capital investment decisions 资本投资决策

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Capital Capital Investment Investment DecisionsDecisions

资本投资决策资本投资决策

CHAPTERCHAPTER

77

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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.

ObjectivesObjectivesObjectivesObjectives

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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.

ObjectivesObjectivesObjectivesObjectives

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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.

1.Non-discounting models

2.Discounting models

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1.1 Payback Method 投资回报法

投资回报期 Payback period =

Original investmentAnnual cash flow

The cash flows is assume to occur evenly （均匀） .

The cash flows is assume to occur evenly （均匀） .

1. Non-discounting models: 非贴现模型

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1.1 Payback MethodExample 1:

Year (Beginning of year) Annual Cash FlowYear (Beginning of year) Annual Cash Flow Unrecovered InvestmentUnrecovered Investment

1 $100,000 $30,0002 70,000 40,0003 30,000 50,0004 ---- 60,0005 ---- 70,000

$30,000 was needed $30,000 was needed in Year 3 to recover in Year 3 to recover

the investmentthe investment

$30,000 was needed $30,000 was needed in Year 3 to recover in Year 3 to recover

the investmentthe investment

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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.

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Ignores the time value of money

Ignores the performance of the investment beyond the payback period

Payback Method 之Deficiency 缺憾Deficiency 缺憾

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1.2 Accounting Rate of Return (ARR)1.2 Accounting Rate of Return (ARR)

ARR = Average income ÷ Original investment or Average investment

Average investment Average investment = (= (II + + SS)/2)/2

Average investment Average investment = (= (II + + SS)/2)/2

I = the original investment

S = salvage value/ residual/ scrap value

Assume that the investment is uniformly consumed

I = the original investment

S = salvage value/ residual/ scrap value

Assume that the investment is uniformly consumed

Average annual net Average annual net cash flows, less cash flows, less

average average depreciationdepreciation

Average annual net Average annual net cash flows, less cash flows, less

average average depreciationdepreciation

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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%

Accounting Rate of Return (ARR 会计回报率 )Accounting Rate of Return (ARR 会计回报率 )

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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.

Accounting Rate of Return ( 续 )Accounting Rate of Return ( 续 )

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附录：基本概念 :Future Value( 终值 ): Time Value of Money 货币的时间价

值

附录：基本概念 :Future Value( 终值 ): Time Value of Money 货币的时间价

值

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

2. Discounting models 贴现模型 :

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Future Value: Time Value of Money （续）

Future Value: Time Value of Money （续）

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)

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?

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Present ValuePresent Value 现值现值Present ValuePresent Value 现值现值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

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Answer:DiscountPresent Year Cash Factor

Value1 $100 0.893$ 89.302 100 0.79779.703 100 0.712 71.20

2.402* $240.20

Annuity 年金Annuity 年金

* 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.

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%.

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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.

2.1 The Net Present Value(NPV) Method2.1 The Net Present Value(NPV) Method2.1 The Net Present Value(NPV) Method2.1 The Net Present Value(NPV) Method

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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 is 12 %.

The Net Present Value MethodThe Net Present Value MethodThe Net Present Value MethodThe Net Present Value Method

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题解：题解： STEP 1. STEP 1. 各项各项 CASH-FLOWCASH-FLOW 的确认的确认Year:0 1 2 3 4 5

Step 1. CASH-FLOW IDENTIFICATION:Step 1. CASH-FLOW IDENTIFICATION:

Equipment (320)

Working capital (40)

Revenues 300 300 300 300 300

Operating expenses (180) (180) (180) (180) (180)

Salvage 40

Recovery of working capital 40

Step 2. Sum of CFsStep 2. Sum of CFsNCFsNCFs (360) 120 120 120 120 200

Step 3. NPV ANALYSIS:Step 3. NPV ANALYSIS:

Discount factor 1 0.893 0.797 0.712 0.636 0.567

PV (360) 107 96 85 76 113

NPV 117.960

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书上“书上“ STEP 2BSTEP 2B”” ：或可查“：或可查“ Present Value of an Annuity of $1Present Value of an Annuity of $1”” 表表YEAR CASH FLOW DISCOUNT FACTOR PRESENT VALUE

0 $-360,000 1.000 $-360,0001-4 120,000 3.307 364,4005 200,000 0.567 113,400

Net present value $117,840

年金年金现值系现值系

数数

*Can anybody tell me why this is different?

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Reinvestment Assumption 再投资假设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.


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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.


Decision Criteria 决策标准 for NPV

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Decision Criteria for NPV

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.


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The internal rate of return (IRR) is the discount rate that sets the project’s NPV at zero, i.e., P = I for the IRR.

