1. CAPITAL INVESTMENT DECISIONS CHAPTER 12 Professor Debbie Garvin, JD; CPA – ACG2071

2. Four Popular Methods of Capital Budgeting Analysis MethodAdvantage/Disadvantage Payback period in years Quick and easy to calculate, used for shorter life span investments Accounting Rate of Return (ARR) Net Present Value (NPV) More difficult to calculate, used for longer life span investments, considers time value of money Internal Rate of Return (IRR) Capital Budgeting - Acquisition of assets used for a long period of time and which require large sums of money 2

3. Cash Basis vs. Accrual Basis  Cash versus accrual basis  Accrual basis required by Generally Accepted Accounting Principles (GAAP)  Capital budgeting focuses on cash flows  Only Accounting Rate of Return method uses accrual- based accounting income 3

4. Cash Flows  Cash inflows include:  Future cash revenue  Any future savings in ongoing cash operating costs  Any future residual value of the asset  Cash outflows include:  Initial investment – treated separately from other cash outflows  Ongoing cash operating expenses such as repairs & maintenance  What about depreciation expense? 4

5. Capital Budgeting Process  Identify potential investments  Estimate the net cash inflows  Analyze the various potential investments  Choose among alternative capital investments by screening out less favorable  Capital rationing  Post-audit analysis 5

6. a.Budget capital investments b.Project investments’ cash flows c.Perform post-audits d.Make investments e.Use feedback to reassess investments already made f.Identify potential capital investments g.Screen/analyze investments using one or more of the methods discussed Place the following activities in sequence to illustrate the capital budgeting process: 6

7. Use Payback Period for Capital Investments  Payback –length of time it takes to recover the cost of the capital outlay Amount invested Expected annual net cash inflows over life 7

8. Payback Period = Amount invested Expected annual net cash inflows Amount invested Expected annual net cash inflows $2,480,000 $310,000 = 8 years to recover investment Since payback (8 yrs) occurs after facility must be replaced, should Gator Co. purchase the new facility? 8 Gator Co. considering acquiring new practice facility. Purchase price is $2,480,000. Owners believe new facility will generate net cash inflows of $310,000 annually for its five year useful life.

9. Payback with Unequal Net Cash Inflows Accumulate net cash inflows until amount invested recovered Payback = 5 years + ($88,000/$250,00 0) = 5.352 years Net Cash Flow YearsAmount InvestedAnnualAccumulated 0$1,418,000- - - 1 $300,000 2- - -$280,000$580,000 3- - -$250,000$830,000 4- - -$250,000$1,080,000 5- - -$250,000$1,330,000 6- - -$250,000$1,580,000 7- - -$250,000$1,830,000 8- - -$250,000$2,080,000 9- - -$250,000$2,330,000 10- - -$30,000$2,360,000 Useful Life 9

10. Criticism of Payback Method  Focuses only on time, not on profitability  Considers only those cash flows that occur during the payback period.  Paintball Facility estimated to generate $942,000 after Payback Period:  Year 6 - $162,000 ($250,000 < $88,000)  Year 7, 8 & 9 - $750,000 ($250,000/yr.)  Year 10 - $ 30,000  Total $942,000  Time Value of money ignored 10

11. Payback Period 11

12. Accounting Rate of Return  Measures the average annual rate of return over the asset’s life  Focuses on the operating income, not the net cash inflow, that an asset generates. Average annual operating income from asset Either Initial Investment or Average amount invested in asset * ARR = * As page 718 of text says, we will use initial investment to compute ARR even though some managers prefer to use average investment. So for exam purposes, we will use initial investment. 12

