Prepared by Ken Hartviksen INTRODUCTION TO CORPORATE FINANCE Laurence Booth W. Sean Cleary.

Prepared byPrepared byKen HartviksenKen Hartviksen

INTRODUCTION TOINTRODUCTION TO CORPORATE FINANCECORPORATE FINANCELaurence Booth Laurence Booth •• W. Sean Cleary W. Sean Cleary

CHAPTER 14CHAPTER 14 Cash Flow Estimation and Cash Flow Estimation and

Capital Budgeting DecisionsCapital Budgeting Decisions

CHAPTER 14 – Cash Flow Estimation and Capital Budgeting Decisions

14 - 3

Lecture AgendaLecture Agenda

• Learning ObjectivesLearning Objectives• Important TermsImportant Terms• General Guidelines for Capital Project AnalysisGeneral Guidelines for Capital Project Analysis• Estimating and Discounting Cash FlowsEstimating and Discounting Cash Flows• Sensitivity to InputsSensitivity to Inputs• Replacement DecisionsReplacement Decisions• Inflation and Capital Budgeting DecisionsInflation and Capital Budgeting Decisions• Summary and ConclusionsSummary and Conclusions


14 - 4

Learning ObjectivesLearning Objectives

1.1. How to estimate the future cash flows associated How to estimate the future cash flows associated with potential investmentswith potential investments

2.2. How to determine whether these investments are How to determine whether these investments are the result of expansion or replacement decisionsthe result of expansion or replacement decisions

3.3. How to conduct a sensitivity analysis to see how How to conduct a sensitivity analysis to see how the value changes as key inputs varythe value changes as key inputs vary

4.4. Why real option valuation techniques have Why real option valuation techniques have become an important trend in project evaluationbecome an important trend in project evaluation

5.5. How mistakes can easily be made in dealing with How mistakes can easily be made in dealing with inflationinflation


14 - 5

Important Chapter TermsImportant Chapter Terms

• Capital cost (CCapital cost (C00))• Decision treeDecision tree• Ending (or terminal) Ending (or terminal)

after-tax cash flow after-tax cash flow (ECF(ECFnn))

• Expansion projectsExpansion projects• Expected annual after-Expected annual after-

tax cash flows (CFtax cash flows (CFtt))• ExternalitiesExternalities• Initial after-tax cash flow Initial after-tax cash flow

(CF(CF00))• Marginal or incremental Marginal or incremental

cash flowscash flows

• NPV break-even pointNPV break-even point• Opportunity costsOpportunity costs• Real option valuation Real option valuation

(ROV)(ROV)• Replacement projectsReplacement projects• Salvage value (SVSalvage value (SVnn))• Scenario analysisScenario analysis• Sensitivity analysisSensitivity analysis• Sunk costsSunk costs


14 - 6

Cash Flows and Capital BudgetingCash Flows and Capital BudgetingIntroductionIntroduction

• Decisions are only as good as the information Decisions are only as good as the information used to make them.used to make them.

• This chapter focuses on approaches used to This chapter focuses on approaches used to estimate future cash flows associated with estimate future cash flows associated with capital project proposals capital project proposals


14 - 7

Project Evaluation TechniquesProject Evaluation TechniquesRequired Information and EstimatesRequired Information and Estimates

• All evaluation approaches (NPV, IRR, Discounted All evaluation approaches (NPV, IRR, Discounted Payback, and PI) require the same data:Payback, and PI) require the same data:– Estimate of initial cost (Estimate of initial cost (CFCF00))

– Net incremental after-tax cash flows Net incremental after-tax cash flows CFBT(1-T)CFBT(1-T)– Cost of Capital Cost of Capital (k)(k)– Estimate of useful life Estimate of useful life (n)(n)

– Ending Cash flows Ending Cash flows (ECF(ECFnn))

– Corporate tax rateCorporate tax rate (T) (T)– Capital Cost Allowance Rate Capital Cost Allowance Rate (d)(d)

• This chapter provides you with guidelines for identifying This chapter provides you with guidelines for identifying relevant information and testing the decision’s relevant information and testing the decision’s sensitivities to variations in those input variables.sensitivities to variations in those input variables.


14 - 8

Cash Flows EstimationCash Flows EstimationGeneral GuidelinesGeneral Guidelines

• Cash flows should be:Cash flows should be:1.1. After-taxAfter-tax2.2. Incremental or marginalIncremental or marginal3.3. Do not include interest or dividendsDo not include interest or dividends4.4. Adjust initial cash outlay and terminal cash flows for additional working Adjust initial cash outlay and terminal cash flows for additional working

capital requirementscapital requirements5.5. Treat sunk costs as irrelevantTreat sunk costs as irrelevant6.6. Opportunity costs should be factored into the cash flow estimatesOpportunity costs should be factored into the cash flow estimates

• Determine the appropriate time horizon for the projectDetermine the appropriate time horizon for the project• Ignore intangible considerationsIgnore intangible considerations• Ignore externalitiesIgnore externalities• Consider the effect of all project interdependencies on Consider the effect of all project interdependencies on

cash flow estimates.cash flow estimates.• Treat inflation consistentlyTreat inflation consistently• Undertake all social investments required by law.Undertake all social investments required by law.


14 - 9

The Capital Budgeting Cash FlowsThe Capital Budgeting Cash FlowsThe Basic Cash Flow PatternThe Basic Cash Flow Pattern

• The following slide graphically illustrates the basic The following slide graphically illustrates the basic cash flow patterns involved in a capital project:cash flow patterns involved in a capital project:– There is an initial investment at t = 0 There is an initial investment at t = 0 (CF(CF00 ) )

– There follows an annual stream of after-tax cash flow benefits There follows an annual stream of after-tax cash flow benefits (CF (CF t t ))

– At the end of the useful life, ending cash flow benefits after tax are At the end of the useful life, ending cash flow benefits after tax are received received (ECF(ECF n n ) )

)()( 0 CFECFPVCFsAnnualPVNPV n [ 14-5]


14 - 10

The Capital Budgeting Cash FlowsThe Capital Budgeting Cash FlowsThe Basic Cash Flow PatternThe Basic Cash Flow Pattern

Initial After-Tax Cash Flow (CF0)

Expected Annual After-Tax Operating Cash Flows (CF tt)

t=1 2 3 n-1 n

CF1 CF2 CF3 CFN-1 CFN

Terminal Cash Flow (ECFn)

n

tt

tt k

CFCFofPV

1 )1(

If CF 0 < PV of CFt , then benefits exceeds costs, the NPV is positive.

