microsoft project management - msp

8/8/2019 Microsoft Project Management - MSP

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1.040/1.4011.040/1.401

Project ManagementProject ManagementSpring 2007Spring 2007

Project Financing & EvaluationProject Financing & Evaluation

Dr. SangHyun Lee

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental Engineering

Massachusetts Institute of TechnologyMassachusetts Institute of Technology


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AS 2: Student PresentationAS 2: Student Presentation

10 minute presentation followed by 5 minute discussion10 minute presentation followed by 5 minute discussion

1 or 2 presentations from Feb. 20 to Mar. 191 or 2 presentations from Feb. 20 to Mar. 19 TopicsTopics

Your past project experience (strongly recommended if you have aYour past project experience (strongly recommended if you have any)ny)

Size of project is not important!Size of project is not important! Project main figuresProject main figures

Main managerial aspectsMain managerial aspects

Project management practicesProject management practices

Problems, strengths, weaknesses, risksProblems, strengths, weaknesses, risks

Your learningYour learning

Emerging construction technologies (e.g., 4D CAD, Virtual RealitEmerging construction technologies (e.g., 4D CAD, Virtual Reality, Sensing,y, Sensing, ))

Volunteers for next week?Volunteers for next week?


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PreliminariesPreliminaries

MIT Server access: to be announcedMIT Server access: to be announced

AS1 Survey due by tonight 12 pmAS1 Survey due by tonight 12 pm

TP1 and AS2 are outTP1 and AS2 are out Pictures will be taken before you leavePictures will be taken before you leave

Who we areWho we are DonDont memorize course content. Understand it.t memorize course content. Understand it.


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OutlineOutline

Session Objective & ContextSession Objective & Context

Project FinancingProject Financing OwnerOwner ProjectProject ContractorContractor Additional IssuesAdditional Issues

Financial EvaluationFinancial Evaluation Time value of moneyTime value of money Present valuePresent value RatesRates Interest FormulasInterest Formulas NPVNPV IRR & payback periodIRR & payback period

Missing factorsMissing factors


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Session ObjectiveSession Objective

The role of project financingThe role of project financing

Mechanisms for project financingMechanisms for project financing

Measures of project profitabilityMeasures of project profitability


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Project Management PhaseProject Management Phase

FEASIBILITYDESIGN

PLANNINGDEVELOPMENT CLOSEOUT OPERATIONS

Financing & Evaluation

Risk


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Context: Feasibility PhasesContext: Feasibility Phases

Project ConceptProject Concept

Land Purchase & Sale ReviewLand Purchase & Sale Review Evaluation (scope, size, etc.)Evaluation (scope, size, etc.)

Constraint surveyConstraint survey

Site constraintsSite constraints Cost modelsCost models

Site infrastructural issuesSite infrastructural issues

Permit requirementsPermit requirements

Summary ReportSummary Report

Decision to proceedDecision to proceed

Regulatory process (obtain permits, etc)Regulatory process (obtain permits, etc) Design PhaseDesign Phase


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Lecture 2Lecture 2 -- ReferencesReferences

More details on:More details on:

Hendrickson PM for Construction onHendrickson PM for Construction on--line textbookline textbook Chapter 7Chapter 7


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OutlineOutline


Project FinancingProject Financing

OwnerOwner ProjectProject ContractorContractor Additional IssuesAdditional Issues




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FinancingFinancingGrossGross CashflowsCashflows

($35,000,000)

($30,000,000)

($25,000,000)

($20,000,000)

($15,000,000)

($10,000,000)($5,000,000)

$0

$5,000,000

$10,000,000

1 2 3 4 5 6 7 8 9 10 11

owner cum cashflow

contractor cum cashflow

years 1 2 3 4 5 6 7 8 9 10OWNERinvestment ($10,000,000) ($20,000,000)operation incomes $2,000,000 $4,000,000 $6,000,000 $6,000,000 $6,000,000 $6,000,000 $6,000,000owner cashflow $0 ($10,000,000) ($20,000,000) $2,000,000 $4,000,000 $6,000,000 $6,000,000 $6,000,000 $6,000,000 $6,000,000owner cum cashflow $0 ($10,000,000) ($30,000,000) ($28,000,000) ($24,000,000) ($18,000,000) ($12,000,000) ($6,000,000) $0 $6,000,000

CONTRACTORcosts ($4,000,000) ($7,000,000) ($14,000,000) $0 $0 $0 $0 $0 $0 $0revenues $0 $10,000,000 $20,000,000 $0 $0 $0 $0 $0 $0 $0contractor cashflow ($4,000,000) $3,000,000 $6,000,000 $0 $0 $0 $0 $0 $0 $0contractor cum cashf ($4,000,000) ($1,000,000) $5,000,000 $5,000,000 $5,000,000 $5,000,000 $5,000,000 $5,000,000 $5,000,000 $5,000,000

Owner investment = contractor revenue


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($35,000,000)

($30,000,000)

($25,000,000)

($20,000,000)

($15,000,000)

($10,000,000)($5,000,000)

$0

$5,000,000

$10,000,000

1 2 3 4 5 6 7 8 9 10 11

owner cum cashflow





Design/Preliminary Construction


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($35,000,000)

($30,000,000)

($25,000,000)

($20,000,000)

($15,000,000)

($10,000,000)($5,000,000)

$0

$5,000,000

$10,000,000

1 2 3 4 5 6 7 8 9 10 11

owner cum cashflow





Early expenditure

Takes time to get revenue

Design/Preliminary Construction


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Aims to bridge this gap in the most beneficial way!Aims to bridge this gap in the most beneficial way!


