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- 1. 3-1 Chapter 13 Capital Budgeting Techniques © Pearson Education Limited 2004 Fundamentals of Financial Management, 12/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI
- 2. 3-2 After studying Chapter 13, you should be able to: Understand the payback period (PBP) method of project evaluation and selection, including its: (a) calculation; (b) acceptance criterion; (c) advantages and disadvantages; and (d) focus on liquidity rather than profitability. Understand the three major discounted cash flow (DCF) methods of project evaluation and selection – internal rate of return (IRR), net present value (NPV), and profitability index (PI). Explain the calculation, acceptance criterion, and advantages (over the PBP method) for each of the three major DCF methods. Define, construct, and interpret a graph called an “NPV profile.” Understand why ranking project proposals on the basis of IRR, NPV, and PI methods “may” lead to conflicts in ranking. Describe the situations where ranking projects may be necessary and justify when to use either IRR, NPV, or PI rankings. Understand how “sensitivity analysis” allows us to challenge the singlepoint input estimates used in traditional capital budgeting analysis. Explain the role and process of project monitoring, including “progress reviews” and “post-completion audits.”
- 3. 3-3 Capital Budgeting Techniques Project Evaluation and Selection Potential Difficulties Capital Rationing Project Monitoring Post-Completion Audit
- 4. 3-4 Project Evaluation: Alternative Methods Payback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI)
- 5. 3-5 Proposed Project Data Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be $10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be $40,000.
- 6. 3-6 Independent Project For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake. Independent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.
- 7. 3-7 Payback Period (PBP) 0 1 2 3 -40 K 10 K 12 K 15 K 4 10 K PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow. 5 7K
- 8. 3-8 Payback Solution (#1) 0 -40 K (-b) Cumulative Inflows 1 2 10 K 10 K 12 K 22 K PBP 3 (a) 15 K 37 K(c) 4 10 K(d) 47 K =a+(b-c)/d = 3 + (40 - 37) / 10 = 3 + (3) / 10 = 3.3 Years 5 7K 54 K
- 9. 3-9 Payback Solution (#2) 0 1 2 -40 K 10 K 12 K 15 K 10 K -40 K -30 K -18 K -3 K 7K PBP Cumulative Cash Flows 3 4 5 7K 14 K = 3 + ( 3K ) / 10K = 3.3 Years Note: Take absolute value of last negative cumulative cash flow value.
- 10. 3-10 PBP Acceptance Criterion The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type. Should this project be accepted? Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]
- 11. 3-11 PBP Strengths and Weaknesses Strengths: Weaknesses: Easy to use and understand Does not account for TVM Can be used as a measure of liquidity Does not consider cash flows beyond the PBP Easier to forecast ST than LT flows Cutoff period is subjective
- 12. 3-12 Internal Rate of Return (IRR) IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow. CF1 CF2 + ICO = 1 (1+IRR) (1+IRR)2 +...+ CFn (1+IRR)n
- 13. 3-13 IRR Solution $10,000 $12,000 $40,000 = + + (1+IRR)1 (1+IRR)2 $15,000 $10,000 $7,000 + + (1+IRR)3 (1+IRR)4 (1+IRR)5 Find the interest rate (IRR) that causes the discounted cash flows to equal $40,000.
- 14. IRR Solution (Try 10%) $40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + 7,000(PVIF10%,5) $40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621) $40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347 = $41,444 [Rate is too low!!] 3-14 $
- 15. IRR Solution (Try 15%) $40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + 7,000(PVIF15%,5) $40,000 = $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $ 7,000(.497) $40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479 = $36,841 [Rate is too high!!] 3-15 $
- 16. 3-16 IRR Solution (Interpolate) .05 X .10 IRR $40,000 .15 X .05 = $41,444 $36,841 $1,444 $4,603 $1,444 $4,603
- 17. 3-17 IRR Solution (Interpolate) .05 X .10 IRR $40,000 .15 X .05 = $41,444 $36,841 $1,444 $4,603 $1,444 $4,603
- 18. 3-18 IRR Solution (Interpolate) .05 X .10 $41,444 IRR $40,000 .15 $1,444 $4,603 $36,841 X = ($1,444)(0.05) $4,603 X = .0157 IRR = .10 + .0157 = .1157 or 11.57%
- 19. 3-19 IRR Acceptance Criterion The management of Basket Wonders has determined that the hurdle rate is 13% for projects of this type. Should this project be accepted? No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]
- 20. 3-20 IRRs on the Calculator We will use the cash flow registry to solve the IRR for this problem quickly and accurately!
