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Capital Investment Decisions 资本投资决策

CHAPTER 7. Capital Investment Decisions 资本投资决策. Objectives. 1. Explain what a capital investment decision is, and distinguish between independent 独立 and mutually 相互 exclusive 排斥 capital investment decisions.

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Capital Investment Decisions 资本投资决策

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  1. CHAPTER 7 Capital Investment Decisions 资本投资决策

  2. Objectives 1.Explain what a capital investment decision is, and distinguish between independent独立 and mutually相互 exclusive排斥 capital investment decisions. 2. Compute the payback period and accounting rate of return for a proposed investment, and explain their roles in capital investment decisions. 3. Use net present value净现值analysis for capital investment decisions involving independent projects.

  3. Objectives 4. Use the internal rate of return内在回报率to assess the acceptability of independent projects. 5. Discuss the role and value of post-audits. 6. Explain why NPV净现值 is better than IRR内在报酬率 for capital investment decisions involving mutually exclusive projects. 7. Convert gross cash flows to after-tax cash flows. 8. Describe capital investment in the advanced manufacturing environment.

  4. Capital investment decisions are concerned with the process of planning, setting goals and priorities, arranging financing, and using certain criteria to select long-term assets. • Non-discounting models • Discounting models

  5. 1.1 Payback Method投资回报法 Original investment Annual cash flow • Non-discounting models:非贴现模型 • 投资回报期 Payback period = The cash flows is assume to occur evenly（均匀）.

  6. 1.1 Payback Method Example 1: Unrecovered Investment Year (Beginning of year) Annual Cash Flow 1 $100,000 $30,000 2 70,000 40,000 3 30,000 50,000 4 ---- 60,000 5 ---- 70,000 $30,000 was needed in Year 3 to recover the investment

  7. Payback Method 之作用 The payback period provides information to managers that can be used as follows: • To help control the risks associated with the uncertainty of future cash flows. • To help minimize the impact of an investment on a firm’s liquidity problems. • To help control the risk of obsolescence. • To help control the effect of the investment on performance measures.

  8. Payback Method 之 Deficiency 缺憾 • Ignores the time value of money • Ignores the performance of the investment beyond the payback period

  9. 1.2 Accounting Rate of Return (ARR) • ARR = Average income ÷ Original investment or • Average investment Average annual net cash flows, less average depreciation Average investment = (I + S)/2 I = the original investment S = salvage value/ residual/ scrap value Assume that the investment is uniformly consumed

  10. Accounting Rate of Return (ARR会计回报率) Example 2: Suppose that some new equipment requires an initial outlay(支出) of $80,000 and promises total cash flows of $120,000 over the next five years (the life of the machine). What is the ARR? Answer:The average cash flow is $24,000 ($120,000 ÷ 5) and the average depreciation is $16,000 ($80,000 ÷ 5). ARR = ($24,000 – $16,000) ÷ $80,000 = $8,000 ÷ $80,000 = 10%

  11. Accounting Rate of Return (续) • Reasons for Using ARR • A screening measure to ensure that new investment will not adversely(反向地) affect net income • To ensure a favorable effect on net income so that bonuses can be earned (increased) • ARR 之缺点 • The major deficiency of the accounting rate of return is that it ignores the time value of money.

  12. 附录：基本概念:Future Value(终值): Time Value of Money货币的时间价值 2. Discounting models贴现模型: • Let: F = future value • i = the interest rate • P = the present value or original outlay • n = the number or periods • Future value can be expressed by the formula: F = P(1 + i)n • : as compounding of interest 复利 • : future value factor终值系数

  13. Future Value: Time Value of Money （续） Example3: Assume the investment is $1,000. The interest rate is 8%. What is the future value if the money is invested for one year? Two? Three? Answer: F = $1,000(1.08) = $1,080.00 (after one year) F = $1,000(1.08)2 = $1,166.40 (after two years) F = $1,000(1.08)3 = $1,259.71 (after three years)

  14. Present Value现值 • P= F/(1 + i)n • The discount factor(present value factor现值系数), 1/(1 + i) n, is computed for various combinations of i and n. • Example 4: Compute the present value of $300 to be received three years from now. The interest rate is 12%. • Answer: From Exhibit 18B-1, the discount factor is 0.712. Thus, the present value (P) is: • P = F(df) • = $300 x 0.712 • = $213.60

  15. Annuity 年金 Example 5: Calculate the present value of a $100 per year annuity, to be received for the next three years. The interest rate is 12%. • Answer: • Discount Present Year Cash Factor Value • 1 $100 0.893 $ 89.30 • 2 100 0.797 79.70 • 3 100 0.712 71.20 • 2.402* $240.20 * Notice that it is possible to multiply the sum of the individual discount factors (查表: 2.402) by $100 to obtain the same answer. See (580页)Exhibit 18B.2(年金现值系数表) for these sums which can be used as discount factors for uniform series.