ACCEPT the Project


14 - 11

The Capital Budgeting Cash FlowsThe Capital Budgeting Cash FlowsDeconstructing the Basic Cash Flow PatternDeconstructing the Basic Cash Flow Pattern

• The basic cash flow pattern can be The basic cash flow pattern can be deconstructed into:deconstructed into:– Initial investment Initial investment (CF(CF00 ) )

– Annual stream of after-tax cash flows throughout the Annual stream of after-tax cash flows throughout the project life (project life (CF CF t t ) )

– Ending cash flows Ending cash flows (ECF(ECF n n ) )


14 - 12


CF CF 00

There is an initial investment at t = 0 There is an initial investment at t = 0 (CF(CF00 ) ) consists of:consists of:

• CC 0 0 the initial capital cost of the asset the initial capital cost of the asset

• ΔΔNWCNWC00 the change in net working capital the change in net working capital

• OC the opportunity costs associated with the projectOC the opportunity costs associated with the project

000 OCNWCCCF [ 14-1]


14 - 13


CFCFtt

There follows an annual stream of after tax cash flow There follows an annual stream of after tax cash flow benefits (benefits (CF CF t t ) consisting of:) consisting of:

• Operating after-tax cash flow benefits (OCF Operating after-tax cash flow benefits (OCF t t ) = CFBT) = CFBTtt (1 – T) (1 – T)

• Tax shield benefits from CCATax shield benefits from CCA

)()1( TCCAtCFBTCF ttt [ 14-2]


14 - 14


ECFECFnn

At the end of the useful life, ending cash flow benefits received At the end of the useful life, ending cash flow benefits received (ECF(ECF n n ) in the absence of tax issues include ) in the absence of tax issues include ::

• SV SV nn the estimated salvage value in year n for the asset the estimated salvage value in year n for the asset purchasedpurchased

• ΔΔNWC NWC nn the net working capital investment released at the the net working capital investment released at the end of the projectend of the project

NWCSVECF nnn [ 14-4]


14 - 15


ECFECFnn

If there are If there are tax issuestax issues the the ECFECF n n consists of:consists of:• SV SV nn the estimated salvage value in year n for the asset the estimated salvage value in year n for the asset

purchasedpurchased• ΔΔNWC NWC nn the net working capital investment released at the the net working capital investment released at the

end of the projectend of the project • Less any taxes payable on the salvage value (capital gains, Less any taxes payable on the salvage value (capital gains,

recapture of depreciation)recapture of depreciation)

])-

T]50.0)C-[(ns)ImplicatioTax With ( 0

TUCC[(SV

SVNWCSVECF

nn

nnnn

[ 14-3]


14 - 16


Putting It All TogetherPutting It All Together• Once you have estimated the cash flows you Once you have estimated the cash flows you

must:must:– Determine their after-tax valuesDetermine their after-tax values– Discount them back to the presentDiscount them back to the present– Sum them in determining the NPVSum them in determining the NPV

(The following slide graphically illustrates the deconstructed cash flow pattern (The following slide graphically illustrates the deconstructed cash flow pattern involved in a capital project)involved in a capital project)


14 - 17

The Capital Budgeting Cash FlowsThe Capital Budgeting Cash FlowsDeconstructing the Cash FlowsDeconstructing the Cash Flows

Initial After-Tax Cash Flow (CF0)

Expected Annual After-Tax Operating Cash Flows (excluding CCA Tax Shield) (OCFt) = CFBT(1 – T)

t=1 2 3 n-1 n


Terminal Cash Flow (ECFn)

CF0 = C0 +Δ NWC0 + OC

Expected Tax Shield Benefits from CCA deduction (CdT)

n

tt

tt k

CFCFofPV

1 )1(

Because the CCA tax shield benefit changes each year in a predictable fashion, we can use a formula to calculate their total present value.


14 - 18

Alternative Approaches to Finding the Tax Alternative Approaches to Finding the Tax Shield Benefit on CCAShield Benefit on CCA

• You will recall that there are two approaches to You will recall that there are two approaches to determining cash flows.determining cash flows.

• We will use alternative (2) found on Table 14-1We will use alternative (2) found on Table 14-1• This allows us to deconstruct the analysis, This allows us to deconstruct the analysis,

separating operating cash flows from the tax separating operating cash flows from the tax shield benefits of CCA.shield benefits of CCA.

(See the following slide)(See the following slide)


14 - 19

Determining Cash Flows after CCADetermining Cash Flows after CCA

(1) Before-tax operating Income (OI) (2) Before-tax Operating Income (OI)

- CCA - Taxes payable on OI

Taxable Income After-tax OI

-Taxes Payable + CCA tax savings

After-tax Income Net Cash Flow

+ CCA (non-cash expense)

Net Cash Flow

Table 14 - 1 Two Ways to Determine Cash Flows After Capital Cost Allowance


14 - 20

Separating Operating Cash Flows from Separating Operating Cash Flows from CCA Tax Shield BenefitsCCA Tax Shield Benefits

t=1 2 3 n-1 n


Typically operating cash flow benefits can be treated as an annuity.

The CCA Tax Shield benefits are a growing perpetuity with a constant negative growth rate.

The only exception to this is the first cash flow. (This is ½ year rule effect.)