- 21. 3-21 Actual IRR Solution Using Your Financial Calculator Steps in the Process Step 1: Press Step 2: Press Step 3: For CF0 Press CF 2nd CLR Work -40000 Enter key keys ↓ keys Step 4: Step 5: Step 6: Step 7: For C01 Press For F01 Press For C02 Press For F02 Press 10000 1 12000 1 Enter Enter Enter Enter ↓ Step 8: For C03 Press Step 9: For F03 Press 15000 1 Enter Enter ↓ ↓ ↓ ↓ ↓ keys keys keys keys keys keys
- 22. 3-22 Actual IRR Solution Using Your Financial Calculator Steps in the Process (Part II) Step 10:For C04 Press Step 11:For F04 Press Step 12:For C05 Press Step 13:For F05 Press 10000 1 7000 1 Enter Enter Enter Enter ↓ ↓ ↓ ↓ keys keys keys keys Step 14: Step 15: Press Press IRR keys key Step 16: Press CPT key Result: Internal Rate of Return = 11.47% ↓ ↓
- 23. 3-23 IRR Strengths and Weaknesses Strengths: Accounts for TVM Considers all cash flows Less subjectivity Weaknesses: Assumes all cash flows reinvested at the IRR Difficulties with project rankings and Multiple IRRs
- 24. 3-24 Net Present Value (NPV) NPV is the present value of an investment project’s net cash flows minus the project’s initial cash outflow. CF1 NPV = (1+k)1 + CF2 (1+k)2 CFn - ICO +...+ (1+k)n
- 25. 3-25 NPV Solution Basket Wonders has determined that the appropriate discount rate (k) for this project is 13%. NPV = $10,000 +$12,000 +$15,000 + (1.13)1 (1.13)2 (1.13)3 $10,000 $7,000 4 + 5 - $40,000 (1.13) (1.13)
- 26. 3-26 NPV Solution NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $ 7,000(PVIF13%,5) - $40,000 NPV = $10,000(.885) + $12,000(.783) + $15,000(.693) + $10,000(.613) + $ 7,000(.543) - $40,000 NPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000 = - $1,428
- 27. 3-27 NPV Acceptance Criterion The management of Basket Wonders has determined that the required rate is 13% for projects of this type. Should this project be accepted? No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ]
- 28. 3-28 NPV on the Calculator We will use the cash flow registry to solve the NPV for this problem quickly and accurately! Hint: If you have not cleared the cash flows from your calculator, then you may skip to Step 15.
- 29. 3-29 Actual NPV Solution Using Your Financial Calculator Steps in the Process Step 1: Press Step 2: Press Step 3: For CF0 Press CF 2nd CLR Work -40000 Enter key keys ↓ keys Step 4: Step 5: Step 6: Step 7: For C01 Press For F01 Press For C02 Press For F02 Press 10000 1 12000 1 Enter Enter Enter Enter ↓ Step 8: For C03 Press Step 9: For F03 Press 15000 1 Enter Enter ↓ ↓ ↓ ↓ ↓ keys keys keys keys keys keys
- 30. 3-30 Actual NPV Solution Using Your Financial Calculator Steps in the Process (Part II) Step 10:For C04 Press Step 11:For F04 Press Step 12:For C05 Press Step 13:For F05 Press 10000 1 7000 1 Step 14: Step 15: ↓ Press Press Enter Enter Enter Enter ↓ ↓ ↓ ↓ keys key ↓ NPV Enter keys keys keys keys Step 16: For I=, Enter 13 Step 17: Press CPT Result: Net Present Value = -$1,424.42 ↓ keys key
- 31. 3-31 NPV Strengths and Weaknesses Strengths: Weaknesses: Cash flows assumed to be reinvested at the hurdle rate. May not include managerial options embedded in the project. See Chapter 14. Accounts for TVM. Considers all cash flows.
