Course 1 : Contemporary Perspectives on Accountingedblog.hkedcity.net/wp-content/blogs/1683/uploads//unit-10-capital... · Non-financial factors affecting capital investment ... Used

Professional Development Programme on Enriching Knowledge of the Business, Accounting and Financial Studies (BAFS) Curriculum

Technology Education Section, Curriculum Development InstituteEducation Bureau, HKSARG

August 2008

Unit 10 : Capital Investment Appraisal

Course 1 : Contemporary Perspectives on Accounting

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Learning objectivesLearning objectives

On completion of this unit, you should be able to:On completion of this unit, you should be able to:

1.1. Explain capital investment decisions. Explain capital investment decisions. 2.2. Apply the basic capital investment appraisal methods Apply the basic capital investment appraisal methods

to evaluate capital projects: accounting rate of return to evaluate capital projects: accounting rate of return (ARR), payback period (PB), net present value (NPV); (ARR), payback period (PB), net present value (NPV); and internal rate of return (IRR).and internal rate of return (IRR).

3.3. Compare the usefulness and limitations of different Compare the usefulness and limitations of different capital investment appraisal methods.capital investment appraisal methods.

4.4. Evaluate nonEvaluate non--financial factors affecting capital financial factors affecting capital investment decisions. investment decisions.

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ContentContent

1.1. Introduction Introduction 2.2. Different types of capital investment decisions and Different types of capital investment decisions and

risksrisks3.3. NonNon--financial factors affecting capital investment financial factors affecting capital investment

decisions decisions 4.4. Financial factors affecting capital investment decisions Financial factors affecting capital investment decisions 5.5. Traditional capital investment appraisal techniques Traditional capital investment appraisal techniques 6.6. Capital investment appraisal techniques using Capital investment appraisal techniques using

discounting cash flow methoddiscounting cash flow method7.7. RecapitulationRecapitulation8.8. Further ReadingsFurther Readings

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OrganisationOrganisation of Unit 10of Unit 10

Capital Investment Appraisal

Factors affecting capital investment decisions: Non-financial factors

Financial factors

Capital investment appraisal techniques

Advantages and disadvantagesAdvantages and disadvantages

Types of capital investments:Internal capital investmentsExternal capital investments

Traditional techniques:Accounting rate of return,

Payback period

Discounted cash flow techniques:Discounted payback period,

Net present value,Internal rate of return

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1. Introduction1. Introduction (1)(1)

Capital budgeting refers to the process of evaluating and prioritizingcapital investment opportunities and deciding which investments in long-term assets are taken.

The final list of approved investments is the capital budget.

Capital investment refers to large expenditures made to acquire long-term assets.

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Cost of capital - the rate of return the company is paying to its long-term investors for the use of their money.

Three main factors for capital investment decisions:i) the investors’ belief about the future of the business;ii) the investors’ attitude to bear the risk of loss; andiii) the selection of the best alternatives to invest.

Activity.

Refer to the Takee BQQ Case, describe the three main factors affecting the capital investment decisions of the owner. Answer on next page

Link to Takee BBQ Case

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AnswerThe three main factors affecting the capital investment

decisions of the owner of Takee BBQ are:

1. the owners’ mission to set up twenty chain stores within two years with a vision that the business will be prosperous;

2. the investors’ attitude towards their risk that people prefer cooking their food at home rather than buying take-out food when the economy is not favourable does not affect the owner’s decision to expand; and

3. the owner will select different models of BBQ grilling machines depending on the cost of capital available in the financial market and the sales demand.


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2. 2. Different types of capital Different types of capital investment decisions and risks investment decisions and risks (1)(1)

A. A. Internal capital investmentInternal capital investment involves involves purchasing plant and machinery, purchasing plant and machinery, research and development and research and development and advertising.advertising.

Two types of internal capital investment Two types of internal capital investment decisions are:decisions are:

a) a) Replacement of longReplacement of long--term assetsterm assetsi) for maintenance of businessi) for maintenance of businessii) for cost reductionii) for cost reduction

b) b) Addition of longAddition of long--term assetsterm assetsi) for expansion of existing productsi) for expansion of existing productsii) for expansion into new products ii) for expansion into new products

Click here for answerGuess an example for each of the four cases above.