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Critical Role of FinancingCritical Role of Financing

Makes projects possibleMakes projects possible Has major impact onHas major impact on

RiskinessRiskiness of constructionof construction

ClaimsClaims

Prices offered by contractors (e.g., high bid price for latePrices offered by contractors (e.g., high bid price for latepayment)payment)

Difficulty of Financing is a major driver towards alternateDifficulty of Financing is a major driver towards alternatedelivery methods (e.g., Builddelivery methods (e.g., Build--OperateOperate--Transfer)Transfer)


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How Does Owner Finance a Project?How Does Owner Finance a Project?

PublicPublic

PrivatePrivate

ProjectProject financingfinancing


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OutlineOutline







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Public FinancingPublic Financing

Sources of fundsSources of funds

General purpose or specialGeneral purpose or special--purpose bondspurpose bonds Tax revenuesTax revenues

Capital grants subsidiesCapital grants subsidies

International subsidized loansInternational subsidized loans

Social benefits important justificationSocial benefits important justification Benefits to region, quality of life, unemployment relief, etc.Benefits to region, quality of life, unemployment relief, etc.

Important consideration: exemption from taxesImportant consideration: exemption from taxes

Public owners face restrictions (e.g. bonding caps)Public owners face restrictions (e.g. bonding caps) Major motivation for public/private partnershipsMajor motivation for public/private partnerships

MARR (Minimum Attractive Rate of Return) much lower (e.g. 8MARR (Minimum Attractive Rate of Return) much lower (e.g. 8--

10%), often standardized10%), often standardized


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Private FinancingPrivate Financing

Major mechanismsMajor mechanisms

EquityEquity Invest corporate equity and retained earningsInvest corporate equity and retained earnings

Offering equity sharesOffering equity shares Stock Issuance (e.g. in capital markets)Stock Issuance (e.g. in capital markets)

Must entice investors with sufficiently high rate of returnMust entice investors with sufficiently high rate of return May be too limited to support the full investmentMay be too limited to support the full investment

May be strategically wrong (e.g., source of money, ownership)May be strategically wrong (e.g., source of money, ownership)

DebtDebt Borrow moneyBorrow money BondsBonds

Because higher costs and risks, require higher returnsBecause higher costs and risks, require higher returns

MARR varies per firm, often high (e.g. 20%)MARR varies per firm, often high (e.g. 20%)


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Private Owners w/Collateral FacilityPrivate Owners w/Collateral Facility

Distinct Financing PeriodsDistinct Financing Periods ShortShort--term construction loanterm construction loan

Bridge DebtBridge Debt

Risky (and hence expensive!)Risky (and hence expensive!)

Borrowed so owner can pay for construction (cost)Borrowed so owner can pay for construction (cost)

LongLong--term mortgageterm mortgage

Senior DebtSenior Debt Typically facility is collateralTypically facility is collateral

Pays for operations and Construction financing debtsPays for operations and Construction financing debts

Typically much lower interestTypically much lower interest

Loans often negotiated as a packageLoans often negotiated as a package

timeconstructionw/o tangible

operationw/ tangible

O li


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OutlineOutline




Financial EvaluationFinancial Evaluation Time value of moneyTime value of money Present valuePresent value

RatesRates Interest FormulasInterest Formulas NPVNPV IRR & payback periodIRR & payback period



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ProjectProject FinancingFinancing

Investment is paid back from the project profit rather than theInvestment is paid back from the project profit rather than thegeneral assets or creditworthiness of the project ownersgeneral assets or creditworthiness of the project owners

For larger projects due to fixed cost to establishFor larger projects due to fixed cost to establish Small projects not much benefitSmall projects not much benefit

Investment in project through special purpose corporationsInvestment in project through special purpose corporations Often joint venture between several partiesOften joint venture between several parties

Need capacity for independent operationNeed capacity for independent operation

BenefitsBenefits

Off balance sheet (liabilities do not belong to parent)Off balance sheet (liabilities do not belong to parent) Limits riskLimits risk

External investors: reduced agency cost (direct investment in prExternal investors: reduced agency cost (direct investment in project)oject)

DrawbackDrawback Tensions among stakeholdersTensions among stakeholders

O liO li


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OutlineOutline








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Contractor Financing IContractor Financing I

Payment schedulePayment schedule

Break out payments into componentsBreak out payments into components Advance paymentAdvance payment

