1. Copyright © 2008 Prentice Hall All rights reserved 9-1 Capital Investment Decisions and the Time Value of Money Chapter 9

2. Copyright © 2008 Prentice Hall All rights reserved 9-2 Objective 1 Describe the importance of capital investments and the capital budgeting process

3. Copyright © 2008 Prentice Hall All rights reserved 9-3 Capital Budgeting: The Process of Making Capital Investment Decisions Companies make capital investments when they acquire capital assets – assets used for a long period of time Capital investments include buying new equipment, building new plants, automating production and developing major commercial websites Capital investments affect operations for many years and usually require large sums of money

4. Copyright © 2008 Prentice Hall All rights reserved 9-4 Four Popular Methods of Capital Budgeting Analysis Payback period Accounting Rate of Return (ARR) Net Present Value (NPV) Internal Rate of Return (IRR)

5. Copyright © 2008 Prentice Hall All rights reserved 9-5 Capital Budgeting Process Identify potential investments Project the investment’s net cash inflows Analyze the investments using one or more of the four methods listed previously

6. Copyright © 2008 Prentice Hall All rights reserved 9-6 Typical Capital Budgeting Process 1. Identify potential capital investments 2. Estimate future net cash inflows 3. Analyze potential investments: a. Screen out undesirable investments using payback and/or ARR b. Further analyze investments using NPV and/or IRR 4. Engage in capital rationing if necessary to choose among alternative investments 5. Perform post-audits

7. Copyright © 2008 Prentice Hall All rights reserved 9-7 Objective 2 Use the payback and accounting rate of return methods to make capital investment decisions

8. Copyright © 2008 Prentice Hall All rights reserved 9-8 Payback Period Payback – the length of time it takes to recover, in net cash inflows, the cost of the capital outlay Amount invested Expected annual net cash inflows When the net cash inflows are equal each year, the computation of the payback period is performed by dividing the amount invested by the expected annual net cash inflows. The result is the payback period in years.

9. Copyright © 2008 Prentice Hall All rights reserved 9-9 Payback with Unequal Net Cash Inflows Accumulate net cash inflows until amount invested is recovered

10. Copyright © 2008 Prentice Hall All rights reserved 9-10 Payback Period DECISION RULE: Payback Period Investments with shorter payback periods are more desirable, all else being equal

11. Copyright © 2008 Prentice Hall All rights reserved 9-11 E9-16: Compute Payback Period with Equal Cash Flows Amount invested Expected annual net cash inflow $1,236,100 $309,025 = 4 years

12. Copyright © 2008 Prentice Hall All rights reserved 9-12 Accounting Rate of Return Average annual operating income from asset Average amount invested in asset Average amount invested in asset = Original Investment + Residual Value 2

13. Copyright © 2008 Prentice Hall All rights reserved 9-13 Accounting Rate of Return Managers compare the accounting rate of return to company’s required minimum rate of return for investments of similar risk If the ARR is less than the required minimum, the investment is rejected

14. Copyright © 2008 Prentice Hall All rights reserved 9-14 Accounting Rate of Return DECISION RULE: Invest in capital assets? Is expected accounting rate of return > the required rate of return? Invest Is expected accounting rate of return < the required rate of return? Do not invest

15. Copyright © 2008 Prentice Hall All rights reserved 9-15 E9-19: Compute and Compare ARR Atlas $160,000 ($1,000,000 + 0)/2 = 32% Veras 240,500 (1,200,000+100,000)/2 = 37%

16. Copyright © 2008 Prentice Hall All rights reserved 9-16 E9-18: ARR with Unequal Cash Flows Average annual operating income: Year 1$310,000 Year 2280,000 Years 3-10 ($240,000 x 8)1,920,000 Total net cash flows $2,510,000 Less: Total depreciation(1,454,000) Total operating income over life$1,056,000 Divided by years of life10 Average annual operating income$105,600

17. Copyright © 2008 Prentice Hall All rights reserved 9-17 E9-18: ARR with Unequal Cash Flows Average annual operating income from asset Average amount invested in asset $105,600 ($1,454,000+0) ÷ 2 = 14.53%