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2A. Worksheet2A. Worksheet

a) a) Replacement of longReplacement of long--term assetsterm assetsi) for maintenance of business, i) for maintenance of business, e.g. __________________e.g. __________________ii) for cost reduction, ii) for cost reduction, e.g. ____________________________e.g. ____________________________

b) b) Addition of longAddition of long--term assetsterm assetsi) for expansion of existing products,i) for expansion of existing products, e.g. ______________e.g. ______________ii) for expansion into new products,ii) for expansion into new products, e.g. ________________e.g. ________________

Answer on next page

2. Different types of capital investment 2. Different types of capital investment decisions and risks decisions and risks (2)(2)

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2A. Answer2A. Answera) a) Replacement of longReplacement of long--term assetsterm assetsi) for maintenance of business, i) for maintenance of business, e.g. to replace a damaged e.g. to replace a damaged

/ worn out machine in production/ worn out machine in productionii) for cost reduction, ii) for cost reduction, e.g. to replace serviceable but e.g. to replace serviceable but

obsolete equipment to obsolete equipment to minimiseminimise scraps in productionscraps in productionb) b) Addition of longAddition of long--term assetsterm assetsi) for expansion of existing products, i) for expansion of existing products, e.g. to buy new e.g. to buy new

machines to increasemachines to increase volume of productionvolume of productionii) for expansion into new products, ii) for expansion into new products, e.g. to buy new e.g. to buy new

machines to produce in new productsmachines to produce in new products

2. Different types of capital 2. Different types of capital investment decisions and risks investment decisions and risks (3)(3)

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B.B. External capital investmentExternal capital investment involves joint involves joint ventures, takeover and merger.ventures, takeover and merger.

C.C. DivestmentDivestment includes cutting unprofitable includes cutting unprofitable segments, selling old plant and machineries segments, selling old plant and machineries or selling subsidiaries.or selling subsidiaries.

Give an example for each of the two types above.Click here for answer

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2 B&C. 2 B&C. Worksheet for answerWorksheet for answer

B.B. External capital investmentExternal capital investment involves joint ventures involves joint ventures and takeover and mergers, e.g. ____and takeover and mergers, e.g. __________________________________.______________________________.

C.C. DivestmentDivestment includes cutting unprofitable segments, includes cutting unprofitable segments, selling old plant and machinery or selling selling old plant and machinery or selling subsidiary companies, e.g. __________subsidiary companies, e.g. _________________________________._______________________.

Answer on next page


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2 B&C. Answer2 B&C. Answer

B.B. External capital investmentExternal capital investment involves joint ventures involves joint ventures and takeover and merger, and takeover and merger, e.g. Sony and Ericsson e.g. Sony and Ericsson joined together to form Sony Ericssonjoined together to form Sony Ericsson..

C.C. DivestmentDivestment includes cutting unprofitable segments, includes cutting unprofitable segments, selling old plant and machineries or selling selling old plant and machineries or selling subsidiaries, subsidiaries, e.g. The Housing Authority sold around e.g. The Housing Authority sold around 180 retail properties and car parking properties to 180 retail properties and car parking properties to form the form the ““Link Real Estate Investment TrustLink Real Estate Investment Trust””..


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2D. Risks in c2D. Risks in capital investmentapital investment

Risks vary with capital investment Risks vary with capital investment types:types:

i)i) Replacement of longReplacement of long--term assetsterm assets-- safest safest

ii)ii) Addition of longAddition of long--term assetsterm assets-- riskierriskier

iii)iii) New venture New venture -- riskiestriskiest


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3. 3. NonNon--financial factors affecting financial factors affecting capital investment decisions capital investment decisions (1)(1)

NonNon--financial factorsfinancial factors -- factors not measured against the factors not measured against the financial requirements established for acceptable financial requirements established for acceptable capital investments capital investments

Examples of nonExamples of non--financial factors are:financial factors are:i) environmental concerns which affect corporate image;i) environmental concerns which affect corporate image;ii) better working conditions which affect product quality;ii) better working conditions which affect product quality;iii) healthier employees result in higher employee morale;iii) healthier employees result in higher employee morale;iv) accommodating working parents to enhance flexible iv) accommodating working parents to enhance flexible

working schedule.working schedule.Provide an example of investment proposal for each of the cases above.