Periodic/monthly progress payment (itemized breakdown structure)Periodic/monthly progress payment (itemized breakdown structure)

Milestone paymentsMilestone payments Often some compromise between contractor and ownerOften some compromise between contractor and owner

Architect certifies progressArchitect certifies progress

Agreed-upon payments retention on payments (usually, about 10%)retention on payments (usually, about 10%)

Often must cover deficit during constructionOften must cover deficit during construction

Can be many months before payment receivedCan be many months before payment received


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SS--curvecurveWorkWork

Man-hours

months


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SS--curvecurve CostCost

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Working days

$K

0

10

20

30

40

50

60

70

80

90

100

Cumulativecosts$K

Daily cost

Cum. costs

Expense & PaymentExpense & Payment


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Expense & PaymentExpense & Payment

Contractor's

expenses

Owner's paymentsAmount(Dollars)

Cumulativen

etcash

flow

(Dollars)

Expenses and payments

Cumulative net cash flow of contractor

0 1 2 3 4 5 6 7 8 9

01 2 3 4 5 6 7

8 9

Time period (Month)

Time period (Month)

+

-

Figure by MIT OCW.


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Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out for

FrontFront--end loaded bids (discounting)end loaded bids (discounting)

Unbalanced bidsUnbalanced bids

Contractor Revenue Projection

0

20

40

60

80

100

120

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Month

Reve

nue

Contractor Revenue Projection

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Month

Revenue


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Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out for

FrontFront--end loaded bids (discounting)end loaded bids (discounting) Unbalanced bidsUnbalanced bids

Contractors frequently borrow fromContractors frequently borrow from Banks (Need to demonstrate low risk)Banks (Need to demonstrate low risk)

Interaction with ownersInteraction with owners Some owners may assist in fundingSome owners may assist in funding

Help secure lowerHelp secure lower--priced loan for contractorpriced loan for contractor

Sometimes assist owners in funding!Sometimes assist owners in funding! Big construction company, small municipalityBig construction company, small municipality

BOTBOT


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Agreed upon in contractAgreed upon in contract

Often structure proposed by ownerOften structure proposed by owner

Should be checked by owner (fairShould be checked by owner (fair--cost estimate)cost estimate) Often based onOften based on MasterformatMasterformat Cost Breakdown StructureCost Breakdown Structure

(Owner standard CBS)(Owner standard CBS)

Certified by third party (Architect/engineer)Certified by third party (Architect/engineer)

Contractor Financing IIIContractor Financing III

OutlineOutline


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OutlineOutline








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Latent CreditLatent Credit

Many people forced to serve as lenders to owner dueMany people forced to serve as lenders to owner due

to delays in paymentsto delays in payments DesignersDesigners

ContractorsContractors

ConsultantsConsultants

CMCM

SuppliersSuppliers

ImplicationsImplications

Good in the shortGood in the short--termterm

Major concern on long run effectsMajor concern on long run effects


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Role of TaxesRole of Taxes

Tax deductions forTax deductions for

DepreciationDepreciation

the process of recognizing the using up of an asset throughthe process of recognizing the using up of an asset throughwear and obsolescence and of subtracting capital expenseswear and obsolescence and of subtracting capital expenses

from the revenues that the asset generates over time infrom the revenues that the asset generates over time in

computing taxable incomecomputing taxable income OthersOthers

OutlineOutline


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OutlineOutline



Owner Project Contractor Additional Issues





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Develop or Not Develop

Is any individual project worthwhile?

Given a list of feasible projects, which one is the best?

How does each project rank compared to the others on

the list?

Project E l tion E mple:Project Evaluation Example:


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Project Evaluation Example:Project Evaluation Example:

Project AProject A Construction=3 yearsConstruction=3 years

Cost = $1M/yearCost = $1M/year

Sale Value=$4MSale Value=$4M

Total Cost?Total Cost?

Profit?Profit?

Project BProject B Construction=6 yearsConstruction=6 years

Cost=$1M/yearCost=$1M/year

Sale Value=$8.5MSale Value=$8.5M

Total Cost?Total Cost?

Profit?Profit?


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Quantitative MethodQuantitative Method

ProfitabilityProfitability Create value for the companyCreate value for the company


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ProfitProfit

TOTALTOTAL

EQUIVAL. $EQUIVAL. $

REVENUESREVENUES 5,500,000.005,500,000.00

COSTSCOSTS 4,600,000.004,600,000.00

Project managementProject management 400,000.00400,000.00

EngineeringEngineering 800,000.00800,000.00

Material & transport 2,200,000.002,200,000.00

Construction/commissioningConstruction/commissioning 1,300,000.001,300,000.00

ContingenciesContingencies 200,000.00200,000.00

GROSS MARGINGROSS MARGIN 900,000.00900,000.00

TimeTime factorfactor??