Example 7: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%

2.2 Internal Rate of Return2.2 Internal Rate of Return 内在回报率内在回报率2.2 Internal Rate of Return2.2 Internal Rate of Return 内在回报率内在回报率

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Year: 0 1 2 3 4 5Equipment (320)

Working capital (40)

Revenues 300 300 300 300 300

Operating expenses (180) (180) (180) (180) (180)

Salvage 40

Recovery of working capital 40

NCFsNCFs (360) 120 120 120 120 200

IRR ANALYSIS:IRR ANALYSIS:

Discount factor 1 0.893 0.797 0.712 0.636 0.567

PV (360) 107 96 85 76 113

NPV(when i=12% ） 117.960

NPV(when i=20%) 31.024

IRR: (IRR: ( 计算方法计算方法 1 ) 1 ) for uneven CFsfor uneven CFsIRR: (IRR: ( 计算方法计算方法 1 ) 1 ) for uneven CFsfor uneven CFs

NPV(when i=28%) (360) 94 73 57 45 58

NPV(when i=28%) (32.876)

IRR=23.6

%

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To approximate( 估算 ) thatIRR =20%+31.02/(31.02+32.88)*8% =24.6%

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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.

IRRIRR ：计算方法：计算方法 22IRRIRR ：计算方法：计算方法 22

Trial & error （试错法试错法） : p.559(18.2)p.559(18.2)

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IRR ANALYSIS:IRR ANALYSIS: multiple-period setting with uniform CFs

Discount factor =

Example 9:

Initial Investment

Annual cash flow

=$180,000

60,000

= 3,000From( 查 ) Exhibit 18B.2, df = 3.000 for 5 years; IRR = 20%

= 3.000

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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 ).

IRR: IRR: Decision Criteria ( 决策标准决策标准 ))IRR: IRR: Decision Criteria ( 决策标准决策标准 ))

18 -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.

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So…

Design A Design B

Annual revenue $179,460 $239,280Annual operating costs 119,460 169,280Annual operating income 60,000 70,000Equipment (purchased before Year 1) 180,000 210,000Project life 5 years 5 years

In Example 10: Bintley Corporation CaseIn Example 10: Bintley Corporation Case

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NPV Compared With IRRNet Cash-flow PATTERNNet Cash-flow PATTERN

Year Design A Design BYear Design A Design B

0 $-180,000 $-210,0001 60,000 70,0002 60,000 70,0003 60,000 70,0004 60,000 70,0005 60,000 70,000

IRR ANALYSISIRR ANALYSIS

Opt. Year Cash Flow Discount Factor Present ValueOpt. Year Cash Flow Discount Factor Present Value

A: 1-5 60,000 3.000 180,000B: 1-5 70,000 3.000 210,000

Check the Table for df; IRRA=20% IRRB=20%

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But…

DESIGN B: NPV ANALYSISDESIGN B: NPV ANALYSIS

Year Cash Flow Discount Factor Present ValueYear Cash Flow Discount Factor Present Value

0 $-210,000 1.000 $-210,0001-5 70,000 3.605 252,350

Net present value $ 42,350

DESIGN A: NPV ANALYSISDESIGN A: NPV ANALYSIS

Year Cash Flow Discount Factor Present ValueYear Cash Flow Discount Factor Present Value

0 $-180,000 1.000 $-180,0001-5 60,000 3.605 216,300

Net present value $ 36,300

NPVA <NPVB

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2.3 Adjusting Forecast for Inflation2.3 Adjusting Forecast for Inflation2.3 Adjusting Forecast for Inflation2.3 Adjusting Forecast for Inflation

Y ear C as h F low D is count F actor P res ent Value

0 ($5,000,000) 1 ($5,000,000)1 3,335,000 0.833 2,779,1672 3,835,250 0.694 2,663,368

Net present value $442,535

Y ear C as h F low D is count F actor P res ent Value

0 ($5,000,000) 1 ($5,000,000)1 3,335,000 0.741 2,470,3702 3,835,250 0.549 2,104,390

Net present value ($425,240)

WITHOUT INFLATIONARY ADJUSTMENT

WITH INFLATIONARY ADJUSTMENT

Example 11 ： i=20% i=20%+inflation rate =20% +15%

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2.4 After-Tax Operating Cash Flows The Income Approach 利润表法

After-tax cash flow = After-tax net income + Noncash expenses

Example 12:Revenues $1,000,000Less: Operating expenses* 600,000Income before taxes $ 400,000Less: Income taxes 136,000Net income $ 264,000

*$100,000 is depreciation

After-tax cash flow = $264,000 + $100,000

= $364,000

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After-tax cash revenues = (1 – Tax rate) * Cash revenuesAfter-tax cash expense = (1 – Tax rate) * Cash expTax 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.

After-Tax Operating Cash Flows Decomposition Approach 分解法 p570

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as Example 12: Revenues= $1,000,000, cash expenses = $500,000, and depreciation = $100,000. Tax rate = 34%.

After-tax cash revenues (1 – .34)($1,000,000) = $660,000Less: After-tax cash expense (1 – .34)($500,000)= -330,000Add: Tax savings (noncash exp.) .34($100,000) = 34,000 Total $364,000

After-Tax Operating Cash Flows Decomposition Approach

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2.5 DepreciationTax-Shielding Effect( 节税效果 )

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.