Click here for answer

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3. Worksheet for answer3. Worksheet for answer

Examples of nonExamples of non--financial investment proposal:financial investment proposal:

i) improving working environment which affects corporate i) improving working environment which affects corporate image;image;

ii) ____________________ which affects product quality;ii) ____________________ which affects product quality;iii) ____________________ results in higher employee morale;iii) ____________________ results in higher employee morale;iv) ____________________ enhances flexible working iv) ____________________ enhances flexible working

schedule for employees.schedule for employees.

Answer on next page

3. Non3. Non--financial factors affecting financial factors affecting capital investment decisionscapital investment decisions (2)(2)

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3. Answer3. AnswerExamples of nonExamples of non--financial investment proposal:financial investment proposal:

i) improving working environment which affects corporate i) improving working environment which affects corporate image;image;

ii) ii) improving working condition in factoryimproving working condition in factory which affects which affects product quality;product quality;

iii) iii) setting up an employee clubsetting up an employee club results in higher employee results in higher employee morale;morale;

iv) iv) arranging interest classes for kidsarranging interest classes for kids enhances flexible enhances flexible working schedule for employees.working schedule for employees.

3. Non3. Non--financial factors affecting capital financial factors affecting capital investment decisions investment decisions (3)(3)

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4. F4. Financial factors affecting capital inancial factors affecting capital investment decisionsinvestment decisions

Financial factorsFinancial factors::

i) expected cash flows; andi) expected cash flows; andii) future profitabilityii) future profitability

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5. 5. Traditional capital investment appraisal Traditional capital investment appraisal techniques techniques (1)(1)

Two traditional capital investment techniques used to compare the attractiveness of competing investment projects:

A. Accounting rate of return (ARR)

B. Payback period (PB)

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Accounting rate of return (ARR)Accounting rate of return (ARR)

Common bases in estimating investment capital:Common bases in estimating investment capital:i)i) Initial capitalInitial capitalii)ii) Average capitalAverage capitaliii)iii) Average net book valueAverage net book value

A. Accounting rate of returnA. Accounting rate of return

Investment capitalInvestment capitalx 100%x 100%Average annual profit Average annual profit

5. Traditional capital investment appraisal 5. Traditional capital investment appraisal techniques techniques (2)(2)

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Example (ARR)Example (ARR)Initial investment in capital asset is $100Initial investment in capital asset is $100Useful life is 5 years, straight line depreciationUseful life is 5 years, straight line depreciationScrap value of capital asset is $20Scrap value of capital asset is $20

525220203636525268688484Net book value (Initial capital less Net book value (Initial capital less accumulated depreciation)accumulated depreciation)

484880806464484832321616Less: Accumulated DepreciationLess: Accumulated Depreciation

100100100100100100100100100100100100Cost (Initial capital)Cost (Initial capital)

24244444444444242444Profit after depreciationProfit after depreciation161616161616161616161616Less: DepreciationLess: Depreciation404020206060606040402020Profit before depreciationProfit before depreciation

AverageAverage$$

Yr 5Yr 5$$

Yr 4Yr 4$$

Yr 3Yr 3$$

Yr 2Yr 2$$

Yr 1Yr 1$$


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Example (ARR)Example (ARR)

Calculation of ARR under different capital investment bases:

Initial capital base: 24 / 100 x 100% = 24%

Average capital base:24 / (100 / 2) x 100% = 48%

Average net book value base:24 / 52 x 100% = 46%

Investment capitalInvestment capital x 100%x 100%Average annual profitAverage annual profit


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Activity in Case StudyActivity in Case Study

Refer to the Refer to the TakeeTakee BBQ Case,BBQ Case,Which capital investment base is adopted by Which capital investment base is adopted by TakeeTakee for calculating the ARR?for calculating the ARR?

The answer is ____________________. The answer is ____________________.