14 - 21

Tax Shield Benefit of CCATax Shield Benefit of CCA

• The tax shield benefit from CCA is equal to the corporate The tax shield benefit from CCA is equal to the corporate tax rate tax rate (T) × CCA(T) × CCA amount. amount.

• As demonstrated in the following slide, assuming the As demonstrated in the following slide, assuming the firm will have taxable operating income in the future, we firm will have taxable operating income in the future, we can predict the maximum amount of CCA the firm can can predict the maximum amount of CCA the firm can claim from the year of acquisition through to infinity.claim from the year of acquisition through to infinity.

• You will note:You will note:– ½ rule effect in the first year½ rule effect in the first year– We assume we claim the maximum CCA in each subsequent year.We assume we claim the maximum CCA in each subsequent year.– We forecast the tax shield benefit by: We forecast the tax shield benefit by: TT× CCA× CCAtt

– Tax shield benefits will be a perpetual stream of cash flows that are Tax shield benefits will be a perpetual stream of cash flows that are going a constant negative compound growth rate going a constant negative compound growth rate (d) where d is the (d) where d is the CCA rateCCA rate


14 - 22

CCA Tax Shield Over TimeCCA Tax Shield Over Time(Assume a corporate Tax Rate ‘T’ of 40%)(Assume a corporate Tax Rate ‘T’ of 40%)

Year UCC of pool Addition CCA @ 10% T(CCA)1 0 100,000 5,000 2,0002 95,000 0 9,500 3,8003 85,500 0 8,550 3,4204 76,950 0 7,695 3,0785 69,255 0 6,926 2,7706 62,330 0 6,233 2,4937 56,097 0 5,610 2,2448 50,487 0 5,049 2,0199 45,438 0 4,544 1,818

$100,000 asset is acquired in year 1. No asset pool disposals. CCA rate

(d) = 10%

Tax Shield = T(CCA)Lets

graph this

series of tax

shield benefits the firm

is forecast

to receive.


14 - 23

CCA Tax Shield Over TimeCCA Tax Shield Over Time(A Graphical Representation)(A Graphical Representation)

0500

1000150020002500300035004000

Tax Shield

1 3 5 7 9 11 13 15 17 19

Year

T(CCA) at 10% on $100,000

Asymptotic Curve


14 - 24

ObservationsObservations

• In the foregoing you can now readily see:In the foregoing you can now readily see: CCA provides large tax shields in the early years of the CCA provides large tax shields in the early years of the

asset’s lifeasset’s life residual values remain in the pool long after the asset residual values remain in the pool long after the asset

was acquired…this means that the firm will never fully was acquired…this means that the firm will never fully recoup the original cost of the asset … as the firm’s recoup the original cost of the asset … as the firm’s asset base ages, cash flows generated from CCA will asset base ages, cash flows generated from CCA will not enable the firm to replace the original asset.not enable the firm to replace the original asset.

• Now we can learn how to find the present value of Now we can learn how to find the present value of a perpetual stream of forecast cash flows.a perpetual stream of forecast cash flows.


14 - 25

Present Value of the CCA Tax ShieldPresent Value of the CCA Tax Shield(Assume a corporate Tax Rate ‘T’ of 40% and Discount rate of 12%)(Assume a corporate Tax Rate ‘T’ of 40% and Discount rate of 12%)

(1) (2) (3) (4) (5) (6) = (4) × (5)

Year UCC of pool Addition CCA @ 10% T(CCA)

Present Value

Factor at 12%

Present Value

1 0 100,000 5,000 2,000 0.893 $1,7862 95,000 0 9,500 3,800 0.797 3,0293 85,500 0 8,550 3,420 0.712 2,4344 76,950 0 7,695 3,078 0.636 1,9565 69,255 0 6,926 2,770 0.567 1,5726 62,330 0 6,233 2,493 0.507 1,2637 56,097 0 5,610 2,244 0.452 1,0158 50,487 0 5,049 2,019 0.404 816

Sum (1:8) = $13,871

This is the sum of the first 8 years of tax savings…it would be an infinitely long process to find the actual sum of an infinite stream of cash flows.

We must develop a formula-based solution to this problem.

Multiplying T(CCA) by the PVIF we can estimate the present value of the tax shield benefit for each year into the future.


14 - 26

Present Value of the CCA Tax ShieldPresent Value of the CCA Tax Shield

• In Chapter 7 you learned about the constant growth In Chapter 7 you learned about the constant growth DDM:DDM:

• This model assumes the first dividend becomes the This model assumes the first dividend becomes the base amount and all future cash flows grow at a base amount and all future cash flows grow at a constant compound rate from constant compound rate from t =1t =1 through infinity: through infinity:

gk

D

gk

gDP

cc

100

)1([ 7-7]

)1(

)1(...

)1(

)1(

)1(

)1( 02

20

1

10

0ccc k

gD

k

gD

k

gDP

[ 7-6]


14 - 27

Present Value of the CCA Tax ShieldPresent Value of the CCA Tax Shield

• The constant growth DDM:The constant growth DDM:

• The Tax Shield benefit to CCA (ignoring the ½ year The Tax Shield benefit to CCA (ignoring the ½ year rule for a moment) is the same except:rule for a moment) is the same except:– Cash flow at time one is the CCA tax shield at Cash flow at time one is the CCA tax shield at t = 1 and is calculated ast = 1 and is calculated as

((TdCTdC00) – this is the numerator) – this is the numerator

– The growth is negative (declining balance) –The growth is negative (declining balance) – two negatives equal a two negatives equal a positive!positive!