- 32. 3-32 Net Present Value Profile Net Present Value $000s 15 Sum of CF’s Thre e 10 5 Plot NPV for each discount rate. of th e se p oint IRR s ar NPV@13% 0 -4 0 3 6 9 12 Discount Rate (%) e ea sy n 15 ow!
- 33. 3-33 Creating NPV Profiles Using the Calculator Hint: As long as you do not “clear” the cash flows from the registry, simply start at Step 15 and enter a different discount rate. Each resulting NPV will provide a “point” for your NPV Profile!
- 34. Profitability Index (PI) PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow. Method #1: 3-34 CF1 PI = (1+k)1 + CF2 CFn +...+ (1+k)2 (1+k)n << OR >> Method #2: PI = 1 + [ NPV / ICO ] ICO
- 35. 3-35 PI Acceptance Criterion PI = $38,572 / $40,000 = .9643 (Method #1, 13-34) Should this project be accepted? No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00 ]
- 36. 3-36 PI Strengths and Weaknesses Strengths: Weaknesses: Same as NPV Same as NPV Allows comparison of different scale projects Provides only relative profitability Potential Ranking Problems
- 37. 3-37 Evaluation Summary Basket Wonders Independent Project Method Project Comparison Decision PBP 3.3 3.5 Accept IRR 11.47% 13% Reject NPV -$1,424 $0 Reject PI .96 1.00 Reject
- 38. 3-38 Other Project Relationships Dependent -- A project whose acceptance depends on the acceptance of one or more other projects. Mutually Exclusive -- A project whose acceptance precludes the acceptance of one or more alternative projects.
- 39. 3-39 Potential Problems Under Mutual Exclusivity Ranking of project proposals may create contradictory results. A. Scale of Investment B. Cash-flow Pattern C. Project Life
- 40. 3-40 A. Scale Differences Compare a small (S) and a large (L) project. END OF YEAR NET CASH FLOWS Project S Project L 0 -$100 -$100,000 1 0 0 2 $400 $156,250
- 41. 3-41 Scale Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project IRR S 100% L 25% NPV $ PI 231 3.31 $29,132 1.29
- 42. 3-42 B. Cash Flow Pattern Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project. END OF YEAR 0 1 2 3 NET CASH FLOWS Project D Project I -$1,200 -$1,200 1,000 100 500 600 100 1,080
- 43. 3-43 Cash Flow Pattern Calculate the IRR, NPV@10%, and PI@10%. Which project is preferred? Project IRR NPV PI D 23% $198 1.17 I 17% $198 1.17
- 44. 3-44 600 Plot NPV for each project at various discount rates. 400 Project I 200 NPV@10% IRR Project D 0 -200 Net Present Value ($) Examine NPV Profiles 0 5 10 15 20 Discount Rate (%) 25
- 45. 3-45 Net Present Value ($) -200 0 200 400 600 Fisher’s Rate of Intersection 0 At k<10%, I is best! Fisher’s Rate of Intersection At k>10%, D is best! 5 10 15 20 Discount Rate ($) 25
- 46. 3-46 C. Project Life Differences Let us compare a long life (X) project and a short life (Y) project. END OF YEAR 0 1 2 3 NET CASH FLOWS Project X Project Y -$1,000 -$1,000 0 2,000 0 0 3,375 0
- 47. 3-47 Project Life Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project IRR NPV PI X 50% $1,536 2.54 Y 100% $ 818 1.82
- 48. 3-48 Another Way to Look at Things 1. Adjust cash flows to a common terminal year if project “Y” will NOT be replaced. Compound Project Y, Year 1 @10% for 2 years. Year CF 0 1 2 -$1,000 $0 $0 Results: IRR* = 34.26% 3 $2,420 NPV = $818 *Lower IRR from adjusted cash-flow stream. X is still Best.