13. Gator Co. considering producing CD players & DVRs. Products require different specialized machines, each costing $1m. Each machine has a 5-yr life & zero residual value with the following predicted net cash inflows: YearAnnual Net Cash Inflows: CD PlayersDVRs 1 $312,500 $500,000 2 312,500 350,000 3 312,500 300,000 4 312,500 250,000 5 312,500 40,000 Gator will only consider if ARR exceeds 8% Average annual operating income from asset Initial Investment ARR CD Player = Initial cost of investment – Residual value Useful life of asset (in years) Annual depreciation = ARR = $312,500 avg. cash inflow - $200,000 depreciation = 11.25% $1,000,000 initial investment $1,000,000 – $0 5 years Annual depreciation = = $200,000 dep./yr. 13

14. ARR of DVR - Unequal Net Cash Calculate the average annual net cash inflows ARR = Average annual operating income Initial Investment ARR DVR = $288,000 avg. cash inflow - $200,000 depreciation = 8.8% $1,000,000 ARR CD = 11.25% If asset has residual value, how would that change the ARR? Annual Cash Flows - - - $500,000 350,000 300,000 250,000 40,000 $1,440,000 Compute Annual Cash Flows $1,440,000 / 5 year useful life = $288,000 average cash inflow Compute Annual Depreciation Expense $1,000,000 5 yrs = $200,000 annual depr. exp. 14

15. Accounting Rate of Return 15

16. Compute Payback Period - Equal Cash Inflows Quicksilver is considering acquiring a manufacturing plant. The purchase price is $1,236,100. The owners believe the plant will generate net cash inflows of $309,025 annually. It will have to be replaced in eight years. What is payback period? Payback Period = Amount invested Expected annual net cash inflows $1,236,100 $309,025 = 4 years to pay back 16

17. Compute Payback Period - Unequal Cash Inflows Sikes Hardware is adding new product line that will require an investment of $1,500,000. Mngrs estimate this investment will have a ten-year life & generate net cash inflows of $315,000 the first year, $285,000 the second year, and $240,000 each year thereafter for eight years. The investment has no residual value. Compute the payback period. YearsAmount InvestedAnnualAccumulated 0$1,500,000- - - 1 2 3 4 5 6 $240,000 $1,800,000 $1,560,000 $1,320,000 $1,080,000 $840,000 $240,000 $600,000$285,000 $315,000 Payback = 5 yrs + $180,000(needed cash in Yr. 6 to get to $1.5m ÷ 240,000 net cash inflow year 6 = 5.75 yrs 17

18. ARR with Unequal Cash Flows Average annual operating income: Year 1 net cash inflow$ 315,000 Year 2 net cash inflow 285,000 Years 3-10 ($240,000 x 8) 1,920,000 Total net cash flows $2,520,000 Less: Total depreciation(1,500,000) Total operating income over life$1,020,000 Divided by years of life ÷ 10 Average annual operating income$102,000 Co. adding new product line that will require an investment of $1,500,000. Mgr. estimates investment will have a 10-year life and generate net cash inflows of $315,000 in yr 1, $285,000 in yr 2, and $240,000 each yr thereafter for 8 yrs. w/no residual value. Compute ARR 18

19. ARR with Unequal Cash Flows (cont.) Average annual operating income from asset Initial Investment $102,000 $1,500,000 = 6.8% ARR ARR = Co. adding new product line that will require an investment of $1,500,000. Mgr. estimates investment will have a 10-year life and generate net cash inflows of $315,000 in yr. 1, $285,000 in yr. 2, and $240,000 each yr. thereafter for 8 yrs. w/no residual value. Compute ARR 19

20. Time Value of Money  Two main principles:  Invested money earns income over time  Cash received sooner is preferred over cash received later 20

21. Time Value of Money Factors  Principal amount (p) Single lump sum Annuity Ordinary annuity Annuity due  Number of periods (n)  Interest rate (i) Simple interest Compound interest 21

22. Simple Interest Calculation  Simple interest means interest is calculated only on the principal amount. Compute simple interest at 6% on 5 yr. $10,000 Investment Simple Interest YearInterest CalculationSimple Interest 1$10,000 x 6% =$600 2$10,000 x 6% =$600 3$10,000 x 6% =$600 4$10,000 x 6% =$600 5$10,000 x 6% =$600 Total Interest after 5 years$3,000 22