18. Copyright © 2008 Prentice Hall All rights reserved 9-18 Objective 3 Use the time value of money to compute the present and future values of single lump sums and annuities

19. Copyright © 2008 Prentice Hall All rights reserved 9-19 Time Value of Money The fact that invested money earns income over time is called the time value of money This is why we prefer to receive cash sooner, rather than later

20. Copyright © 2008 Prentice Hall All rights reserved 9-20 Factors That Affect Time Value of Money Principal – amount of the investment  Lump sum  Annuity Number of periods – number of times interest is computed Interest rate – annual percentage  Simple interest  Compound interest

21. Copyright © 2008 Prentice Hall All rights reserved 9-21 Present Value & Future Value 123456 Future Value Present Value Time Periods

22. Copyright © 2008 Prentice Hall All rights reserved 9-22 Future Value ? Interest = $1,000 x.10 $100 Principal =1,000 Future value after 1 year$1,100 1 yr $1,000 10% Present Value Future Value 2 yrs3 yrs

23. Copyright © 2008 Prentice Hall All rights reserved 9-23 Future Value ? Future value after 1 year$1,100 Plus 10% interest110 Future value after 2 years$1,210 Plus 10% interest121 Future value after 3 years$1,331 1 yr $1,000 10% Present Value Future Value 2 yrs3 yrs

24. Copyright © 2008 Prentice Hall All rights reserved 9-24 Future Value ? Or use the Future Value of $1 table Future value = Present value x table factor = $1,000 x 1.331 = $1,331 1 yr $1,000 10% Present Value Future Value 2 yrs3 yrs

25. Copyright © 2008 Prentice Hall All rights reserved 9-25 Future Value of an Annuity 1 yr 0 $1,000 10% Present Value Future Value 2 yrs $1,000 3 yrs $1,000 Year 3$1,000 Year 2 Future value of $1,000 in 1 year ($1,000 + ($1,000 x 10%)1,100 Year 1 Future value of $1,000 in 2 years ($1,100 + ($1,100 x 10%)1,210 $3,310

26. Copyright © 2008 Prentice Hall All rights reserved 9-26 Future Value of an Annuity 1 yr 0$1,000 10% Present Value Future Value 2 yrs $1,000 3 yrs $1,000 Future value = Payment x table factor = $1,000 x 3.310 = $3,310

27. Copyright © 2008 Prentice Hall All rights reserved 9-27 E9-20: Compare Retirement Savings Plans Using Future Value Concepts Plan 1 Future value = Payment x table factor = $3,000 x 164.494 = $493,482 Plan 2 Future value = Payment x table factor = $7,500 x 21.384 = $160,380

28. Copyright © 2008 Prentice Hall All rights reserved 9-28 E9-20: Compare Retirement Savings Plans Using Future Value Concepts Plan 1 Future value of $1 = present value x table factor = $493,482 x 2.594 = $1,280,092 Plan 2 Future value of $1 = present value x table factor = $160,380 x 2.594 = $416,026

29. Copyright © 2008 Prentice Hall All rights reserved 9-29 Present Value 1 yr ? $1,100 10% Present value x 1.10 = $1,100 Present value = $1,100/1.10 Present value = $1,000 Present Value Future Value

30. Copyright © 2008 Prentice Hall All rights reserved 9-30 Present Value 1 yr ? $1,100 10% Present value x 1.10 = $1,100 Present value = $1,100/1.10 Present value = $1,000 Present Value Future Value 2 yrs Present value x 1.10 = $1,000 Present value = $1,000/1.10 Present value = $909

31. Copyright © 2008 Prentice Hall All rights reserved 9-31 Present Value of $1 Table 1 yr ? $1,100 10% Present Value Future Value 2 yrs Present Value = Future Value x Table Factor = $1,100 x 0.826 = $909

32. Copyright © 2008 Prentice Hall All rights reserved 9-32 Present Value of an Annuity 1 yr ? $1,100 10% Present Value Future Value 2 yrs Present Value of $1,100 in one year: $1,100 x 0.909 = $1,000 $1,100 Present Value of $1,100 in two years: $1,100 x 0.826 = $909 $1,000 + $909 = $1,909

33. Copyright © 2008 Prentice Hall All rights reserved 9-33 Present Value of an Annuity Table 1 yr ? $1,100 10% Present Value Future Value 2 yrs $1,100 Present Value of Annuity = Payments x Table Factor = $1,100 x 1.736 = $1,909.60

34. Copyright © 2008 Prentice Hall All rights reserved 9-34 E9-22: Fund Future Cash Flows Req. 1 Present value of annuity = Payment x table factor = $30,000 x ? = ? Req. 2 Present value of annuity = Payment x table factor = $30,000 x ? = ?

