1. Ch. 10: Capital Budgeting Techniques and Practice  2000, Prentice Hall, Inc.

2. Capital Budgeting: the process of planning for purchases of long- term assets. n example: Suppose our firm must decide whether to purchase a new plastic molding machine for $125,000. How do we decide? n Will the machine be profitable? n Will our firm earn a high rate of return on the investment?

3. Decision-making Criteria in Capital Budgeting How do we decide if a capital investment project should be accepted or rejected?

4. n The Ideal Evaluation Method should: a) include all cash flows that occur during the life of the project, b) consider the time value of money, c) incorporate the required rate of return on the project. Decision-making Criteria in Capital Budgeting

5. Payback Period n How long will it take for the project to generate enough cash to pay for itself?

6. Payback Period n How long will it take for the project to generate enough cash to pay for itself? 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

7. Payback Period n How long will it take for the project to generate enough cash to pay for itself? 012345 8 6 7 (500) 150 150 150 150 150 150 150 150 Payback period = 3.33 years.

8. n Is a 3.33 year payback period good? n Is it acceptable? n Firms that use this method will compare the payback calculation to some standard set by the firm. n If our senior management had set a cut- off of 5 years for projects like ours, what would be our decision? n Accept the project. Payback Period

9. Drawbacks of Payback Period n Firm cutoffs are subjective. n Does not consider time value of money. n Does not consider any required rate of return. n Does not consider all of the project’s cash flows.

10. Drawbacks of Payback Period n Does not consider all of the project’s cash flows. n Consider this cash flow stream! 012345 8 6 7 (500) 150 150 150 150 150 (300) 0 0

11. Drawbacks of Payback Period n Does not consider all of the project’s cash flows. n This project is clearly unprofitable, but we would accept it based on a 4- year payback criterion! 012345 8 6 7 (500) 150 150 150 150 150 (300) 0 0

12. Other Methods 1) Net Present Value (NPV) 2) Profitability Index (PI) 3) Internal Rate of Return (IRR) Each of these decision-making criteria: n Examines all net cash flows, n Considers the time value of money, and n Considers the required rate of return.

13. Net Present Value  NPV = the total PV of the annual net cash flows - the initial outlay. NPV = - IO ACF t ACF t (1 + k) t nt=1 

14. Net Present Value  Decision Rule:  If NPV is positive, accept.  If NPV is negative, reject.

15. NPV Example n Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

16. NPV Example 0 1 2 3 4 5 250,000 100,000 100,000 100,000 100,000 100,000 n Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

17. Net Present Value (NPV) NPV is just the PV of the annual cash flows minus the initial outflow. Using TVM: P/Y = 1 N = 5 I = 15 PMT = 100,000 PV of cash flows = $335,216 PV of cash flows = $335,216 - Initial outflow: ($250,000) - Initial outflow: ($250,000) = Net PV $85,216 = Net PV $85,216

18. NPV with the HP10B: n -250,000 CFj n 100,000 CFj n 5 shift Nj n 15 I/YR n shift NPV n You should get NPV = 85,215.51.

19. NPV with the HP17BII: n Select CFLO mode. n FLOW(0)=? -250,000 INPUT n FLOW(1)=? 100,000 INPUT n #TIMES(1)=1 5 INPUT EXIT n CALC 15 I% NPV n You should get NPV = 85,215.51

20. NPV with the TI BAII Plus: n Select CF mode.

21. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER

22. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER n C01=? 100,000 ENTER

23. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER n C01=? 100,000 ENTER n F01= 1 5 ENTER

24. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER n C01=? 100,000 ENTER n F01= 1 5 ENTER n NPV I= 15 ENTER

25. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER n C01=? 100,000 ENTER n F01= 1 5 ENTER n NPV I= 15 ENTER CPT

26. NPV with the TI BAII Plus: n Select CF mode. n CFo=? -250,000 ENTER n C01=? 100,000 ENTER n F01= 1 5 ENTER n NPV I= 15 ENTER CPT n You should get NPV = 85,215.51