10 gk

DP

c

)(

))()(()( 00

dk

dTC

dk

TdCShieldTaxCCAPV


14 - 28

Present Value of Tax Savings Lost on Present Value of Tax Savings Lost on Salvage Value – an Salvage Value – an ECFECF

• We will use this version of the formula to calculate the We will use this version of the formula to calculate the present value of tax savings lost on the salvage value present value of tax savings lost on the salvage value of the asset (when the ½ net addition rule does not of the asset (when the ½ net addition rule does not apply)apply)

• The PV of tax savings lost at time The PV of tax savings lost at time nn = =

)(

))()((

dk

dTSV

dk

TdSVValueSalvageonLostShieldTaxCCAofPV nn

n


14 - 29

Present Value of Tax Savings Lost on Present Value of Tax Savings Lost on Salvage Value – an Salvage Value – an ECFECF

• The PV of tax savings lost at time n =The PV of tax savings lost at time n =

• The last step in finding the Present value of this amount is The last step in finding the Present value of this amount is to discount the value back to t = 0.to discount the value back to t = 0.

• So…the equation becomes:So…the equation becomes:

)(

))()((1

dk

dTSV

dk

TdSVValueSalvageonLostShieldTaxCCAofPV nn

n

k)(1

1

)1()(

))()((

n0 dk

dTSV

kdk

TdSV

ValueSalvageonLostShieldTaxCCAofPV nn

n


14 - 30

Present Value of the Tax Savings on CCAPresent Value of the Tax Savings on CCAAssuming the ½ Year RuleAssuming the ½ Year Rule

Adjusting the Formula for the ½ year Net Addition RuleAdjusting the Formula for the ½ year Net Addition Rule

• We multiply the first factor by (1+.5k) / (1+ k) to produce a We multiply the first factor by (1+.5k) / (1+ k) to produce a formula that will estimate the present value of tax savings formula that will estimate the present value of tax savings from CCA (time 1 through infinity) assuming ½ year net from CCA (time 1 through infinity) assuming ½ year net addition rule.addition rule.

• For a graphical depiction of this formula see the following For a graphical depiction of this formula see the following slide.slide.

1

501)( 0

k

)k.(

dk

dTCShieldTaxCCAPV


14 - 31


0500

1000150020002500300035004000

Tax Shield

1 3 5 7 9 11 13 15 17 19

Year

T(CCA) at 10% on $100,000

1

501)( 0

k

)k.(

dk

dTCShieldTaxCCAPV

This formula calculations the PV of tax savings on CCA from time 1 through infinity assuming the ½ year net addition rule.


14 - 32

Present Value of the Tax Savings on CCAPresent Value of the Tax Savings on CCAAdjusting for ½ Year Rule – An ExampleAdjusting for ½ Year Rule – An Example

• We can now use the formula to solve for the present of the We can now use the formula to solve for the present of the tax savings on CCA for an asset that is never sold (no salvage tax savings on CCA for an asset that is never sold (no salvage value):value):

• This formula assumes:This formula assumes:– CC00 = $100,000 = $100,000 (Initial cost of a depreciable asset)(Initial cost of a depreciable asset)– dd = 10% = 10% (CCA rate)(CCA rate)– k = 12%k = 12% (Cost(Cost of capital or discount rate) of capital or discount rate)– T =T = 40% 40% (Corporate tax rate)(Corporate tax rate)

• Notice the answer is greater than the spread sheet example Notice the answer is greater than the spread sheet example ($13,871) because the spreadsheet summed only the first 8 cash ($13,871) because the spreadsheet summed only the first 8 cash flows whereas the formula finds the sum of the present values of the flows whereas the formula finds the sum of the present values of the tax shield benefits for an infinite stream.tax shield benefits for an infinite stream.

27.207,17$12.1

06.1

22.

000,4$

12.1

)12(.5.1

1.12.

)4)(.1(.000,100$

1

501)( 0

k

)k.(

dk

dTCShieldTaxCCAPV


14 - 33

Formula for PV of Tax Savings on CCAFormula for PV of Tax Savings on CCAAssuming a Salvage Value at Assuming a Salvage Value at t = nt = n

• Finally we can incorporate planned disposal of Finally we can incorporate planned disposal of the asset we will acquire.the asset we will acquire.

• Disposal value is the ‘salvage value’ (SV) at Disposal value is the ‘salvage value’ (SV) at t = t = nn

(See the following two slides for graphical depiction of the effect of a salvage (See the following two slides for graphical depiction of the effect of a salvage value)value)

)1(

1

)(

))()((

)1(

)5.01())()(()( 0

kkd

TdSV

k

k

kd

TdCShieldTaxCCAPV

nn

[ 14-7]


14 - 34


0500

1000150020002500300035004000

Tax Shield

1 3 5 7 9 11 13 15 17 19

Year

T(CCA) at 10% on $100,000 By selling the asset after the end of the 10th fiscal year, we

lose CCA in years 11 through

infinity.

1

1)(0

kdk

dTSVSVonLostSavingsTaxCCAPV n

n


14 - 35


0500

1000150020002500300035004000

Tax Shield

1 3 5 7 9 11 13 15 17 19

Year

T(CCA) at 10% on $100,000

1

1

)1(

)5.1()( 0

0 kdk

dTSV

k

k

dk

dTCSavingsTaxCCAPV n

n

We subtract the PV of tax savings

lost on the Salvage Value

from the PV of tax saving from t = 1

through infinity to get the PV of tax savings benefits

years 1 – 10.


14 - 36

Expected Annual After-Tax Cash Flows Expected Annual After-Tax Cash Flows (CF(CFtt))

As illustrated in Equation 14-2 expected Annual As illustrated in Equation 14-2 expected Annual After-Tax Cash Flows are:After-Tax Cash Flows are:– The cash flows that are estimated to occur as a result of The cash flows that are estimated to occur as a result of

the investment decision, comprisingthe investment decision, comprising • the associated expected incremental increase in after-tax the associated expected incremental increase in after-tax

operating income andoperating income and• Any incremental tax savings (or additional taxes paid) that Any incremental tax savings (or additional taxes paid) that

result from the initial investment outlay.result from the initial investment outlay.