Answer on next page


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Answer (Case Study)Answer (Case Study)

Refer to the Refer to the TakeeTakee BBQ Case,BBQ Case,Which capital investment base is adopted by Which capital investment base is adopted by TakeeTakee for for calculating the ARR?calculating the ARR?

The answer is The answer is average net book value.average net book value.


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Advantages and disadvantages of ARRAdvantages and disadvantages of ARR

Advantages: Advantages: 1.1. Simple to calculate.Simple to calculate.

Disadvantages:Disadvantages:1.1. Ignore the timing of cash flows generated.Ignore the timing of cash flows generated.2.2. Indicate accounting profit only.Indicate accounting profit only.3.3. No universally acceptable method in calculating ARR.No universally acceptable method in calculating ARR.


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B. Payback period (PB)B. Payback period (PB)

Payback periodPayback period (PB) is the expected number of (PB) is the expected number of years required for a projectyears required for a project’’s planned cash flows to s planned cash flows to cover up the initial investment.cover up the initial investment.

The usual decision is to accept the project with the The usual decision is to accept the project with the shortest payback period.shortest payback period.


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B. Example (PB)B. Example (PB)Project AProject A Project B Project B Project CProject C

YearYear Cash flow CumulativeCash flow Cumulative Cash flow CumulativeCash flow Cumulative Cash flow CumulativeCash flow CumulativeCash flowCash flow Cash flowCash flow Cash flowCash flow

$ $ $ $ $ $ $ $ $ $ $ $ 00 --3,6003,600 --3,6003,600 --3,6003,600 --3,6003,600 --3,6003,600 --3,6003,60011 +1,000+1,000 --2,6002,600 +1,000 +1,000 --2,600 +1,000 2,600 +1,000 --2,6002,60022 +1,200+1,200 --1,4001,400 +1,000 +1,000 --1,600 +1,000 1,600 +1,000 --1,6001,60033 +1,400+1,400 NILNIL +1,100 +1,100 --500 +800500 +800 --80080044 +1,000 +500 +1,000 +200+1,000 +500 +1,000 +20055 +500+500 +700+70066 +300+300 +1,000+1,000

PaybackPayback 3 years + (500/1,000) years 3 year3 years + (500/1,000) years 3 years + (800/1,000) yearss + (800/1,000) yearsperiod:period: = = 3 years3 years = = 3.50 years3.50 years = = 3.80 years3.80 years


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Exercise (PB)Exercise (PB)Calculate the payback period for the following cash Calculate the payback period for the following cash

flowsflows::Year 0 1 2 3 4

Cash flow ($200,000) $60,000 $60,000 $60,000 $60,000

Payback period = ? years



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Answer (PB)Answer (PB)

Payback period isPayback period is

3 years + (20,000 / 60,000) years = 3.33 years


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Advantages and disadvantages of PBAdvantages and disadvantages of PB

Advantages:Advantages:

1.1. Simple to calculate.Simple to calculate.2.2. Used as a screening device to eliminate obviously Used as a screening device to eliminate obviously

inappropriate projects. inappropriate projects. 3.3. Indicate a projectIndicate a project’’s liquidity rather than profit.s liquidity rather than profit.4.4. Tend to in bias of shortTend to in bias of short--term projects term projects –– to to minimiseminimise

both financial risk and business risk for unstable both financial risk and business risk for unstable companies.companies.

5.5. Used in capital rationing situation to identify those Used in capital rationing situation to identify those projects which generate additional cash for projects which generate additional cash for investment quickly.investment quickly.


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Advantages and disadvantages of PBAdvantages and disadvantages of PB

Next page

Disadvantages:

1. Ignore the time value of money.

2. Ignore cash flows after the payback period.

3. Unable to distinguish between projects with the same PB.

4. May lead to excessive investment in short-term projects.

5. Ignore the possible variability of those cash flows.


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Exercise (PB)Exercise (PB)You have to choose between two mutually exclusive projects A You have to choose between two mutually exclusive projects A and B with the same amount of initial investment.and B with the same amount of initial investment.