27. Profitability Index

28. NPV = - IO ACF t ACF t (1 + k) t nt=1

29. Profitability Index PI = IO ACF t (1 + k) n t=1  t NPV = - IO ACF t ACF t (1 + k) t nt=1

30.  Decision Rule:  If PI is greater than or equal to 1, accept.  If PI is less than 1, reject. Profitability Index

31. PI with the HP10B: n -250,000CFj n 100,000 CFj n 5 shift Nj n 15 I/YR n shift NPV n Add back IO:+ 250,000 n Divide by IO:/ 250,000 = n You should get PI = 1.34

32. Internal Rate of Return (IRR) n IRR: the return on the firm’s invested capital. IRR is simply the rate of return that the firm earns on its capital budgeting projects.

33. Internal Rate of Return (IRR)

34. NPV = - IO ACF t ACF t (1 + k) t nt=1

35. Internal Rate of Return (IRR) NPV = - IO ACF t ACF t (1 + k) t nt=1 n t=1  IRR: = IO ACF t (1 + IRR) t

36. Internal Rate of Return (IRR) n IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay. n This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM is the IRR of a bond. n t=1  IRR: = IO ACF t (1 + IRR) t

37. Calculating IRR n Looking again at our problem: n The IRR is the discount rate that makes the PV of the projected cash flows equal to the initial outlay. 0 1 2 3 4 5 250,000 100,000 100,000 100,000 100,000 100,000

38. IRR with your Calculator n IRR is easy to find with your financial calculator. n Just enter the cash flows as you did with the NPV problem and solve for IRR. n You should get IRR = 28.65%!

39. IRR  Decision Rule:  If IRR is greater than or equal to the required rate of return, accept.  If IRR is less than the required rate of return, reject.

40. n IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) n Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

41. n IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) n Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300

42. n IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) n Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300 1

43. n IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) n Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300 1 2

44. n IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) n Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300 1 2 3

45. Summary Problem n Enter the cash flows only once. n Find the IRR. n Using a discount rate of 15%, find NPV. n Add back IO and divide by IO to get PI. 0 1 2 3 4 5 (900) 300 400 400 500 600

46. Summary Problem n IRR = 34.37%. n Using a discount rate of 15%, NPV = $510.52. NPV = $510.52. n PI = 1.57. 0 1 2 3 4 5 (900) 300 400 400 500 600

47. Capital Rationing n Suppose that you have evaluated 5 capital investment projects for your company. n Suppose that the VP of Finance has given you a limited capital budget. n How do you decide which projects to select?

48. Capital Rationing n You could rank the projects by IRR:

49. Capital Rationing IRR5% 10% 15% 20% 25% $ 1 n You could rank the projects by IRR:

50. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 2

51. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 23

52. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 23 4

53. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 23 4 5

54. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 23 4 5 $X Our budget is limited so we accept only projects 1, 2, and 3.

55. Capital Rationing n You could rank the projects by IRR: IRR5% 10% 15% 20% 25% $ 1 23 $X Our budget is limited so we accept only projects 1, 2, and 3.

56. Problems with Project Ranking 1) Mutually exclusive projects of unequal size (the size disparity problem) n The NPV decision may not agree with IRR or PI. n Solution: select the project with the largest NPV.

57. Size Disparity example Project A yearcash flow yearcash flow 0(135,000) 0(135,000) 1 60,000 1 60,000 2 60,000 2 60,000 3 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07

58. Size Disparity example Project B yearcash flow yearcash flow 0 (30,000) 0 (30,000) 1 15,000 1 15,000 2 15,000 2 15,000 3 15,000 3 15,000 required return = 12% IRR = 23.38% NPV = $6,027 PI = 1.20 Project A yearcash flow 0(135,000) 1 60,000 2 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07