14 - 37

Forecasting Expected Annual After-Tax Forecasting Expected Annual After-Tax Cash Flows (CFCash Flows (CFtt))

Example 14 - 2 from your textApproach 1

Year 1 Year 2 Year 3 Year 4 Year 5Operating Income $125,000 $125,000 $125,000 $125,000 $125,000- CCA Expense -97,500 -165,750 -116,025 -81,218 -56,852Taxable Income $27,500 -$40,750 $8,975 $43,782 $68,148- Taxes payable @ 45% 12,375 -18,338 4,039 19,702 30,667After-tax income $15,125 -$22,413 $4,936 $24,080 $37,481+ CCA expense $97,500 $165,750 $116,025 $81,218 $56,852Net cash flow $112,625 $143,338 $120,961 $105,298 $94,333

Approach 2Year 1 Year 2 Year 3 Year 4 Year 5

Operating Income $125,000 $125,000 $125,000 $125,000 $125,000- Taxes Payable on Operating income @ 45% 56250 56250 56250 56250 56250After-tax Operating Income $68,750 $68,750 $68,750 $68,750 $68,750+ CCA tax savings (CCA * T) 43,875 74,588 52,211 36,548 25,583Net cash flow $112,625 $143,338 $120,961 $105,298 $94,333

Spreadsheets Spreadsheets can be useful can be useful in making in making detailed detailed forecasts of forecasts of the the incremental incremental operating operating cost and cost and benefits benefits associated associated with the with the project.project.

Operating cash flows are

an annuity where as net cash flow is

not.


14 - 38

Decomposing Expected Annual After-Tax Decomposing Expected Annual After-Tax Cash Flows (CFCash Flows (CFtt))

We have already seen that since the CCA tax We have already seen that since the CCA tax shield (CCAshield (CCAtt)(T) changes each year and )(T) changes each year and potentially involve an infinite series, we potentially involve an infinite series, we separately calculate its present value using a separately calculate its present value using a formula.formula.



14 - 39

Decomposing Expected Annual After-Tax Decomposing Expected Annual After-Tax Cash Flows (CFCash Flows (CFtt))

• Since the operating cash flow benefits after-Since the operating cash flow benefits after-tax are often equal each year, we can find tax are often equal each year, we can find their present value simply using the Present their present value simply using the Present Value Factor of an Annuity:Value Factor of an Annuity:

)1(

11

)1()( k

kTCFBTFlowsCashOperatingPV

n

[ 14-6]


14 - 40

Decomposing Expected Annual After-Tax Cash Decomposing Expected Annual After-Tax Cash Flows (CFFlows (CFtt))

Example of the PV of the Operating Cash Flow AnnuityExample of the PV of the Operating Cash Flow Annuity

Using Example 14 – 2:Using Example 14 – 2:– Operating income Operating income

excluding CCA before tax = excluding CCA before tax = $125,000$125,000

– Tax rate = 45%Tax rate = 45%– Useful life = 5 yearsUseful life = 5 years– Discount rate (Discount rate (kk) = 10%) = 10%– The present vale of the The present vale of the

operating income annuity =operating income annuity = 616,260$7908.3750,68$

.1

(1.1)1

-1.45) - $125,000(1

)1(

11

)1()(

5

kk

TCFBTFlowsCashOperatingPVn


14 - 41

Ending (or Terminal) After-Tax Cash Ending (or Terminal) After-Tax Cash Flows (ECFFlows (ECFnn))

• Ending cash flows include:Ending cash flows include:– Salvage value of the asset (SVSalvage value of the asset (SVnn))

– Recovery of the net investment in working capital (NWCRecovery of the net investment in working capital (NWCnn))

– Less any taxes payable in the event of a capital gain on the sale of the Less any taxes payable in the event of a capital gain on the sale of the asset or a recapture of depreciation.asset or a recapture of depreciation.

])-

T]50.0)C-[(ns)ImplicatioTax With ( 0

TUCC[(SV

SVNWCSVECF

nn

nnnn

[ 14-3]


14 - 42

CCA Tax Shield with a Recapture of CCA Tax Shield with a Recapture of DepreciationDepreciation

• Equation 14 -8 Is used when the salvage value of the asset Equation 14 -8 Is used when the salvage value of the asset is greater than the UCC of the pool of assets at the time of is greater than the UCC of the pool of assets at the time of disposal.disposal.

• A recapture of depreciation must be included in income in A recapture of depreciation must be included in income in the year it occurs and is subject to tax at the firm’s tax rate the year it occurs and is subject to tax at the firm’s tax rate ((TT ) )

)1(

))((

)1(

1

)(

))()((

)1(

)5.01())()(()( 0

k

TUCCSV

kkd

TdSV

k

k

kd

TdCShieldTaxCCAPV

nnn

nn

[ 14-8]


14 - 43

Capital Gain on Asset DisposalCapital Gain on Asset Disposal

• Equation 14 – 9 is used when you expect to sell the asset Equation 14 – 9 is used when you expect to sell the asset for a price that is greater than its original cost.for a price that is greater than its original cost.

• The difference between the SV and CThe difference between the SV and C00 is the capital gain. is the capital gain.

• 50% of a realized capital gain is subject to tax at the 50% of a realized capital gain is subject to tax at the

corporate tax rate (corporate tax rate (T T ))

)1(

))(5)(.()( 0

k

TCSVPaidTaxesGainsCapitalPV

nn

[ 14-9]


14 - 44

NPV Using the Decomposed NPV Using the Decomposed ComponentsComponents

• Equation 14-10, on the following slides, shows how the Equation 14-10, on the following slides, shows how the decomposed components are recombined to determine the decomposed components are recombined to determine the projects NPVprojects NPV

• Remember NPV =Remember NPV =+ Present value of after-tax operating cash flowsPresent value of after-tax operating cash flows+ Present value of CCA tax shield Present value of CCA tax shield + Present value of the salvage value (ECF)Present value of the salvage value (ECF)+ Present value of the recovery of net working capital investment (ECF)Present value of the recovery of net working capital investment (ECF)- Taxes payable on realized capital gain and/or recapture of depreciation Taxes payable on realized capital gain and/or recapture of depreciation