______ years______ years______ years______ yearsPayback period:Payback period:

800800300300CC55

800800300300CC44

300300500500CC33

500500500500CC22

500500500500CC11

(1,500)(1,500)(1,500)(1,500)CC00

Project BProject B$$

Project AProject A$$

Cash flow atCash flow atYear i (Year i (CCii))



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Answer (PB)Answer (PB)

•• PB for Project A is PB for Project A is 3 years3 years•• PB for Project B is 3 years + 2/8 years = PB for Project B is 3 years + 2/8 years = 3.25 years3.25 years

Further discussion:Further discussion:Using the PB decision rule, you will choose Project A.Using the PB decision rule, you will choose Project A.•• However, Project B is clearly the better alternative However, Project B is clearly the better alternative

because of the greater total cash inflows over the life because of the greater total cash inflows over the life of the project. Will that affect your decision?of the project. Will that affect your decision?

Back to exercise


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6. Capital investment appraisal techniques using 6. Capital investment appraisal techniques using discounted cash flow method discounted cash flow method (1)(1)

Investment appraisal is concerned with long-run decisions where revenue and costs arise at intervals over a period. Since monies spent or received at different times cannot be compared directly, future cash flows are discounted to their present value by a particular rate at a common date.

Two features of discounted cash flow techniques:

i) use of cash flows; andii) taking into account the time value of

money.

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Time value of money

The impact of capital investments will generate cash inflows for a long period of time, e.g. buying a machine to produce products to generate cash upon selling these products in the future.

For making comparisons involving time element, an appreciation of the concept of time value of money is crucial.

Generally speaking, saving or investing a dollar instead of spending it today results in a future amount greater than a dollar, since interest or income will be earned on money not spent today.

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Time value of money perspective can be appreciated via:

A. the concept of future value and the compoundingtechnique

B. the concept of present value and the discountingtechnique

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A. Future value and compounding technique:

Future value (FV) refers to an amount to which current saving will increase based on a certain interest rate and a certain time period; the process of growth is known as compounding.

Compounding is a process of accumulating value over time, from a single money amount (deposit/payment) or a series of equal deposits/payments (annuity).

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Example (future value)

What is the future value of $1,000 put in a one-year time deposit at an annual interest rate of 5%?

Answer (future value)

Future value = $1,000 + ($1,000 x 5%) = $1,050

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B. Present value and discounting technique

Present value (PV) refers to the current value of a future amount based on a certain interest rate and a certain period.

Discounting is a process of reducing future value to present value. It is used to determine the current value of a desired amount for the future.

The technique for calculating PV in capital investment appraisal is generally referred to as the discounted cash flow (DCF) method.

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Example (DCF)Example (DCF)

Peter will have a 10% return per Peter will have a 10% return per annum for money deposited with a annum for money deposited with a financial institution. financial institution.

What is the amount required to be What is the amount required to be deposited now in order to receive deposited now in order to receive $10,000 at the end of one year?$10,000 at the end of one year?



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Answer (DCF)Answer (DCF)

Let z be the money deposited at present:Let z be the money deposited at present:z x (1+10%) = $10,000z x (1+10%) = $10,000z = $10,000 / (1 + 10%)z = $10,000 / (1 + 10%)z = z = $9,090.9$9,090.9

In the above calculation, In the above calculation, 1 / (1 + 10%) is a discount 1 / (1 + 10%) is a discount factorfactor to convert $10,000 into a present value of to convert $10,000 into a present value of $9,090.9.$9,090.9.


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Exercise (DCF) (ContExercise (DCF) (Cont’’d)d)

At the 10% discount rate, what would be the discount At the 10% discount rate, what would be the discount factor at the end of 2nd year, 3rd year and 4th year?factor at the end of 2nd year, 3rd year and 4th year?