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Quantitative MethodQuantitative Method

ProfitabilityProfitability Create value for the companyCreate value for the company

Opportunity CostOpportunity Cost Time Value of MoneyTime Value of Money

A dollar today is worth more than a dollar tomorrowA dollar today is worth more than a dollar tomorrow

Investment relative to bestInvestment relative to best--case scenariocase scenario E.g. Project AE.g. Project A -- 8% profit, Project B8% profit, Project B -- 10% profit10% profit


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Money Is Not EverythingMoney Is Not Everything

Social BenefitsSocial Benefits HospitalHospital

SchoolSchool

Highway built into a remote villageHighway built into a remote village

Intangible Benefits (Intangible Benefits (E.gE.g, operating and competitive, operating and competitive

necessity)necessity) New warehouseNew warehouse

New cafeteriaNew cafeteria

OutlineOutline


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OutlineOutline



Owner Project Contractor Additional issues




i C diB i C di


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Basic CompoundingBasic Compounding

Suppose we invest $x in a bank offering interest rate iSuppose we invest $x in a bank offering interest rate i

If interest is compounded annually, asset will be worthIf interest is compounded annually, asset will be worth

$x(1+i) after 1 year$x(1+i) after 1 year

$x(1+i)$x(1+i)

22

after 2 yearsafter 2 years $x(1+i)$x(1+i)33 after 3 yearsafter 3 years ..

$x(1+i)$x(1+i)nn after n yearsafter n years

$x

0 1 $x(1+i) 2 $x(1+i)22 n $x(1+i)nn

Ti V l f MTi V l f M


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Time Value of MoneyTime Value of Money

If we assumeIf we assume That money can always be invested in the bank (or someThat money can always be invested in the bank (or some

other reliable source) now to gain a return with interest laterother reliable source) now to gain a return with interest later

That as rational actors, we never make an investment whichThat as rational actors, we never make an investment whichwe know to offer less money than we could get in the bankwe know to offer less money than we could get in the bank

ThenThen Money in theMoney in thepresentpresent can be thought as ofcan be thought as ofequal worthequal worth toto

a larger amount of money in the futurea larger amount of money in the future Money in theMoney in the futurefuture can be thought of as having an equalcan be thought of as having an equal

worth to a lesserworth to a lesser present valuepresent value of moneyof money

E i l f P V lE i l f P V l


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Equivalence of Present ValuesEquivalence of Present Values

Given a source of reliable investments, we areGiven a source of reliable investments, we are

indifferent between any cash flows with theindifferent between any cash flows with the

same present valuesame present valuethey havethey have equal worthequal worth

This indifferences arises because we canThis indifferences arises because we canconvert one to the other with no extra expenseconvert one to the other with no extra expense

OutlineOutline


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Owner Project Contractor Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present valuePresent value



Ti V l f M R i iTi V l f M R i it


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Time Value of Money: RevisitTime Value of Money: Revisit

If we assumeIf we assume That money can always be invested in the bank (or someThat money can always be invested in the bank (or some

other reliable source) now to gain a return with interest laterother reliable source) now to gain a return with interest later

That as rational actors, we never make an investment whichThat as rational actors, we never make an investment whichwe know to offer less money than we could get in the bankwe know to offer less money than we could get in the bank

ThenThen Money in theMoney in thepresentpresent can be thought as ofcan be thought as ofequal worthequal worth toto

a larger amount of money in the futurea larger amount of money in the future Money in theMoney in the futurefuture can be thought of as having an equalcan be thought of as having an equal

worth to a lesserworth to a lesser present valuepresent value of moneyof money

P t V l (R )P t V l (R )


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Present Value (Revenue)Present Value (Revenue)

How is it that some future revenueHow is it that some future revenue rrat timeat time tthas ahas a presentpresentvaluevalue??

Answer: Given that we are sure that we will be gaining revenueAnswer: Given that we are sure that we will be gaining revenue rr

at timeat time tt, we can take and spend an immediate loan from the, we can take and spend an immediate loan from thebankbank

We choose size of this loanWe choose size of this loan llso that at timeso that at time tt, the total size of the loan, the total size of the loan

(including accrued interest) is(including accrued interest) is rr

The loanThe loan llis the present value ofis the present value ofrr

ll== PV(PV(rr))

F t t P t RF t re to Pre ent Re en e


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Future to Present RevenueFuture to Present Revenue

x

t

-x

tPV(x)

0 Ill pay this back to the bank later

I can borrow this from the bank now

tPV(x)

If I know this is coming

The net result is that I can convert a sure xat time t

into a (smaller) PV(x) now!

Pr nt V l (C t)Present Value (Cost)


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Present Value (Cost)Present Value (Cost)

How is it that some future costHow is it that some future cost ccat timeat time tthas ahas a present valuepresent value?? Answer: Given that we areAnswer: Given that we are suresurethat we will bear costthat we will bear cost ccat timeat time tt,,

we immediately deposit a sum of moneywe immediately deposit a sum of moneyxxinto the bank yieldinginto the bank yielding

a known returna known return We choose size of depositWe choose size of deposit xxso that at timeso that at time tt, the total size of the, the total size of the

investment (including accrued interest) isinvestment (including accrued interest) is cc

We can then pay offWe can then pay offccat timeat time ttby retrieving this money from the bankby retrieving this money from the bank

The size of the deposit (immediate cost)The size of the deposit (immediate cost) xxis theis thepresent valuepresent valueofofcc..