  16. 2.1 The Net Present Value(NPV) Method • NPV = P – I • where: • P = the sum of present value of the project’s future net cash inflows • I = the present value of the project’s cost (usually the initial outlay) • Net present value is the difference between the present value of the cash inflows and outflows associated with a project.

  17. The Net Present Value Method • Example 6: Brannon Company has developed new earphones for portable CD and tape players that are expected to generate an annual revenue of $300,000. Necessary production equipment would cost $320,000 and can be sold in five years for $40,000. • In addition, working capital营运资金 is expected to increase by $40,000 and is expected to be recovered at the end of five years. Annual operating expenses are expected to be $180,000. The required(期望的) rate of return is12 %.

  18. 题解： STEP 1. 各项CASH-FLOW的确认

  19. 书上“STEP 2B”：或可查“Present Value of an Annuity of $1”表 YEAR CASH FLOW DISCOUNT FACTOR PRESENT VALUE 0 $-360,000 1.000 $-360,000 1-4 120,000 3.307 364,400 5 200,000 0.567 113,400 Net present value $117,840 年金现值系数 *Can anybody tell me why this is different?

  20. Reinvestment Assumption再投资假设 The Net Present Value Method • The NVP model assumes that all cash flows generated by a project are immediately reinvested to earn the required rate of return throughout the life of the project.

  21. Decision Criteria决策标准 for NPV The Net Present Value Method • If NPV = 0, this indicates: • 1. The initial investment has been recovered(弥补) • 2. The required rate of return has been recovered • Thus, break even has been achieved and we are indifferent(无关) about the project.

  22. Decision Criteria for NPV The Net Present Value Method • If the NPV > 0 this indicates: • 1. The initial investment has been recovered • 2. The required rate of return has been recovered • 3. A return in excess of 1. and 2. has been received • Thus, the products should be manufactured.

  23. 2.2 Internal Rate of Return内在回报率 • Theinternal rate of return (IRR)is the discount rate that sets the project’s NPV at zero, i.e., P = I for the IRR. • Example7: A project requires a $10,000 investment and will return $12,000 after only one year. What is the IRR? • $12,000/(1 + i) = $10,000 • 1 + i = 1.2 • I = 20%

  24. IRR: (计算方法1 ) for uneven CFs

  25. To approximate(估算) that IRR =20%+31.02/(31.02+32.88)*8% =24.6%

  26. IRR：计算方法2 Trial & error （试错法 ）: p.559(18.2) • Example 8: multiple-period setting with uniform (一致) CFs：I = CF(df) , I=120000, CF=49950, n= 3 years • so df = I/CF = investment ÷ annual CF • = 120,000 ÷ 49,950 =2.402 • Seen in the Table “Present Value of an Annuity of $1” (反查)in Ex.18B.2 in p.580, the corresponding discount rate is 12%. • If the df is not exactly in the Table 18B.2, then approximate the IRR with the interpolation as well.

  27. Example 9: IRR ANALYSIS: multiple-period setting with uniform CFs Initial Investment Discount factor = Annual cash flow $180,000 60,000 = = 3.000 From(查) Exhibit 18B.2, df = 3.000 for 5 years; IRR = 20% = 3,000

  28. IRR: Decision Criteria (决策标准) • If the IRR > Cost of Capital, the project should be accepted(接受). • If the IRR = Cost of Capital, acceptance or rejection is equal. • If the IRR < Cost of Capital, the project should be rejected(拒绝).

  29. 2.3 Mutually Exclusive排斥 projects:NPV Compared With IRR • There are two major differences between net present value and the internal rate of return: • NPV assumes cash inflows are reinvested at the required rate of return whereas the IRR method assumes that the inflows are reinvested at the internal rate of return. • NPV measures the profitability of a project in absolute dollars(绝对值), whereas the IRR method measures it as a percentage(%), NOT dollar amount.