(Refer to present value interest factors table in Appendix 1)(Refer to present value interest factors table in Appendix 1)



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Appendix 1: Extract of present value interest factors table Appendix 1: Extract of present value interest factors table

(PVIF i, n)(PVIF i, n)

0.56450.56450.59630.59630.94200.9420660.62090.62090.64990.64990.95150.9515550.68300.68300.70840.70840.96010.9601440.75130.75130.77220.77220.97060.9706330.82640.82640.84170.84170.98030.9803220.90910.90910.91740.91740.99010.990111

10%10%9%9%……………………....1%1%Interest (i)Interest (i)Period (n)Period (n)

Present Value of $1 Due at the End of n Periods (PVIF i, n)Present Value of $1 Due at the End of n Periods (PVIF i, n)


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Answer (DCF) (ContAnswer (DCF) (Cont’’d)d)

The present value interest factors The present value interest factors PVIF (10%, n) PVIF (10%, n) are:are:

Year 1 0.9090Year 1 0.9090Year 2 0.8264Year 2 0.8264Year 3 0.7513Year 3 0.7513Year 4 0.6830Year 4 0.6830


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Three major DCF methodsThree major DCF methods

A.A. Discounted payback period (DPB)Discounted payback period (DPB)B.B. Net present value (NPV)Net present value (NPV)C.C. Internal rate of return (IRR)Internal rate of return (IRR)


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A. Discounted payback period (DPB)A. Discounted payback period (DPB)•• Use the projectUse the project’’s cost of capital to discount the expected cash flow. s cost of capital to discount the expected cash flow. •• Apply payback period on the discounted cash flowApply payback period on the discounted cash flow

2 years + (41.32 / 60.11) years = 2 years + (41.32 / 60.11) years = 2.7 years2.7 yearsDiscounted payback Discounted payback periodperiod

18.7918.79--41.3241.32--90.9190.91--100100Cumulative discounted Cumulative discounted cash flowcash flow

60.1160.1149.5949.599.099.09--100100Discounted cash flowDiscounted cash flow

808060601010--100100Cash flow at the end of Cash flow at the end of yearyear

Yr 4Yr 4$$

Yr 3Yr 3$$

Yr 2Yr 2$$

Yr 1Yr 1$$

YearYear


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Advantages and disadvantages of DPBAdvantages and disadvantages of DPBAdvantages:

1. Used as a screening device to eliminate obviously inappropriate projects.

2. Indicate a project’s liquidity rather than profit.3. A more exact calculation on the time value of cash inflows

than just the nominal value.4. Tend to bias in favour of short-term projects – to minimise

both financial risk and business risk for unstable companies.5. Used in a capital rationing situation to identify those projects

which generate additional cash for investment quickly.


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Advantages and disadvantages of DPBAdvantages and disadvantages of DPBDisadvantages:

1. Ignore cash flows after the payback period.2. Unable to distinguish between projects with the same

DPB.3. May lead to excessive investment in short-term projects.4. Ignore the possible variability of those cash flows.

DPB solves one problem of using payback period for capital investment appraisal. What is it?

By taking into account the time value of money, DPB gives more accurate results.


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B.B. Net Present Value (NPV)Net Present Value (NPV)The projectThe project’’s cash flows are discounted to its present s cash flows are discounted to its present value at the cost of capitalvalue at the cost of capital

NPV = CF0 + CF1 /(1+ k)1 + CF2 /(1+ k)2 + …… + CFn /(1+ k) n

n= Σ CFt /(1 + k) t

t=0

CF is the expected net cash flow in the period, k is the project’s cost of capital,0 means year 0 (present) , 1 means end of period 1, etc


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StandStand--alone and mutually exclusive projectsalone and mutually exclusive projects

(a)(a) StandStand--alone project alone project -- there is no there is no competing alternativecompeting alternative

(b)(b) Mutually exclusive project Mutually exclusive project –– choose choose only one of the capital investments only one of the capital investments and reject othersand reject others


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B. Net Present Value (NPV)B. Net Present Value (NPV)

Decision rule:Decision rule:(i)(i) For For standstand--alone projectalone project::

If NPV > 0 If NPV > 0 acceptacceptIf NPV < 0 If NPV < 0 rejectreject

(ii)(ii) For For mutually exclusive projectmutually exclusive project::If both NPVIf both NPVAA and NPVand NPVB B > 0> 0and NPVand NPVAA > NPV> NPVBB,,choose Project A over Project Bchoose Project A over Project B


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Example (NPV)Example (NPV)

Project A is a standProject A is a stand--alone project:alone project:Year 0 Year 1 Year 2Year 0 Year 1 Year 2 Year 3Year 3 Year 4Year 4--$9,500 +$3,000 +$4,700 +$4,800$9,500 +$3,000 +$4,700 +$4,800 +$3,200+$3,200

What is the NPV of Project A if the cost of capital (k) is 20%? What is the NPV of Project A if the cost of capital (k) is 20%? Is the project acceptable?Is the project acceptable?