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Net operating cash flows $300,000Less: Depreciation 0Taxable income $300,000Less: Income taxes (@ 34%) 102,000 Net income $198,000

Depreciation 之Tax-Shielding Effect 是如何得来的 :

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:

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Net operating cash flows $300,000

Less: Depreciation 100,000 Taxable income $200,000

Less: Income taxes (@ 34%) -68,000

Net income $132,000

Now assume 再设 allowing a deduction for depreciation:

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

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Year Depreciation Deduction

2003 $2,000 (half-year amount)2004 4,0002005 4,0002006 4,0002007 4,0002008 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).

2.5.1 Straight-Line 直线 DepreciationThe annual depreciation is $4,000 ( = $20,000 ÷ 5). However, due to the half-year convention, only $2,000 can be deducted in 2003.

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The tax laws classify most assets into the following three classes (class = Allowable years):

Class Types of Assets3 Most small tools5 Cars, light trucks, computer equipment7 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.

2.5.2 MACRS Depreciation Rates2.5.2 MACRS Depreciation Rates2.5.2 MACRS Depreciation Rates2.5.2 MACRS Depreciation Rates

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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.

MACRS Depreciation RatesMACRS Depreciation RatesMACRS Depreciation RatesMACRS Depreciation Rates

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MACRS rates

MACRS Depreciation Rates for MACRS Depreciation Rates for Five-Year AssetsFive-Year Assets

Year Percentage of Cost AllowedYear Percentage of Cost Allowed

1 20.00%

2 32.00

3 19.20

4 11.52

5 11.52

6 5.76

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Example for MACRS Method P572

Tax Tax Tax Discount Present Discount PresentYear Depreciation Year Depreciation Rate Savings Rate Savings Factor ValueFactor Value

1 $4,000 0.40 $1,600.00 0.909 $1,454.402 6,400 0.40 2,560.00 0.826 2,114.563 3,840 0.40 1,536.00 0.751 1,153.544 2,304 0.40 921.60 0.683 629.455 2,304 0.40 921.60 0.621 572.316 1,152 0.40 460.80 0.564 259.89

i=10% Net present value = $6,184.15

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对照 : Straight-Line Depreciation

Tax Tax Discount PresentTax Tax Discount PresentYear Depreciation Rate Savings Factor ValueYear Depreciation Rate Savings Factor Value

1 $2,000 0.40 $ 800.00 0.909 $ 727.202 4,000 0.40 1,600.00 0.826 1,321.603 4,000 0.40 1,600.00 0.751 1,201.604 4,000 0.40 1,600.00 0.683 1,092.805 4,000 0.40 1,600.00 0.621 993.606 2,000 0.40 1,600.00 0.564 451.20

Net present value $5,788.00

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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

3. Under the Advanced manufacturing environment (p573)

3. Under the Advanced manufacturing environment (p573)

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3.2 How Estimates of Operating Cash Flows Differ?

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%.

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每年：每年： FMSFMS** Status quoInvestment (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

3.2 How Estimates of Operating Cash Flows Differ ？


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INCREMENTAL BENEFIT EXPLAINEDINCREMENTAL BENEFIT EXPLAINED 解释解释

Direct benefits:Direct labor $1,500,000Scrap 废料 reduction 减少 500,000Setups 生产准备 200,000

$2,200,000Intangible benefits (quality质量方面 savings):

Rework 返工 $ 200,000Warranties 售后服务 400,000Maintenance of competitive position 1,000,000

1,600,000Indirect benefits:

Production scheduling 安排 $ 110,000Payroll 工资核算 90,000

200,000 Total

$4,000,000

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Present value ($4,000,000 * 5.65 十年 ) $22,600,000Investment 18,000,000 Net present value $ 4,600,000

But if eliminate intangible and indirect benefits:Present value ($2,200,000 * 5.65) $12,430,000Investment 18,000,000 Net present value $(5,570,000)



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3.3 Salvage value is also important. Uncertainty of salvage value could make huge difference. As p.575 or the case we mentioned above. * Sensitivity analysis( 敏感度分析， what-if analysis) for uncertainty.

3.4 To chose discount rate:

Should be “a firm’s cost of capital 资本成本” . (p.576)As presented in the previous NPV and IRR interpretations, it can be seen that being overly conservative ( 过分谨慎 ) with discount rates can prove more damaging 损害 .

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1) The analysis should consider the conditions of non-financial information, e.g. …

2) Issues of Ethics: Segment managers may fraud the estimates of operating CFs, maybe for the reasons of competitions, or for pursuing their prospected projects to be proved.

3) Post-audit of capital projects (p.561) * Case:* Benefits of a postaudit: • Whether the resources are used wisely• Its impact on the behavior of managers.• More objective results are obtainable.

* A postaudit has limitations, and it is costly.

3.5 Others3.5 Others

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The EndThe EndThe EndThe End

Capital Investment Capital Investment DecisionsDecisions

capital investment decisions 资本投资决策

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