35. Copyright © 2008 Prentice Hall All rights reserved 9-35 E9-23: Choosing a Lottery Payout Option Using Present Value Option 1: Present value of $1 = $12,000,000 x ? = ? Option 2: Present value annuity = $2,250,000 x ? = ?

36. Copyright © 2008 Prentice Hall All rights reserved 9-36 E9-23: Choosing a Lottery Payout Option Option 3: Present value of $1 = $10,000,000 x ? = ?

37. Copyright © 2008 Prentice Hall All rights reserved 9-37 Objective 4 Use discounted cash flow models to make capital investment decisions

38. Copyright © 2008 Prentice Hall All rights reserved 9-38 Discounted Cash Flow Models Recognize time value of money Two methods  Net present value  Internal rate of return Compare amount of investment with its expected net cash inflows

39. Copyright © 2008 Prentice Hall All rights reserved 9-39 Net Present Value Method Discount cash inflows to their present value and then compare with capital outlay required by the investment Discount rate (hurdle rate or required rate of return) – required minimum rate of return given riskiness of investment Proposal is acceptable when NPV is ≥ zero The higher the NPV, the more attractive the investment

40. Copyright © 2008 Prentice Hall All rights reserved 9-40 Net Present Value DECISION RULE: Invest in capital assets? Is NPV positive? Invest Is NPV negative? Do not invest

41. Copyright © 2008 Prentice Hall All rights reserved 9-41 E9-25: Calculate NPV – Equal Annual Cash Flows Cash Flow When?Type of cash flow PV factor 14% PV Project A NPV (272,000) Now 60,000Yrs 1-8Annuity4.639278,340 $6,340

42. Copyright © 2008 Prentice Hall All rights reserved 9-42 Cash Flow When?Type of cash flow PV factor 12% PV Project B NPV E9-24 (380,000) Now 70,000Yrs 1-9Annuity5.328 372,960 $(7,040)

43. Copyright © 2008 Prentice Hall All rights reserved 9-43 Net Present Value for Unequal Cash Inflows When annual cash inflows are unequal, you must use the present value of one table applied to each annual cash inflow

44. Copyright © 2008 Prentice Hall All rights reserved 9-44 E9-27: Calculate NPV – Unequal Cash Flows Cash Flow When?Type of cash flow PV factor 14% PV NPV (900,000) Now 260,000Yr 1Lump sum.877228,020 $(19,935) 250,000Yr 2Lump sum.769192,250 225,000Yr 3Lump sum.675151,875 210,000Yr 4Lump sum.592124,320 200,000Yr 5Lump sum.519103,800 175,000Yr 6Lump sum.456 79,800

45. Copyright © 2008 Prentice Hall All rights reserved 9-45 E9-27 2. Cash Flow When?Type of cash flow PV factor 14% PV NPV 75,000Yr 7.40030,000 Lump sum 50,000Yr 7.400 20,000 Lump sum (100,000)(45,600)Yr 6Lump sum.456 $4,400

46. Copyright © 2008 Prentice Hall All rights reserved 9-46 Profitability Index Number of dollars returned for every dollar invested Present value of net cash inflows Investment

47. Copyright © 2008 Prentice Hall All rights reserved 9-47 E9-29: Capital Rationing Decision Present value of net cash inflows Investment A: $1,695,000 ÷ $1,500,000 = 1.13 B: $1,960,000 ÷ $1,750,000 = 1.12 C: $2,200,000 ÷ $2,000,000 = 1.10

48. Copyright © 2008 Prentice Hall All rights reserved 9-48 Internal Rate of Return Rate of return a company can expect to earn by investing in the project The interest rate that will cause the present value to equal zero