Future to Present CostFuture to Present Cost


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Future to Present CostFuture to Present Cost

x

tPV(x)

I retrieve this back from the bank later

I can deposit this in the bank now

t

The net result is that I can convert a sure cost xat time t

into a (smaller) cost of PV(x) now!

PV(x)

-x

t0

If I know this cost is coming

SummarySummary


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SummarySummary

Because we can flexibly switch from one such value to anotherBecause we can flexibly switch from one such value to another

without cost, we can view these values as equivalentwithout cost, we can view these values as equivalent

FV

tv

v0

PV

SummarySummary


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SummarySummary

Because we can flexibly switch from one such value to anotherBecause we can flexibly switch from one such value to another

without cost, we can view these values as equivalentwithout cost, we can view these values as equivalent

FV

tv

v0

PV

Given a reliable source offering annual returnGiven a reliable source offering annual return ii(i.e., interest) we(i.e., interest) we

can shift without additional costs between cashcan shift without additional costs between cash vvat timeat time 00 andand

v(1+i)v(1+i)tt at timeat time tt

= v= v(1+(1+ii))tt

OutlineOutline


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Project FinancingProject Financing Owner Project Contractor Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present value



RR


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RatesRates

Difference between PV (Difference between PV (vv) and FV () and FV (==v(1+i)v(1+i)tt)) depends ondepends on iiandand tt..

RR t


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RatesRates

Difference between PV (Difference between PV (vv) and FV () and FV (==v(1+i)v(1+i)tt)) depends ondepends on iiandand tt..

Interest RateInterest Rate

Contractual arrangement between a borrower and a lenderContractual arrangement between a borrower and a lender

Discount Rate (real change in value to a person or group)Discount Rate (real change in value to a person or group) Worth of Money + RiskWorth of Money + Risk

Discount Rate > Interest RateDiscount Rate > Interest Rate

Minimum Attractive Rate of Return (MARR)Minimum Attractive Rate of Return (MARR) Minimum discount rate accepted by the market corresponding to thMinimum discount rate accepted by the market corresponding to the riskse risks

of a project (i.e., minimum standard of desirability)of a project (i.e., minimum standard of desirability)

Choice of Discount RateChoice of Discount Rate


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Choice of Discount RateChoice of Discount Rate

GDP = Gross Domestic Product

r = rf+ ri + rr

Where:

r

rf

ri

rr

rr =

is the discount rate

the risk free interest rate. Normally government bond

Rate of inflation. It is measured by either by consumer priceindex or GDP deflator

Risk factor consisting of market risk, industry risk, firmspecific risk and project risk

Market Risk

Industry Risk

Firm Specific Risk

Project Risk

Figure by MIT OCW.

OutlineOutline


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Rates Interest FormulasInterest Formulas NPVNPV IRR & payback periodIRR & payback period


Interest FormulasInterest Formulas


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Interest FormulasInterest Formulas

ii= Effective interest rate per interest period (discount rate or= Effective interest rate per interest period (discount rate or MARR)MARR)

n = Number of compounding periodsn = Number of compounding periods

PV = Present ValuePV = Present Value

FV = Future ValueFV = Future Value

A = Annuity (i.e., a series of payments of set size) at endA = Annuity (i.e., a series of payments of set size) at end--ofof--periodperiod

Interest Formulas: PaymentInterest Formulas: Payment


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yy

Single Payment Compound Amount Factor (F=Single Payment Compound Amount Factor (F=PPFactorFactor)) Factor that will make your present value future value in singleFactor that will make your present value future value in single paymentpayment

(F/P,(F/P, ii, n) = (1 +, n) = (1 + ii))nn

P

n0

F

1 2



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y

Single Payment Present Value Factor (P=Single Payment Present Value Factor (P=FFFactorFactor)) Factor that will make your future value present value in singleFactor that will make your future value present value in single paymentpayment

(P/F,(P/F, ii, n) = 1/ (1 +, n) = 1/ (1 + ii))nn = 1/ (F/P,= 1/ (F/P, ii, n), n)

P

n0

F

1 n-1



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-- ExampleExample

If you wish to have $100,000 at the end of five yearsIf you wish to have $100,000 at the end of five yearsin an account that pays 12 percent annually, howin an account that pays 12 percent annually, howmuch would you need to deposit now?much would you need to deposit now?



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-- ExampleExample


(P/F, 0.12, 5) or (F/P, 0.12, 5)?(P/F, 0.12, 5) or (F/P, 0.12, 5)?