  30. So… In Example 10: Bintley Corporation Case Design A Design B Annual revenue $179,460 $239,280 Annual operating costs 119,460 169,280 Annual operating income 60,000 70,000 Equipment (purchased before Year 1) 180,000 210,000 Project life 5 years 5 years

  31. NPV Compared With IRR Net Cash-flow PATTERN Year Design A Design B 0 $-180,000 $-210,000 1 60,000 70,000 2 60,000 70,000 3 60,000 70,000 4 60,000 70,000 5 60,000 70,000 IRR ANALYSIS Opt. Year Cash Flow Discount Factor Present Value A: 1-5 60,000 3.000 180,000 B: 1-5 70,000 3.000 210,000 Check the Table for df; IRRA=20% IRRB=20%

  32. But… DESIGN A: NPV ANALYSIS Year Cash Flow Discount Factor Present Value 0 $-180,000 1.000 $-180,000 1-5 60,000 3.605 216,300 Net present value $ 36,300 DESIGN B: NPV ANALYSIS Year Cash Flow Discount Factor Present Value 0 $-210,000 1.000 $-210,000 1-5 70,000 3.605 252,350 Net present value $ 42,350 NPVA <NPVB

  33. 2.3 Adjusting Forecast for Inflation Example11： i=20% i=20%+inflation rate =20% +15%

  34. 2.4 After-Tax Operating Cash FlowsThe Income Approach 利润表法 • After-tax cash flow = After-tax net income + Noncash expenses • Example12: • Revenues $1,000,000 • Less: Operating expenses* 600,000 • Income before taxes $ 400,000 • Less: Income taxes 136,000 • Net income $ 264,000 • *$100,000 is depreciation • After-tax cash flow = $264,000 + $100,000 • = $364,000

  35. After-Tax Operating Cash FlowsDecomposition Approach 分解法 p570 • After-tax cash revenues = (1 – Tax rate) * Cash revenues • After-tax cash expense = (1 – Tax rate) * Cash exp • Tax savings (noncash expenses) = (Tax rate) * Noncash exp • Total operating cash is equal to the after-tax cash revenues, less the after-tax cash expenses, plus the tax savings on noncash expenses.

  36. After-Tax Operating Cash FlowsDecomposition Approach asExample12: Revenues= $1,000,000, cash expenses = $500,000, and depreciation = $100,000. Tax rate = 34%. After-tax cash revenues (1 – .34) ($1,000,000) = $660,000 Less: After-tax cash expense (1 – .34)($500,000)= -330,000 Add: Tax savings (noncash exp.) .34 ($100,000) = 34,000 Total $364,000

  37. 2.5 DepreciationTax-Shielding Effect(节税效果) • Depreciation is a non-cash expense and is not a cash flow. Depreciation, however SHIELDs (= protects) revenues from being taxed and, thus, creates a cash inflow equal to the tax savings.

  38. Depreciation 之Tax-Shielding Effect 是如何得来的: Assume设 initially that tax laws DO NOT allow depreciation to be deducted to arrive at taxable income. If a company had before-tax operating cash flows of $300,000 and depreciation of $100,000, we have the statement as following: Net operating cash flows $300,000 Less: Depreciation 0 Taxable income $300,000 Less: Income taxes (@ 34%) 102,000 Net income $198,000

  39. Now assume再设 allowing a deduction for depreciation: • Net operating cash flows $300,000 • Less: Depreciation 100,000 Taxable income $200,000 • Less: Income taxes (@ 34%) -68,000 • Net income $132,000 Notice that the taxes saved are： ($102,000 – $68,000)= $34,000 . Thus, the firm has additional cash available of $34,000. This savings节约 can be computed as：multiplying the tax rate by the amount of depreciation claimed,i.e.: 34% * $100,000 = $34,000

  40. 2.5.1 Straight-Line直线 Depreciation The annual depreciation is $4,000 ( = $20,000 ÷ 5). However, due to the half-year convention, only $2,000 can be deducted in 2003. Year Depreciation Deduction 2003 $2,000 (half-year amount) 2004 4,000 2005 4,000 2006 4,000 2007 4,000 2008 2,000 (half-year amount) Assume that the asset is disposed of in April 2005. Only $2,000 of depreciation can be claimed, so the book value would be $12,000 ($20,000 – $8,000).