(ECF)(ECF)

- Initial investment in the asset (CFInitial investment in the asset (CF00))

- Initial investment in net working capital (CFInitial investment in net working capital (CF00))


14 - 45

NPV Using the Decomposed NPV Using the Decomposed ComponentsComponents

)(

)()()(

0 CFPaidTaxesGainsCapitalPV

ECFPVShieldTaxCCAPVCFsOperatingPVNPV n

[ 14-10]


14 - 46

Sensitivity to InputsSensitivity to Inputs

• Stress testing NPV models to determine the Stress testing NPV models to determine the sensitivity of the decision to input variables sensitivity of the decision to input variables is an important part of risk assessmentis an important part of risk assessment

• There are two common approaches:There are two common approaches:– Sensitivity analysis – an examination of how an Sensitivity analysis – an examination of how an

investment’s NPV changes as the value of one input investment’s NPV changes as the value of one input at a time is changedat a time is changed

– Scenario analysis – an examination of how an Scenario analysis – an examination of how an investment’s NPV changes in response to varying investment’s NPV changes in response to varying scenarios in terms of one or more estimates, such scenarios in terms of one or more estimates, such as sales or costsas sales or costs


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Sensitivity to InputsSensitivity to InputsScenario AnalysisScenario Analysis

Input variables are often given discrete forecast Input variables are often given discrete forecast ranges:ranges:

– Best caseBest case

– Most likelyMost likely

– Worst caseWorst case

The analyst will be interested in what the NPV might The analyst will be interested in what the NPV might be in the worst combination of cases for example:be in the worst combination of cases for example:

– Worst case operating cash flows (low)Worst case operating cash flows (low)

– Worst case initial cost (high)Worst case initial cost (high)

– Worst case new working capital investment (high)Worst case new working capital investment (high)


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Sensitivity to InputsSensitivity to InputsReal Option Valuation (ROV)Real Option Valuation (ROV)

• ROV and decision tree analysis have dramatically increased ROV and decision tree analysis have dramatically increased understanding of corporate decision-making and the value of understanding of corporate decision-making and the value of flexibility and strategic considerations.flexibility and strategic considerations.

• Decision trees are a schematic way to represent alternative Decision trees are a schematic way to represent alternative decisions and the possible outcomes.decisions and the possible outcomes.

• Table 14-2 (next slide) gives a real options example of three Table 14-2 (next slide) gives a real options example of three alternative ore-price scenarios for a mine. (The most important alternative ore-price scenarios for a mine. (The most important variable in mining projects.)variable in mining projects.)

• This table illustrates that the highest expected cash flows occur This table illustrates that the highest expected cash flows occur when ore prices are most volatile (have the greatest range of when ore prices are most volatile (have the greatest range of prices).prices).

• This illustrates an option that is often overlooked in traditional This illustrates an option that is often overlooked in traditional project analysis…the possibility of shutting down the mine when project analysis…the possibility of shutting down the mine when prices make it uneconomic. (Remember, the mine can be prices make it uneconomic. (Remember, the mine can be returned to production when economic conditions turn more returned to production when economic conditions turn more favourable.)favourable.)


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Real Option Valuation (ROV)Real Option Valuation (ROV)Comparing NPV and IRRComparing NPV and IRR

Scenario 1: Ore Price $12 or $8



Good price (ρ=.5) $12 $14 $16

Cash Flow $400 $600 $800

Bad price (ρ=.5) $8 $6 $4

Cash Flow $0 -$200 -$200

Expected cash flow $200 $200 $300

Table 14 - 2 Real Options Example


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Sensitivity to InputsSensitivity to InputsNPV Break-Even AnalysisNPV Break-Even Analysis

Operating Cash Flow NPV Break-even PointOperating Cash Flow NPV Break-even Point• Solving for the annual operating after-tax Solving for the annual operating after-tax

cash flows that cause NPV = 0.cash flows that cause NPV = 0.– PV (Operating CFs) is the source of value creationPV (Operating CFs) is the source of value creation– The most important part of the viability analysis. The most important part of the viability analysis.


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Sensitivity to InputsSensitivity to InputsOperating Cash Flow NPV Break-Even PointOperating Cash Flow NPV Break-Even Point

Example:Example:CFCF00 = $100,000 = $100,000

PVPV((CCA Tax Shield)CCA Tax Shield) = $20,453 = $20,453

PV(ECFPV(ECFnn)) = $12,834 = $12,834 Approach:Approach:

– Set NPV = 0 and solve for the Set NPV = 0 and solve for the PV of the operating CFPV of the operating CFss::

– Now solve for the annual after-Now solve for the annual after-tax CFtax CF

Conclusion:Conclusion:– The operating cash flows could The operating cash flows could

fall to $10,770 without fall to $10,770 without destroying value.destroying value.

– Now the decision makers can Now the decision makers can assess the threats to this key assess the threats to this key forecast and determine the forecast and determine the likelihood of this occurring.likelihood of this occurring.

713,66$)(

000,100$834,12$453,20$)(00.0$

)()()( 0

CFsOperatingPV

CFsOperatingPV

CFECFPVShieldTaxCCAPVCFsOperatingPVNPV n

770,10$

)194374.6(][713,66$

12.0

)12.1(1

1][)(

12

CFOperatingevenBreak

CFOperatingevenBreak

CFOperatingevenBreakCFsOperatingPV


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Sensitivity to InputsSensitivity to InputsOperating Cash Flow NPV Break-Even PointOperating Cash Flow NPV Break-Even Point

NPV$

$20,000

Operating Cash Flow

Break-even cash flow

0 $50,000 $40,000 $30,000 $20,000 $10,000 $0

It is possible to vary the cash flow assumptions and test the sensitivity of NPV to those changes.

NPV is the dependent variable.