P=?

n0

F=$100,000



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-- ExampleExample


P = FP = F(P/F, 0.12, 5)(P/F, 0.12, 5)

P =P = 100,000100,000 (P/F, 0.12, 5)(P/F, 0.12, 5)

P = 100,000P = 100,000 0.5674 = $56,7400.5674 = $56,740

Interest Formulas: SeriesInterest Formulas: Series


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Uniform Series Compound Amount Factor (F=Uniform Series Compound Amount Factor (F=AAFactorFactor))

Factor that will make your annuity value future value in seriesFactor that will make your annuity value future value in series paymentpayment

(F/A,(F/A, ii, n) =[(1+, n) =[(1+ii))nn -- 1]/1]/ ii

A A A A

n0 1

F

Annuity occurs at the end of the interest periodAnnuity occurs at the end of the interest period

2



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(F/A,(F/A, ii, n) =[(1+, n) =[(1+ii))nn -- 1]/1]/ ii

A A A A

n0 1

FF = A

2



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(F/A,(F/A, ii, n) =[(1+, n) =[(1+ii))nn -- 1]/1]/ ii

A A A A

n0 1

FF = A+A(1+i)

2



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(F/A,(F/A, ii, n) =[(1+, n) =[(1+ii))nn -- 1]/1]/ ii

A A A A

n0 1

F = A + A(1+i) + + A(1 +1 + ii))nn--11

2



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Uniform Series Sinking Fund Factor (A=Uniform Series Sinking Fund Factor (A=FFFactorFactor))

Factor that will make your future value annuity value in seriesFactor that will make your future value annuity value in series paymentpayment

(A/F,(A/F, ii, n) =, n) = ii/ [ (1 +/ [ (1 + ii))nn1] = 1 / (F/A,1] = 1 / (F/A, ii, n), n)

A A A A

n0 1

F

2



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A A A A

n0 1

P

Uniform Series Present Value Factor (P=Uniform Series Present Value Factor (P=AAFactorFactor))

Factor that will make your annuity value present value in seriesFactor that will make your annuity value present value in series paymentpayment

(P/A,(P/A, ii, n) = [ (1 +, n) = [ (1 + ii))nn --1 ] / [1 ] / [ii(1 +(1 + ii))nn]]

2



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A A A A

n0 1




P = A/ (1 +(1 + ii))

2



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A A A A

n0 1




P = A/(1 +(1 + ii) + A/(1 +) + A/(1 + ii))22

2



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A A A A

n0 1




P = A/(1 +(1 + ii) + A/(1 +) + A/(1 + ii))22 + + A/(1 +1 + ii))nn

Verify it!

2



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Uniform Series Capital Recovery Factor (A=Uniform Series Capital Recovery Factor (A=PPFactorFactor))

Factor that will make your present value annuity value in seriesFactor that will make your present value annuity value in series paymentpayment

(A/P,(A/P, ii, n) = [, n) = [ii(1 +(1 + ii))nn / [(1 +/ [(1 + ii))nn1] = 1 / (P/A,1] = 1 / (P/A, ii, n), n)

Verify it!

A A A A

n0 1

P

2



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-- ExampleExample

A ranch is offered for sale in Mexico with a 15 year mortgageA ranch is offered for sale in Mexico with a 15 year mortgagerate at 40% compounded annually, and 20% down payment.rate at 40% compounded annually, and 20% down payment.Annual payments are to be made. The first cost of the ranchAnnual payments are to be made. The first cost of the ranchis 5 million pesos. What yearly payment is required?is 5 million pesos. What yearly payment is required?



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-- ExampleExample


Down Payment = 5,000,000 * 0.2 = 1,000,000Down Payment = 5,000,000 * 0.2 = 1,000,000

P =P = 5,000,0005,000,0001,000,000 = 4,000,0001,000,000 = 4,000,000

A = P * (which factor?)A = P * (which factor?)



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-- ExampleExample


Down Payment = 5,000,000 * 0.2 = 1,000,000Down Payment = 5,000,000 * 0.2 = 1,000,000

P =P = 5,000,0005,000,0001,000,000 = 4,000,0001,000,000 = 4,000,000

A = P * (which factor?) = P * (A/P, 0.4, 15)A = P * (which factor?) = P * (A/P, 0.4, 15)

A = 4,000,000 * 0.40259 = 1,610,400 pesos/yearA = 4,000,000 * 0.40259 = 1,610,400 pesos/year

Equipment ExampleEquipment Example


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$ 20,000 equipment expected to last 5 years$ 20,000 equipment expected to last 5 years

$ 4,000 salvage value$ 4,000 salvage value

Minimum attractive rate of return 15%Minimum attractive rate of return 15%

What are the?What are the?

AA --Annual EquivalentAnnual Equivalent

PP -- Present EquivalentPresent Equivalent



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1 2 3 4 5

A

P

A A A A

i = 15% $4,000

$20,000

(a) A = ?

(b) P= ?

Figure by MIT OCW.