23. Compound Interest Calculation  Compound interest means interest is calculated on the principal and on all interest earned too date Compound Interest YearCompound Interest CalculationCompound Interest 1$10,000 x 6% =$ 600 2($10,000 + 600) x 6% =$ 636 3($10,000 + 600 + 636) x 6% =$ 674 4($10,000 + 600 + 636 + 674) x 6% =$ 715 5($10,000 + 600 + 636 + 674 + 715) x 6% =$ 758 Total Interest$ 3,383 Simple interest = $3,000 Compound interest =$3,383 $ 383 extra interest from compounding 23

24. Present Value & Future Value If invest $10,000 today earning 6% compound interest, what is future value at end of 5 yrs.? Principal + Compound interest = $13,383 from last slide Using table $10,000 x 1.338 = $13,380 24

25. Present Value and Future Value 12345 $13,380 Future Value $10,000 Present Value Time Periods Present value + Interest earned = Future value 25

26. Future Value of an Annuity Table D What if invest $2,000 at end of each yr. for five years? Future value = Amount of each cash installment (Annuity FV factor for i = 6%, n = 5) = $2,000 x (5.637) = $11,274 26

27. Compare Retirement Savings Plan You want to retire at 52 using one of following two plans:  Save $3,000 a year starting now (age 22) for 30 years or  Wait until you are 40 to start saving and then save $7,500 per year for the next 12 years. Assume that you will earn an average of 10% per year. 1. How much out-of-pocket cash will you invest under 2 options? Option 1: $3,000 x 30 years = $90,000 Option 2: $7,500 x 12 years = $90,000 27

28. Compare Retirement Savings Plan 2. What is accumulated savings at age 52? Plan 1: Future value = Payment x (Annuity FV factor, i = 10%, n = 30) = $3,000 x 164.490 (Table D) = $493,470 in Savings Plan 2: Future value = Payment x (Annuity FV factor, i = 10%, n = 12) = $7,500 x 21.384 (Table D) = $160,380 in Savings 28

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30. Compare Retirement Savings Plans - Req #4 Req. 4 If you let the savings continue to grow for ten more years (with no further out-of-pocket investment) what will each investment be worth at age 62? Plan 1: Future value of $1 = present value x table factor (Table C) = $493,470 x 2.594 (i=10%; n=10) = $1,280,061 Plan 2: Future value of $1 = present value x table factor = $160,380 x 2.594 = $416,026 30

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32. Congrats! You’ve Won the Lottery Lottery offers you following (after-tax) payout options: Assume you can earn 8% on your funds, which is best? Option 1: $12,000,000 five years from now Present value of $1 = $12,000,000 x.681(Table A) = $8,172,000 Option 2: $2,250,000 at end of each year for 5 yrs Present value annuity = $2,250,000 x 3.993 (Table B) = $8,984,250 Option 3: $10,000,000 three years from now Present value of $1 = $10,000,000 x.794 (Table A) = $7,940,000 32

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35. Discounted Cash Flow Models  Neither the payback period nor the ARR incorporate time value of money.  Two discounted cash flow models recognize time value of money:  Net present value  Internal rate of return  Both methods rely on present value calculations to compare the amount of investment (initial cost) with its expected (estimated) net cash inflows (all future cash flows such as estimated future increased sales and cost savings netted against the investment’s future cash operating costs) 35

36. Net Present Value Method  Compare discounted cash inflows to their 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 36

37. Net Present Value Method Cash FlowWhen?Type of cash flow PV factor 14% PV Project A NPV = (272,000) Now 60,000*Yrs 1-8Annuity4.639278,340 $6,340 Use NPV to determine whether Co. should invest in following: Project A: Costs $272,000 and offers eight annual net cash inflows of $60,000. Co. requires annual return of 14% on projects like A. 37

