larger investment and move to next alternative. • Step 3 - Repeat step 2 until all alternatives have been compared - the last defender is the best alternative.

  37. Why Use IRR ? • PE - Absolute, IRR relative • If you were CEO which would you rather hear? - We made MARR plus a present value surplus of $268,000. Or, - The investment yielded a 22% return.

  38. IRR on Total Investment Alt 1 2 3 4 5 6 7 8 Yr 0 0 -1000 -2000 -3000 -4000 -5000 -5000 -8000 Yr 1 0 550 875 1400 1950 2215 2275 3615 Yr 3 0 550 875 1400 1950 2215 2275 3615 IRR 0 30% 15% 19% 22% 16% 17% 17% Yr 2 0 550 875 1400 1950 2215 2275 3615

  39. Alt 1 2 3 4 5 6 7 8 Projects - 1 2 3 1,3 1,4 2,3 1,3,4 Yr 0 0 -1000 -2000 -3000 -4000 -5000 -5000 -8000 Yr 1 0 550 875 1400 1950 2215 2275 3615 Yr 3 0 550 875 1400 1950 2215 2275 3615 Yr 2 0 550 875 1400 1950 2215 2275 3615 Example - IRR on Increment

  40. Calculations - IRR on Incremental Investment • Defender 1 Challenger 2 : Cash flow on difference: - 1000 550 550 550 IRR = 29.9% > MARR therefore reject 1. • Defender 2 Challenger 3 : Cash flow on the difference: -1000 325 325 325 IRR = -1.3% < MARR therefore reject option 3. • Defender 2 Challenger 4 : -2000 850 850 850 IRR = 13.2% < MARR therefore reject option 4.

  41. Calculations - IRR on Incremental Investment Cont... • Defender 2 Challenger 5: -3000 1400 1400 1400 IRR = 18.9% >MARR therefore reject 2 • Defender 5 Challenger 7: -1000 325 325 325 IRR = -1.3% < MARR therefore option 5 is best • Conclusion: invest in plan 1 and 3. The remaining $1000 to be invested at a min of MARR elsewhere.

  42. General Conclusions • The two methods provide consistent results. Option 5 has the highest PE evaluated at MARR. Option 5 is the largest investment that yields at least MARR on each increment of investment. • Although not calculated, Option 5 also would have the highest FE and AE evaluated at MARR.

  43. General Conclusions Cont... • Option 5 is not however the largest investment that gains at least MARR. Option 7 represents a $1,000 increase in investment over option 5 and has an IRR of 17.3 %. Why is this not chosen? • As demonstrated during the IRR on incremental investment analysis, the IRR on the $1,000 increment is -1.3% hence, it actually loses money. Therefore, the remaining $1,000 should be invested elsewhere.

  44. SUMMARY – Capital Budgeting • When dealing with multiple investment alternatives with various dependencies, we need to organize them into mutually exclusive projects that cover all feasible investment combinations. • Independent Projects vs Dependent Projects • PE/FE/AE on total investment • PE and IRR on incremental investment.

  45. Projects with unequal lives • Two options • Study period • Least common multiple

  46. Study Period • Could be a company policy - say 5 yrs • A period for which accurate estimates of future cash flows are available • A period that coincides with the life of one of the projects • Any other period that the analyst thinks makes sense

  47. Example - Materials handling A factory is considering three options for improving their materials handling system: A $9 200 Option Initial Cost Labour/yr Hydro /yr Maintenance/yr Taxes &insurance/yr service life(yrs) B $15 000 3 300 400 2 400 300 10 C $25 000 1 450 600 3 075 500 15 Which option is best? (MARR =9%)

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