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A =A = --20,000 * (A/P, 0.15, 5) + 4,000 * (A/F, 0.15, 5)20,000 * (A/P, 0.15, 5) + 4,000 * (A/F, 0.15, 5)

== --20,000 * (0.2983) + 4,000 * (0.1483)20,000 * (0.2983) + 4,000 * (0.1483)

== --5,3735,373

P =P = --20,000 + 4,000 * (P/F, 0.15, 5)20,000 + 4,000 * (P/F, 0.15, 5)

== --20,000 + 4,000 * (0.4972)20,000 + 4,000 * (0.4972)

== --18,01118,011

OutlineOutline


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Rate Interest Formulas NPVNPV IRR & payback periodIRR & payback period


Net Present ValueNet Present Value


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Suppose we had a collection (or stream, flow) of costsSuppose we had a collection (or stream, flow) of costs

and revenues in the futureand revenues in the future

The net present value (NPV) is the sum of the presentThe net present value (NPV) is the sum of the present

values for all of these costs and revenuesvalues for all of these costs and revenues

Treat revenues as positive and costs as negativeTreat revenues as positive and costs as negative

Calculation of Net Present ValueCalculation of Net Present Value


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Total Revenue (R) (+) Various Costs (C) (-)

Calculate Gross Return

Calculate Net Return

PV of Net Return

NPV of the Project

Tax (-)

Discount Rate (r)

Initial Invest (-I)

Net Present Value Decision RuleNet Present Value Decision Rule


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Accept a project which has 0 or positive NPVAccept a project which has 0 or positive NPV

Alternatively,Alternatively,

Use NPV to choose the best among a set ofUse NPV to choose the best among a set of(mutually exclusive) alternative projects(mutually exclusive) alternative projects Mutually exclusive projects: the acceptance of a project precludMutually exclusive projects: the acceptance of a project precludeses

the acceptance of one or more alternative projects.the acceptance of one or more alternative projects.

> Accept the project

NPV = 0 Indifferent to the project< Reject the project

Project Evaluation ExampleProject Evaluation ExampleRevisit: Which one is better?Revisit: Which one is better?


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Project AProject A

Construction=3 yearsConstruction=3 years

Cost = $1M/yearCost = $1M/year Sale Value = $4MSale Value = $4M

Total Cost?Total Cost? Profit?Profit?

Project BProject B

Construction=6 yearsConstruction=6 years

Cost = $1M/yearCost = $1M/year Sale Value = $8.5MSale Value = $8.5M

Total Cost?Total Cost? Profit?Profit?

Drawing out the examplesDrawing out the examples


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Project AProject A

Project BProject B

$1M

$4M

$1M

1

$8.5M

6

$1M $1M $1M

$1M

$1M$1M

Assume 10% discount rate

0 32

$1M

0 1

Or Using Interest FormulasOr Using Interest Formulas


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Project AProject A

--$1M * (P/A, 0.1, 3) + $4M * (P/F, 0.1, 3)$1M * (P/A, 0.1, 3) + $4M * (P/F, 0.1, 3)

Project BProject B

--$1M * (P/A, 0.1, 6) + $8.5M * (P/F, 0.1, 6)$1M * (P/A, 0.1, 6) + $8.5M * (P/F, 0.1, 6)

Assume 10% discount rate

Four Independent ProjectsFour Independent Projects


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The cash flow profiles of four independent projects are shownThe cash flow profiles of four independent projects are shown

below. Using a MARR of 20%, determine the acceptability ofbelow. Using a MARR of 20%, determine the acceptability of

each of the projects on the basis of the net present valueeach of the projects on the basis of the net present value

criterion for accepting independent projects.criterion for accepting independent projects.

SolutionSolution


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[NPV1]20%= -77 + (235)(P/F, 0.2, 5) = -77 + 94.4= 17.4

[NPV2]20%= -75.3 + (28)(P/A, 0.2, 5) = -75.3 + 83.7= 8.4

Year 0 1 2 3 4 5

-$75.3 M

$28 M each year

Year 0 1 2 3 4 5

$235 M

-$77 M

NPV1 Cash Flow

NPV2 Cash Flow

SolutionSolution[NPV3]20%

= -39.9 + (28)(P/A, 20%, 4) - (80)(P/F, 20%, 5)39 9 72 5 32 2


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= -39.9 + 72.5 - 32.2= 0.4

[NPV4]20%= 18 + (10)(P/F, 20%, 1) - (40)(P/F, 20%, 2)

- (60)(P/F, 20%, 3) + (30)(P/F, 20%, 4)+ (50)(P/F, 20%, 5)

= 18 + 8.3 - 27.8 - 34.7 + 14.5 + 20.1 = -1.6

Source: Hendrickson and Au, 1989/2003

Year 0 1 2 3 4 5

-$39.9 M

$28 M each year

-$80 M

Year 0 1 2 3 4 5

$18 M $10 M

-$40 M-$60 M

$30 M$50 M

NPV3 Cash Flow

NPV4 Cash Flow

SolutionSolution


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[NPV1] = 17.4[NPV2] = 8.4[NPV3] = 0.4

[NPV4] = -1.6


Discount Rate in NPVDiscount Rate in NPV


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NPV (and PV) is relative to a discount rateNPV (and PV) is relative to a discount rate

In the absence of risk or inflation, this is just the interest rIn the absence of risk or inflation, this is just the interest rate of theate of the reliablereliable

sourcesource (opportunity cost)(opportunity cost)

Correct selection of the discount rate is fundamental. If too hiCorrect selection of the discount rate is fundamental. If too high, projectsgh, projects

that could be profitable can be rejected. If too low, the firm wthat could be profitable can be rejected. If too low, the firm will acceptill accept

projects that are too risky without proper compensation.projects that are too risky without proper compensation.