38. 38 A B ABAB

39. Cash FlowWhen?Type of cash flowPV factor 12%PV Project B NPV (380,000) Now 70,000 Yrs 1-9 Annuity5.328372,960 $ (7,040) Project B: Costs $380,000 and offers nine annual net cash inflows of $70,000. Co. demands an annual return of 12% on investments of this nature. 39

40. Net Present Value 40

41. Net Present Value for Unequal Cash Inflows  When annual cash inflows are unequal, you must use the present value applied to each annual cash inflow individually 41

42. Calculate NPV - Unequal Annual Cash Inflows YearPV Factor (i = 14%)Net Cash InflowPV of each year’s net cash inflow disc. at 14% Year 1 (n = 1)0.877 x $260,000 =$228,020 Year 2 (n = 2)0.769 x $250,000 =192,250 Year 3 (n = 3)0.675 x $225,000 =151,875 Year 4 (n = 4)0.592 x $210,000 =124,320 Year 5 (n = 5)0.519 x $200,000 =103,800 Year 6 (n = 6)0.456 x $175,000 =79,800 Total PV net cash inflows$1,320,000880,065 Initial Investment(900,000) NPV of the Project$(19,935) Co. deciding whether to automate one phase of production process. New Equip has a 6-yr. life & will cost $900,000. Projected net cash inflows are shown. Compute NPV. Should Co. invest in equipment? Co. requires 14% rate of return 42

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44. Calculate NPV - Unequal Annual Cash Inflows Cash FlowWhen? Type of cash flowPV factor 14% PV Additional NPV 75,000 Yr. 7.400 30,000 Lump sum 50,000 * Yr. 7.400 20,000 Lump sum (100,000)(45,600) Yr. 6Lump sum.456 $4,400 Assume Co. could refurbish equip at end of 6 years for $100,000. Equip could then be used 1 more yr., providing net cash inflows of $75,000 in Yr. 7. Refurbished equip would have a $50,000 residual value at end of Yr. 7. Should Co. refurbish after 6 years? (Additional cash flow must be discounted back to PV) NPV from Part 1: (19,935) New NPV w/ additional facts (15, 535) Overall investment still negative 44

45. Profitability Index  Useful when choosing among alternative projects  Useful when projects require different initial investments.  Is the number of dollars returned for every dollar invested 45

46. Capital Rationing Decision Project A Project B Project C Present value of net cash inflows $1,695,000 $1,960,000 $2,200,000 Investment ($1,500,000) ($1,750,000) ($2,000,000) NPV $ 195,000 $ 210,000 $ 200,000 Each project yields positive NPV w/Project B having highest NPV, choose Project B? Use Profitability Index Profitability Index = Present value of net cash inflows ÷ Initial 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 Co. considering 3 capital investment proposals, but can only pursue one proposal. Which investment should they pursue? Net Present Value already computed. 46

47. Internal Rate of Return  Rate of return a company can expect to earn by investing in a project  Find the discount rate that makes the cost of investment equal to PV of investment’s net cash inflows  The interest rate that will cause the present value to equal zero 47

48. Internal Rate of Return Steps required to calculate IRR w/equal net cash inflows Step 1: Identify the expected net cash receipts Step 2: Find discount rate that makes total present value of net cash receipts = present value of cash outflows Step 3: On the present value of an annuity of $1 table (B), scan the row corresponding to the expected life Choose column closest to annuity factor calculated in Step 2 When investment is annuity we can develop formula for Annuity PV factor: Annuity PV factor = Investment’s Cost ÷ Annual (equal) Net Cash Inflows 48

49. 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  We could use a calculator programmed with the IRR function to determine the discount rate  We could also use a spreadsheet programmed with the IRR function to determine the discount rate  We will use trial & error procedure on Exam 49