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Answer (NPV)Answer (NPV)

NPV = -$9,500 + $3,000/(1.2) 1 + $4,700/(1.2) 2 + $4,800/(1.2) 3 + $3,200/(1.2) 4

= $582ConclusionProject A is acceptable as it generates cash more than the present value of capital investment.

NPV = CF0 + CF1 /(1+ k) 1 + CF2 /(1+ k) 2 + …… + CFn /(1+ k) nn

= Σ CFt /(1 + k) t

t=0


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Advantages and disadvantages of NPVAdvantages and disadvantages of NPV

Advantages:Advantages:1.1. Take into account the time value of moneyTake into account the time value of money2.2. Consider total cash flows from the projectConsider total cash flows from the project3.3. Use cash flows instead of the arbitrary Use cash flows instead of the arbitrary

accounting profitaccounting profit

Disadvantages:Disadvantages:1.1. Difficult to determine the appropriate discount Difficult to determine the appropriate discount

rate (cost of capital)rate (cost of capital)


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C.C. Internal rate of return (IRR)Internal rate of return (IRR)IRR is the return on investment or the interest rate that equates the present value of a project’s expected cash inflows to the present value of its expected cash outflows.

IRR may not be calculated directly. It can be found either by drawing a graph, using a financial calculator, looking up the Present Value Interest Factors table (using linear interpolation to work out calculations) or using Microsoft Excel program.


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Example (IRR)Example (IRR)

Next page

Project Z is being evaluated for which the cash flows have been estimated as follows:Year 0 Year 1 Year 2 Year 3 Year 4

-$9,500 +$4,000 +$4,000 +$4,000 +$4,000

The cost of capital is 20%

What is the IRR for Project Z? Is the project acceptable?


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Present Value Interest Factors Table MethodPresent Value Interest Factors Table Method

Next page

IRR is the interest rate that equates the present value of the project’s cash inflows ($4,000 per year for year 1 to 4) to its initial investment ($9,500).Relating the IRR concept to the present value table method, we can define IRR through the NPV equation, where IRR is simply the interest rate (k) at which NPV equals zero (i.e. when the present value of all cash inflows equals to present value of all cash outflows).

Let NPV = 0 CF0 + CF1 /(1+ k) 1 + CF2 /(1+ k) 2 + …… + CFn/(1+ k) n = 0


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Present Value Interest Factors Table MethodPresent Value Interest Factors Table Method

In the above example,0 = CF0 + CF1 /(1+ IRR)1 + CF2 /(1+ IRR)2 + CF3 /(1+ IRR)3

+ CF4 /(1+ IRR)4

- CF0 = CF1 /(1+ IRR)1 + CF2 /(1+ IRR)2 + CF3 /(1+ IRR)3

+ CF4 /(1+ IRR)4

Since CF1 = CF2 = CF3 = CF4 = $4,000, the annuity equation can beused to solve for IRR: PVA = PMT (PVIFA i, n) where PVA is present value annuity, PMT is periodic payment

Initial investment = Present value of the projectsOutlay (= CF0) = expected net cash inflows

PVIFA i, n = Investment outlay/PMTPVIFA i, 4 = $9,500/$4,000 = 2.375

Next page


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Present Value Interest Factors Table MethodPresent Value Interest Factors Table MethodThis is a PVIFA for 4 years, using the table in Appendix 2, we find i to bebetween 24% (2.4043) and 28% (2.2410). (a) Looking up the PVIFA (i, n) table in Appendix 2, we find that the

present value of 24% is $117 i.e. 2.4043 x $4,000 - $9,500.(b) The present value of 28% is -$536 i.e. 2.2410 x $4,000 - $9,500.(c) The difference of NPV between (a) 24% and (b) 28% is $653 i.e. $117

+ $536.