49. Copyright © 2008 Prentice Hall All rights reserved 9-49 Internal Rate of Return Step 1: Identify the expected net cash receipts Step 2: Find the discount rate that makes total present value of net cash receipts = present value of cash outflows Annuity PV factor = Investment ÷ Annual Net Cash Receipts

50. Copyright © 2008 Prentice Hall All rights reserved 9-50 Internal Rate of Return Step 3: On the present value of an annuity of $1 table, scan the row corresponding to the expected life Choose column closest to annuity factor you calculated in Step 2

51. Copyright © 2008 Prentice Hall All rights reserved 9-51 Internal Rate of Return DECISION RULE: Invest in capital assets? Does the IRR exceed required rate of return? Invest Is the IRR less than required rate of return? Do not invest

52. Copyright © 2008 Prentice Hall All rights reserved 9-52 E9-26: Calculate IRR of Equal Cash Flows Project A: PVA = Payment x Table Factor 272,000 = 60,000 x Factor 4.533 = Factor Between 14% and 16%

53. Copyright © 2008 Prentice Hall All rights reserved 9-53 E9-26: Calculate IRR of Equal Cash Flows Project B: PVA = Payment X Table Factor 380,000 = 70,000 x Factor 5.429 = Factor Between 10% and 12%

54. Copyright © 2008 Prentice Hall All rights reserved 9-54 IRR with Unequal Periodic Cash Flows Trial and error procedure is needed to determine the discount rate making the project’s NPV equal to zero

55. Copyright © 2008 Prentice Hall All rights reserved 9-55 E9-28: Compute IRR for Unequal Cash Flows Compute net present value at 10%: Cash Flow When?Type of cash flow PV factor 10% PV $60,200 (950,000) Now 500,000Yr 1.909454,500 400,000Yr 2 Lump sum.826 330,400 Lump sum 300,000Yr 3.751 225,300 Lump sum Since the NPV is positive, the IRR must be higher than 10%. Try 12% next.

56. Copyright © 2008 Prentice Hall All rights reserved 9-56 E9-28: Compute IRR – Unequal Cash Flows Compute net present value at 12%: Cash Flow When?Type of cash flow PV factor 12% PV (950,000) Now 500,000Yr 1.893446,500 400,000Yr 2 Lump sum.797 318,800 Lump sum $28,900 300,000Yr 3.712 213,600 Lump sum Since the NPV is positive, the IRR must be higher than 12%. Try 14% next.

57. Copyright © 2008 Prentice Hall All rights reserved 9-57 E9-28: Compute IRR – Unequal Cash Flows Compute net present value at 14%: Cash Flow When?Type of cash flow PV factor 14% PV (950,000) Now 500,000Yr 1.877438,500 400,000Yr 2 Lump sum.769 307,600 Lump sum $(1,400) 300,000Yr 3.675 202,500 Lump sum

58. Copyright © 2008 Prentice Hall All rights reserved 9-58 Objective 5 Compare and contrast the four capital budgeting methods

59. Copyright © 2008 Prentice Hall All rights reserved 9-59 Comparison of Capital Budgeting Models Payback Period Simple Focus is the time it takes to recover cash Ignores cash flows after payback period Highlights risks of investments with longer cash recovery periods Ignores time value of money

60. Copyright © 2008 Prentice Hall All rights reserved 9-60 Comparison of Capital Budgeting Models Accounting Rate of Return Only method that uses accrual accounting Shows how investment will affect operating income Measures profitability of asset over its entire life Ignores time value of money

61. Copyright © 2008 Prentice Hall All rights reserved 9-61 Comparison of Capital Budgeting Models Net Present Value Incorporates time value of money and net cash flows Indicates if asset will earn minimum required rate of return Shows excess (deficiency) of present value of cash inflows over cost Profitability index can be computed for capital rationing decisions

62. Copyright © 2008 Prentice Hall All rights reserved 9-62 Comparison of Capital Budgeting Models Internal Rate of Return Incorporates time value of money and net cash flows Computes unique rate of return No additional steps needed for capital rationing decisions

63. Copyright © 2008 Prentice Hall All rights reserved 9-63 End of Chapter 9