50. Internal Rate of Return 50

51. Slides 37 & 39: Calculate IRR (Equal Cash Inflows) Compute IRR of each project and use info to identify which is better inv. Project A costs $272,000, offers 8 annual net cash inflows of $60,000. Co. requires annual return of 14% on projects like A. IRR found by first finding Annuity PV factor of the following equation & then finding interest rate associated with that PV factor: $272,000 (Inv. Cost) = 4.533 Annuity PV factor (i = ?; n = 8) $ 60,000 (Amount of annual net cash inflow) Using PV of Annuity of $1 table, we find that 4.533 is between 14% (4.639) & 16% (4.344). Thus the internal rate of return is between 14% & 16%. Using business calculator, IRR is 14.69% 14.69% is discount rate that makes Project’s inv. cost = PV of inv.’s net cash inflows, so Proj. A’s internal rate of return is 14.69% 51

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53. Calculate IRR of Project B (SL. 39) Project B: Costs $380,000 and offers nine equal annual net cash inflows of $70,000. Salon Products demands an annual return of 12% on investments of this nature. IRR found by first finding Annuity PV factor that will solve the following equation & then finding interest rate associated with that PV factor: $380,000 (Inv. Cost) = 5.429 Annuity PV factor (i = ?, n = 9) $ 70,000 (Amount of equal annual net cash inflow) Using PV of Annuity of $1 table, we find that 5.429 is between 10% (5.759) & 12% (5.328). Thus the internal rate of return is between 10% & 12%. Using business calculator, IRR is 11.51% Which Project has higher IRR? 53

54. Gator Co. considering equip investment costing $950,000. Projected net cash inflows over equip.’s 3 yr. life: Yr. 1: $500,000; Yr.2: $400,000; Yr.3: $300,000. Gator’s hurdle rate is 10% What is IRR? The IRR is the interest rate at which the NPV of the investment is zero. Since the net cash inflows are not equal, we cannot use the annuity table to find the IRR. Rather, we must discount each cash flow back to its present value using the PV factors found in the Present Value of $1 table. Begin trial- and-error process using Ritter’s 10% hurdle rate. YearNet Cash InflowPV factor i = 10%Present Value 1$500,0000.909$ 454,500 2400,0000.826 330,400 3300,0000.751 225,300 Present value of net cash inflows $1,010,200 Investment (950,000) NPV $ 60,200 YearNet Cash InflowPV factor i = 12%Present Value 1$500,0000.893$ 446,500 2400,0000.797 318,800 3300,0000.712 213,600 Present value of net cash inflows $ 978,900 Investment (950,000) NPV $ 28,900 Since NPV positive, IRR must be higher than 10%, try 12% Since NPV still positive, IRR must be higher than 12% IRR w/unequal cash flows 54

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56. 56 YearNet Cash Inflow PV factor i = 14%Present Value 1$500,0000.877$ 438,500 2400,0000.769 307,600 3300,0000.675 202,500 Present value of net cash inflows $ 948,600 Investment (950,000) NPV ($ 1,400) Try 14%: NPV now negative, but close to zero. The IRR is somewhere between 12% and 14%, but closer to 14%. Using business calculator, we can find the exact IRR of 13.92%

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58. Comparison of Capital Budgeting Models  Payback Period  Simple  Focus is the time it takes to recover cash  Highlights risks of investments with longer cash recovery periods  Disadvantages  Ignores cash flows after payback period  Ignores time value of money  So often used for initial screening of several different investment proposals 58

59. 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  Disadvantage: Ignores time value of money 59

60.  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  Disadvantage: Difficult to compare investments of different sizes  However, Profitability index can be computed for capital rationing decisions among several potential investments all w/positive Net Present Value Comparison of Capital Budgeting Models 60

61.  Internal Rate of Return  Incorporates time value of money and net cash flows  Shows actual rate of return being earned on investment by equating PV of net cash inflows to investment’s cost. Interest rate which brings investment’s NPV to zero  No additional steps needed for capital rationing decisions  Disadvantage: Assumes that all cash inflows are reinvested at a rate equal to the IRR Comparison of Capital Budgeting Models 61

62. END OF SEGMENT Debbie Garvin, JD; CPA – ACG2071