By using linear interpolation method,IRR = 24% (a) + 4% (117(a)/653(c)) = 24.72%

ConclusionProject Z is acceptable as the IRR, 24.72% exceeds the cost of capital, 20%.


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Appendix 2: Extract of Present Value Interest Factor Appendix 2: Extract of Present Value Interest Factor

Annuity table (PVIFA i, n)Annuity table (PVIFA i, n)

2.75942.75943.02053.02055.79555.7955662.53202.53202.74542.74544.85344.8534552.24102.24102.40432.40433.90203.9020441.86841.86841.98131.98132.94102.9410331.39161.39161.45681.45681.97041.9704220.78130.78130.80650.80650.99010.990111

28%28%24%24%……………………....1%1%Interest (i)Interest (i)Period (n)Period (n)

Present Value of an annuity of $1 per period for n Periods (PVIFPresent Value of an annuity of $1 per period for n Periods (PVIF i, ni, n))

Back to Question


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Decision rule of IRR methodDecision rule of IRR methodIRR is the interest rate that equals the present value of a IRR is the interest rate that equals the present value of a projectproject’’s cash inflows to its outflows (i.e. when NPV = 0).s cash inflows to its outflows (i.e. when NPV = 0).If IRR > cost of capital (k),If IRR > cost of capital (k), the rate of return is greater than its the rate of return is greater than its cost. Some return is left over to increase shareholderscost. Some return is left over to increase shareholders’’returns.returns.(a) For stand(a) For stand--alone project:alone project:

If IRR > k If IRR > k AAcceptcceptOtherwise, rejectOtherwise, reject

(b) For mutually exclusive project:(b) For mutually exclusive project:If both IRRIf both IRRA A and IRRand IRRBB > k, and> k, andIRRIRRAA > IRR> IRRBB choose Project A over Project B;choose Project A over Project B;If both IRRIf both IRRAA and IRRand IRRBB < k, reject both projects< k, reject both projects Click here for answer


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Advantages and disadvantages of IRRAdvantages and disadvantages of IRR

Advantage:Advantage:IRR is commonly used because its IRR is commonly used because its principle is easily understood.principle is easily understood.

Disadvantage:Disadvantage:IRR is a relative measure of the return. IRR is a relative measure of the return. It does not reflect the size of the It does not reflect the size of the project and the timing of cash flows.project and the timing of cash flows.


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7. Recapitulation7. Recapitulation

After you have read the above materials, you should be able to:

1. Understand what is capital investment decision and capital budgeting.

2. Using non-financial and financial factors to evaluate capital investments.

3. Calculate accounting rate of return (ARR), payback period (PB), discounted payback period (DPB), net present value (NPV) and internal rate of return (IRR).

4. Explain the advantages and disadvantages of different capital investment appraisal methods.

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8. Further Readings 8. Further Readings (1)(1)

1. Lucey, Terry, Management Accounting, 5th Edition, Chapter 17-18, Investment Appraisal I & II, London: Continuum, 2003. (ISBN 0-8264-6359-2)

2. Drury, Colin, Management and Costing Accounting, 6th Edition, Chapter 13-14, Capital Investment Decisions: 1 & 2, London: Thomson, 2004. (ISBN 1-84480-028-8)

3. Brigham, Eugene and Houston, Joel, Fundamentals of Financial Management, 10th Edition, Chapter 10, The Basics of Capital Budgeting, Ohio: Thomson 2004. (ISBN 0-324-20306-3)

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8. Further Readings 8. Further Readings (2)(2)

• Li, Andy T M and Ng, Patrick P H, Principles of Accounting, Volume 2, 2nd Edition, Chapter 27, Investment Appraisal, Hong Kong: Pilot Publishing 2007. (ISBN 962-397-772-7)

• 王怡心，管理會計，修訂二版，第十一及十二章，資本預算決策，台北:三民書局〈二○○二年一月〉，第315-370頁。〈ISBN 957-14-3525-2〉

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End of the UnitEnd of the Unit

This is the end of Unit 7. This is the end of Unit 7. Please go to the Please go to the Unit Unit Assessment Assessment before before attempting the next unit.attempting the next unit.

EndEnd--ofof--unit Assessmentunit Assessment

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