59. Size Disparity example Project B yearcash flow yearcash flow 0 (30,000) 0 (30,000) 1 15,000 1 15,000 2 15,000 2 15,000 3 15,000 3 15,000 required return = 12% IRR = 23.38% NPV = $6,027 PI = 1.20 Project A yearcash flow 0(135,000) 1 60,000 2 60,000 3 60,000 required return = 12% IRR = 15.89% NPV = $9,110 PI = 1.07

60. Problems with Project Ranking 2) The time disparity problem with mutually exclusive projects. n NPV and PI assume cash flows are reinvested at the required rate of return for the project. n IRR assumes cash flows are reinvested at the IRR. n The NPV or PI decision may not agree with the IRR. n Solution: select the largest NPV.

61. Time Disparity example Project A yearcash flow yearcash flow 0 (48,000) 0 (48,000) 1 1,200 1 1,200 2 2,400 2 2,400 3 39,000 3 39,000 4 42,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20

62. Time Disparity example Project B yearcash flow yearcash flow 0 (46,500) 0 (46,500) 1 36,500 1 36,500 2 24,000 2 24,000 3 2,400 3 2,400 4 2,400 4 2,400 required return = 12% IRR = 25.51% NPV = $8,455 PI = 1.18 Project A yearcash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20

63. Time Disparity example Project B yearcash flow yearcash flow 0 (46,500) 0 (46,500) 1 36,500 1 36,500 2 24,000 2 24,000 3 2,400 3 2,400 4 2,400 4 2,400 required return = 12% IRR = 25.51% NPV = $8,455 PI = 1.18 Project A yearcash flow 0 (48,000) 1 1,200 2 2,400 3 39,000 4 42,000 required return = 12% IRR = 18.10% NPV = $9,436 PI = 1.20

64. Mutually Exclusive Investments with Unequal Lives n Suppose our firm is planning to expand and we have to select 1 of 2 machines. n They differ in terms of economic life and capacity. n How do we decide which machine to select?

65. n The after-tax cash flows are: Year Machine 1 Machine 2 0 (45,000) (45,000) 0 (45,000) (45,000) 1 20,000 12,000 1 20,000 12,000 2 20,000 12,000 2 20,000 12,000 3 20,000 12,000 3 20,000 12,000 4 12,000 4 12,000 5 12,000 5 12,000 6 12,000 6 12,000 n Assume a required return of 14%.

66. Step 1: Calculate NPV n NPV 1 = $1,433 n NPV 2 = $1,664 n So, does this mean #2 is better? n No! The two NPVs can’t be compared!

67. Step 2: Equivalent Annual Annuity (EAA) method n If we assume that each project will be replaced an infinite number of times in the future, we can convert each NPV to an annuity. n The projects’ EAAs can be compared to determine which is the best project! n EAA: Simply annualize the NPV over the project’s life.

68. EAA with your calculator: n Simply “spread the NPV over the life of the project” n Machine 1: PV = 1433, N = 3, I = 14, solve: PMT = -617.24. solve: PMT = -617.24. n Machine 2: PV = 1664, N = 6, I = 14, solve: PMT = -427.91. solve: PMT = -427.91.

69. n EAA 1 = $617 n EAA 2 = $428 n This tells us that: n NPV 1 = annuity of $617 per year. n NPV 2 = annuity of $428 per year. n So, we’ve reduced a problem with different time horizons to a couple of annuities. n Decision Rule: Select the highest EAA. We would choose machine #1.

70. Step 3: Convert back to NPV 

71. n Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. 

72. Step 3: Convert back to NPV n Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. n NPV 1 = 617/.14 = $4,407 

73. Step 3: Convert back to NPV n Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. n NPV 1 = 617/.14 = $4,407 n NPV 2 = 428/.14 = $3,057  

74. Step 3: Convert back to NPV n Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required rate of return. n NPV 1 = 617/.14 = $4,407 n NPV 2 = 428/.14 = $3,057 n This doesn’t change the answer, of course; it just converts EAA to a NPV that can be compared.  