  41. 2.5.2 MACRS Depreciation Rates • The tax laws classify most assets into the following three classes (class = Allowable years): • ClassTypes of Assets • 3 Most small tools • 5 Cars, light trucks, computer equipment • 7 Machinery, office equipment • Assets in any of the three classes can be depreciated using either straight-line or MACRS (Modified Accelerated Cost Recovery System修正的成本加速回收法) with a half-year convention (“半年惯例”）*A taxpayer claims a half of a year‘s depreciation for the first taxable year, regardless of when the property was actually put into service. It is assumed that the property being depreciated was placed into service at the mid-point of the year. To compensate for this computation, the taxpayer is entitled to another half-year of depreciation at the end of the normal recovery period.

  42. MACRS Depreciation Rates • Half the depreciation for the first year can be claimed regardless of when the asset is actually placed in service. • The other half year of depreciation is claimed in the year following the end of the asset’s class life. • If the asset is disposed of before the end of its class life, only half of the depreciation for that year can be claimed. • As §168(d)(4) of the Federal Income Tax Code.

  43. MACRS Depreciation Rates for Five-Year Assets Year Percentage of Cost Allowed 1 20.00% 2 32.00 3 19.20 4 11.52 5 11.52 6 5.76 MACRS rates

  44. Example for MACRS Method P572 Tax Tax Discount Present Year Depreciation Rate Savings Factor Value 1 $4,000 0.40 $1,600.00 0.909 $1,454.40 2 6,400 0.40 2,560.00 0.826 2,114.56 3 3,840 0.40 1,536.00 0.751 1,153.54 4 2,304 0.40 921.60 0.683 629.45 5 2,304 0.40 921.60 0.621 572.31 6 1,152 0.40 460.80 0.564 259.89 i=10% Net present value = $6,184.15

  45. 对照: Straight-Line Depreciation Tax Tax Discount Present Year Depreciation Rate Savings Factor Value 1 $2,000 0.40 $ 800.00 0.909 $ 727.20 2 4,000 0.40 1,600.00 0.826 1,321.60 3 4,000 0.40 1,600.00 0.751 1,201.60 4 4,000 0.40 1,600.00 0.683 1,092.80 5 4,000 0.40 1,600.00 0.621 993.60 6 2,000 0.40 1,600.00 0.564 451.20 Net present value $5,788.00

  46. 3. Underthe Advanced manufacturing environment (p573) 3.1 How investment is defines? Software, engineering, training and implementation costs are a significant % of the total costs. (Peripheral costs, side-line costs) 3.2 How operating CFs are estimated? 3.3 How salvage value is treated? 3.4 How discount rate is chosen? 3.5 Others: non-financial criteria, Ethics, Post-audit

  47. 3.2 How Estimates of Operating Cash Flows Differ? A company is evaluating a potential investment in a flexible manufacturing system (FMS,灵活制造系统). The choice is to (1) continue producing with its traditional equipment, expected to last 10 years, or (2) to switch转换 to the new system, which is also expected to have a useful life of 10 years. The company’s discount rate is 12%.

  48. 3.2 How Estimates of Operating Cash Flows Differ？ 每年： FMS*Status quo Investment (current outlay): Direct costs $10,000,000 --- Software, engineering 8,000,000 --- Total current outlay支出 $18,000,000 Net after-tax cash flows $ 5,000,000 $1,000,000 Less: After-tax cash flows for status quo现有系统 1,000,000 n/a Incremental增量的 benefit $ 4,000,000 n/a

  49. INCREMENTAL BENEFIT EXPLAINED解释 Direct benefits: Direct labor $1,500,000 Scrap废料reduction减少 500,000 Setups生产准备 200,000 $2,200,000 Intangible benefits (quality 质量方面 savings): Rework 返工 $ 200,000 Warranties售后服务 400,000 Maintenance of competitive position 1,000,000 1,600,000 Indirect benefits: Production scheduling安排 $ 110,000 Payroll工资核算 90,000 200,000 Total $4,000,000

  50. Present value ($4,000,000 * 5.65十年) $22,600,000 Investment 18,000,000 Net present value $ 4,600,000 3.2 How Estimates of Operating Cash Flows Differ？ Butifeliminate intangible and indirect benefits: Present value ($2,200,000 * 5.65) $12,430,000 Investment 18,000,000 Net present value $(5,570,000)

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