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Sensitivity to InputsSensitivity to InputsNPV Break-Even Discount RateNPV Break-Even Discount Rate

Break Even Discount RateBreak Even Discount Rate• IRR of the projectIRR of the project• NPV profile illustrates the range of discount NPV profile illustrates the range of discount

rates that produce a positive NPV.rates that produce a positive NPV.

(See the following two slides as a review of NPV profiles from Chapter 13)(See the following two slides as a review of NPV profiles from Chapter 13)


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NPV$

$260,000

Discount Rate (%)

IRR = 55.8%

0 0% 5% 10% 20% 40% 50% 60%

Required rates of return can change if:

• The general level of interest rates rise in the economy, or

• The risk of the project increases.


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NPV$

$260,000

$146,684

Discount Rate (%)

IRR = 55.8%

0 0% 5% 10% 20% 40% 50% 60%

Even if your estimate of the project’s required return (RADR) is wrong, the project’s NPV remains positive over a wide range of values for k (from 0% to 55%)


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Expansion DecisionsExpansion Decisions

• Expansion projects add something extra to Expansion projects add something extra to the firm in terms of sales or cost savings; the firm in terms of sales or cost savings; their new cash flows are incremental cash their new cash flows are incremental cash flowsflows


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Replacement DecisionsReplacement Decisions

• Involve the replacement of an existing asset Involve the replacement of an existing asset (or assets) with a new one.(or assets) with a new one.– In such cases we must clearly identify the In such cases we must clearly identify the

incremental cash flows paying particular attention to:incremental cash flows paying particular attention to:• The effect on the incremental capital cost (∆CThe effect on the incremental capital cost (∆C00) )

• The effect on the CCA tax shieldThe effect on the CCA tax shield


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Replacement DecisionsReplacement DecisionsIncremental Capital CostIncremental Capital Cost

• Incremental Capital Cost (∆CIncremental Capital Cost (∆C00) = the difference ) = the difference

between the purchase price of the new equipment between the purchase price of the new equipment and the salvage price of the old machine.and the salvage price of the old machine.

• The equipment to be replaced is normally sold. The equipment to be replaced is normally sold. Normally there are no tax consequences on Normally there are no tax consequences on disposal, except when assets are sold at a price disposal, except when assets are sold at a price greater than their original cost (which triggers capital greater than their original cost (which triggers capital gains taxes on the difference)gains taxes on the difference)


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Replacement DecisionsReplacement DecisionsEffects on Capital Cost Allowance Tax ShieldEffects on Capital Cost Allowance Tax Shield

When an asset is removed from the Capital Cost Allowance Class:When an asset is removed from the Capital Cost Allowance Class:• There is no CCA in the year of disposalThere is no CCA in the year of disposal

• The UCC of the pool/class is reduced by the disposal valueThe UCC of the pool/class is reduced by the disposal value

When an asset is added to the Capital Cost Allowance Class:When an asset is added to the Capital Cost Allowance Class:• There is ½ of the normal CCA on the ‘net additions to the pool’ in There is ½ of the normal CCA on the ‘net additions to the pool’ in

that yearthat year

• The UCC of the pool is increased by half of the net addition in the The UCC of the pool is increased by half of the net addition in the first year, and half of the net additions in the second yearfirst year, and half of the net additions in the second year

In replacement decisions we must modify the PV of Tax Shield In replacement decisions we must modify the PV of Tax Shield formula to account for the change (∆) in Cformula to account for the change (∆) in C00 and (∆) in SV and (∆) in SV

(See the following slide for the new formula)(See the following slide for the new formula)


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Replacement DecisionsReplacement DecisionsEffects on Capital Cost Allowance Tax ShieldEffects on Capital Cost Allowance Tax Shield

)1(

1

)(

))()((

)1(

)5.01())()(()( 0

kkd

TdSV

k

k

kd

TdCShieldTaxCCAPV

nn

The replacement of old with new results in a change in the tax shield and affects both the net cost of the

new as well as the salvage value.


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Replacement DecisionsReplacement DecisionsSimple Example Ignoring CCA – Formula ApproachSimple Example Ignoring CCA – Formula Approach

Problem:Problem:• Cost of new machine = Cost of new machine =

$12,000$12,000• Disposal value of old Disposal value of old

machine = $2,000machine = $2,000

• After-tax cash flow benefits:After-tax cash flow benefits:– Year 1 = $5,000Year 1 = $5,000– Year 2 = $5,000Year 2 = $5,000– Year 3 = $8,000Year 3 = $8,000

• Discount rate (k) = 15%Discount rate (k) = 15% 389,3$

000,10$260,6$781,3$348,4$

)000,2$000,12($)15.1(

000,8$

)15.1(

000,5$

)15.1(

000,5$

)1()1()1(

321

033

22

11

Ck

CF

k

CF

k

CFNPV

Incremental capital cost is

the price of the new machine

less the price of the old.


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Replacement DecisionsReplacement DecisionsSimple Example Ignoring CCA – Formula ApproachSimple Example Ignoring CCA – Formula Approach

Incremental Cost (new-old) = $10,000Cost of Capital = 15.0%

Year CashflowAfter-tax

incremental CF PV FactorPresent Value

0 Initial cost -$10,000 1 -$10,0001 ATCF operating benefit 5,000 0.869565 $4,3482 ATCF operating benefit 5,000 0.756144 $3,7813 ATCF operating benefit 8,000 0.657516 $5,260

NPV = $3,389

Problem:Problem:Cost of new machine = Cost of new machine =

$12,000$12,000

Disposal value of old Disposal value of old machine = $2,000machine = $2,000

After-tax cash flow benefits:After-tax cash flow benefits:

Year 1 = $5,000Year 1 = $5,000

Year 2 = $5,000Year 2 = $5,000

Year 3 = $8,000Year 3 = $8,000

Discount rate (k) = 15%Discount rate (k) = 15%


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Replacement DecisionsReplacement DecisionsThe Formula ApproachThe Formula Approach

The deconstructed NPV model can be used in The deconstructed NPV model can be used in replacement decisions.replacement decisions.