- 49. 3-49 Replacing Projects with Identical Projects 2. Use Replacement Chain Approach (Appendix B) when project “Y” will be replaced. 0 1 -$1,000 $2,000 -1,000 -$1,000 Results: $1,000 IRR = 100% 2 3 $2,000 -1,000 $2,000 $1,000 $2,000 NPV* = $2,238.17 *Higher NPV, but the same IRR. Y is Best. Best
- 50. 3-50 Capital Rationing Capital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures during a particular period. Example: Julie Miller must determine what investment opportunities to undertake for Basket Wonders (BW). She is limited to a maximum expenditure of $32,500 only for this capital budgeting period.
- 51. 3-51 Available Projects for BW Project A B C D E F G H ICO $ 500 5,000 5,000 7,500 12,500 15,000 17,500 25,000 IRR 18% 25 37 20 26 28 19 15 NPV $ PI 50 6,500 5,500 5,000 500 21,000 7,500 6,000 1.10 2.30 2.10 1.67 1.04 2.40 1.43 1.24
- 52. 3-52 Choosing by IRRs for BW Project C F E B ICO IRR NPV PI $ 5,000 15,000 12,500 5,000 37% 28 26 25 $ 5,500 21,000 500 6,500 2.10 2.40 1.04 2.30 Projects C, F, and E have the three largest IRRs. The resulting increase in shareholder wealth is $27,000 with a $32,500 outlay.
- 53. 3-53 Choosing by NPVs for BW Project F G B ICO $15,000 17,500 5,000 IRR NPV PI 28% 19 25 $21,000 7,500 6,500 2.40 1.43 2.30 Projects F and G have the two largest NPVs. The resulting increase in shareholder wealth is $28,500 with a $32,500 outlay.
- 54. 3-54 Choosing by PIs for BW Project F B C D G ICO IRR NPV PI $15,000 5,000 5,000 7,500 17,500 28% 25 37 20 19 $21,000 6,500 5,500 5,000 7,500 2.40 2.30 2.10 1.67 1.43 Projects F, B, C, and D have the four largest PIs. The resulting increase in shareholder wealth is $38,000 with a $32,500 outlay.
- 55. 3-55 Summary of Comparison Method Projects Accepted Value Added PI F, B, C, and D $38,000 NPV F and G $28,500 IRR C, F, and E $27,000 PI generates the greatest increase in shareholder wealth when a limited capital budget exists for a single period.
- 56. 3-56 Single-Point Estimate and Sensitivity Analysis Sensitivity Analysis: A type of “what-if” Analysis uncertainty analysis in which variables or assumptions are changed from a base case in order to determine their impact on a project’s measured results (such as NPV or IRR). Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis Utilize a “base-case” to compare the impact of individual variable changes E.g., Change forecasted sales units to see impact on the project’s NPV
- 57. 3-57 Post-Completion Audit Post-completion Audit A formal comparison of the actual costs and benefits of a project with original estimates. Identify any project weaknesses Develop a possible set of corrective actions Provide appropriate feedback Result: Making better future decisions!
- 58. 3-58 Multiple IRR Problem* Let us assume the following cash flow pattern for a project for Years 0 to 4: -$100 +$100 +$900 -$1,000 How many potential IRRs could this project have? Two!! There are as many potential IRRs as there are sign changes. * Refer to Appendix A
- 59. 3-59 NPV Profile -- Multiple IRRs Net Present Value ($000s) 75 Multiple IRRs at k = 12.95% and 191.15% 50 25 0 -100 0 40 80 120 160 Discount Rate (%) 200
- 60. 3-60 NPV Profile -- Multiple IRRs Hint: Your calculator will only find ONE IRR – even if there are multiple IRRs. It will give you the lowest IRR. In this case, 12.95%.

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