Again, in replacement decisions, the focus in on Again, in replacement decisions, the focus in on the net change in operating cash flows, net the net change in operating cash flows, net change in CCA tax shield, and net changes in change in CCA tax shield, and net changes in ending and initial cash flows.ending and initial cash flows.

)()()( 0CFECFPVShieldTaxCCAPVCFsOperatingPVNPV n


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Inflation and Capital Budgeting DecisionsInflation and Capital Budgeting DecisionsThe Impact of InflationThe Impact of Inflation

• Even small rates of inflation over time can have Even small rates of inflation over time can have considerable effects on the economic viability of a considerable effects on the economic viability of a project.project.

• Although inflation is often measured by aggregate Although inflation is often measured by aggregate changes in prices at the retail (CPI consumer price changes in prices at the retail (CPI consumer price index) or wholesale level, these measures often do index) or wholesale level, these measures often do not reflect price changes specific to one company or not reflect price changes specific to one company or one project.one project.

• Inflation MUST be treated consistently in our project Inflation MUST be treated consistently in our project evaluation models (NPV, IRR, PI)evaluation models (NPV, IRR, PI)


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Inflation and Capital Budgeting DecisionsInflation and Capital Budgeting DecisionsTwo Basic ApproachesTwo Basic Approaches

• Inflation can be consistently incorporated by:Inflation can be consistently incorporated by:1.1. Removing it from the nominal discount rate and Removing it from the nominal discount rate and

using nominal cash flow forecastsusing nominal cash flow forecasts

2.2. Leaving the discount rate with an expected inflation Leaving the discount rate with an expected inflation component and estimating real (inflation-adjusted) component and estimating real (inflation-adjusted) cash flowscash flows


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Inflation and Capital Budgeting DecisionsInflation and Capital Budgeting DecisionsRemoving Expected Inflation from the Discount RateRemoving Expected Inflation from the Discount Rate

• As illustrated on the following slide, all discount rates As illustrated on the following slide, all discount rates used have embedded into them an expected rate of used have embedded into them an expected rate of inflation.inflation.

• If we use non-inflation adjusted cash flow forecasts, If we use non-inflation adjusted cash flow forecasts, and then discount using a nominal discount rate, we and then discount using a nominal discount rate, we are ‘over discounting’ because we are using a higher are ‘over discounting’ because we are using a higher rate…but not using inflated forecast cash flows.rate…but not using inflated forecast cash flows.

• You can use the Fisher equation to estimate the You can use the Fisher equation to estimate the embedded inflationary expectations, and then reduce embedded inflationary expectations, and then reduce the nominal discount rate by that amount.the nominal discount rate by that amount.

• Then you are free to discount nominal cash flows.Then you are free to discount nominal cash flows.


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Risk Adjusted Discount RatesRisk Adjusted Discount RatesUsing the CAPMUsing the CAPM

βMarket = 1

Required Return

RF

β

MERM

ProjectProject )( RFERRFk M

βProject = 1.5

ERProject

Risk Premium for project systematic risk

Real rate of return

Premium for expected inflation


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Required Rates of Return (RADR)Required Rates of Return (RADR)ComponentsComponents

• The risk-free rate is The risk-free rate is equal to the real rate of equal to the real rate of return plus expected return plus expected inflation (Fisher inflation (Fisher Equation)Equation)

• The risk premium is The risk premium is based on an estimate of based on an estimate of the risk associated with the risk associated with the project.the project.

PremiumRisk RF RADR

Beta of the Project

Required Return (%)

RF

Risk

Risk Adjusted Discount

Rate Risk Premium

Real Return

Expected Inflation Rate


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Inflation and Capital Budgeting DecisionsInflation and Capital Budgeting DecisionsThe Inflation Adjustment ProcessThe Inflation Adjustment Process

The key thing to remember is:The key thing to remember is:– If you use WACC unadjusted, then you must use If you use WACC unadjusted, then you must use

inflation-adjusted cash flow estimates for operating inflation-adjusted cash flow estimates for operating cash flowscash flows

– If you remove inflation from the discount rate If you remove inflation from the discount rate (WACC), you can use nominal cash flow estimates(WACC), you can use nominal cash flow estimates

The key is consistency.The key is consistency.


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Summary and ConclusionsSummary and Conclusions

In this chapter you have learned:In this chapter you have learned:– Several approaches and guidelines for estimating future Several approaches and guidelines for estimating future

cash flows associated with an investmentcash flows associated with an investment

– The equations used to estimate the present value of future The equations used to estimate the present value of future cash flows cash flows

– How to differentiate between expansion and replacement How to differentiate between expansion and replacement decisionsdecisions

– How to use sensitivity analysis, scenario analysis, what-if How to use sensitivity analysis, scenario analysis, what-if decision tree analysis and NPV break-even analysis.decision tree analysis and NPV break-even analysis.

– How to incorporate inflation into capital budgeting analysis.How to incorporate inflation into capital budgeting analysis.


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CopyrightCopyright

Copyright © 2007 John Wiley & Sons Canada, Ltd. All rights reserved. Copyright © 2007 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Reproduction or translation of this work beyond that permitted by Access Copyright (the Canadian copyright licensing agency) is Access Copyright (the Canadian copyright licensing agency) is unlawful. Requests for further information should be addressed to unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd.the Permissions Department, John Wiley & Sons Canada, Ltd. The The purchaser may make back-up copies for his or her own use only and purchaser may make back-up copies for his or her own use only and not for distribution or resale.not for distribution or resale. The author and the publisher assume no The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of responsibility for errors, omissions, or damages caused by the use of these files or programs or from the use of the information contained these files or programs or from the use of the information contained herein.herein.

Prepared by Ken Hartviksen INTRODUCTION TO CORPORATE FINANCE Laurence Booth W. Sean Cleary.

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Transcript of Prepared by Ken Hartviksen INTRODUCTION TO CORPORATE FINANCE Laurence Booth W. Sean Cleary.