Its choice can easily change the ranking of projects.Its choice can easily change the ranking of projects. ExampleExample

Selection of Discount Rate: Example


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2 pieces of equipment: one needs a human operator (initial cost $10,000, annual $4,200 for

labor); the second is fully automated (initial cost $18,000, annual #3,000 for power).

n=10years.

Is the additional $8,000 in the initial investment of the second equipment worthy the

$1,200 annual savings? (discount rate: 5 or 10%)

Selection of Discount Rate: ExampleSelection of Discount Rate: Example


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2 pieces of equipment: one needs a human operator (initial cost2 pieces of equipment: one needs a human operator (initial cost $10,000, annual $4,200 for$10,000, annual $4,200 for

labor); the second is fully automated (initial cost $18,000, annlabor); the second is fully automated (initial cost $18,000, annual #3,000 for power).ual #3,000 for power).

n=10years.n=10years.

Is the additional $8,000 in the initial investment of the secondIs the additional $8,000 in the initial investment of the second equipment worthy theequipment worthy the

$1,200 annual savings? (discount rate: 5 or 10%)$1,200 annual savings? (discount rate: 5 or 10%)

There is a critical value ofThere is a critical value ofiithat changes the equipment choice (approximately 8.15%)that changes the equipment choice (approximately 8.15%)

Example: The US Federal Highway Administration promulgated a regExample: The US Federal Highway Administration promulgated a regulation in the earlyulation in the early

1970s that the discount rate for all federally funded highways w1970s that the discount rate for all federally funded highways would be zero. This wasould be zero. This was

widely interpreted as a victory for the cement industry over aspwidely interpreted as a victory for the cement industry over asphalt industry. Roads madehalt industry. Roads made

of concrete cost significantly more than those of made of asphalof concrete cost significantly more than those of made of asphalt while requiring lesst while requiring less

maintenance and less replacement [maintenance and less replacement [ShtubShtub et al., 1994]et al., 1994]

OutlineOutline

S i Obj ti & C t tS i Obj ti & C t t


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Session Objective & ContextSession Objective & Context Project FinancingProject Financing

Owner

Project Contractor Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present value Rate Interest Formulas NPV IRR & payback periodIRR & payback period


Internal Rate of Return (IRR)Internal Rate of Return (IRR)


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Defined as the rate of return that makes the NPV of the projectDefined as the rate of return that makes the NPV of the project

equal to zeroequal to zero

To see whether the projectTo see whether the projects rate of return is equal to or highers rate of return is equal to or higher

than the rate of the firm to expect to get from the projectthan the rate of the firm to expect to get from the project

IRR Calculation ExampleIRR Calculation Example


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NPV =NPV = --20,000 + 5,600 (P/A,20,000 + 5,600 (P/A, ii, 5) + 4,000 (P/F,, 5) + 4,000 (P/F, ii, 5), 5)

Machine A

Initial Cost $20,000

5 years

$4,000

$10,000

$4,400

Life

Salvage Value

Annual Receipts

Annual Disbursements

Image by MIT OCW.

Relationship between NPV & IRRRelationship between NPV & IRR


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2520151050

-1,000

1,000(15, 730)

(20, -1,196)

IRR

Interest Rate, i (%)

NetPre

sentValue($)

(10, 3,713)

2,000

3,000

4,000

Image by MIT OCW.

IRR Investment RuleIRR Investment Rule


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Accept a project with IRR larger than MARRAccept a project with IRR larger than MARR

Alternatively,Alternatively,

Maximize IRR across mutually exclusive projects.Maximize IRR across mutually exclusive projects.

> Accept

r- =

r*

Indifferent

< Rejectr = IRR, r = MARR*-

IRR vs. NPVIRR vs. NPV


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Oftentimes, IRR and NPV give the same decision/ranking amongOftentimes, IRR and NPV give the same decision/ranking amongprojects.projects.

IRR only looks atIRR only looks at raterateof gainof gainnotnot sizesizeof gainof gain IRR does not require you to assume (or compute) a discount rate.IRR does not require you to assume (or compute) a discount rate.

IRR ignores capacity to reinvestIRR ignores capacity to reinvest

IRR may not be uniqueIRR may not be unique

NPV

Discount Rate

IRR vs. NPVIRR vs. NPV


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Oftentimes, IRR and NPV give the same decision/ranking amongOftentimes, IRR and NPV give the same decision/ranking amongprojects.projects.

IRR only looks atIRR only looks at raterateof gainof gainnotnot sizesizeof gainof gain IRR does not require you to assume (or compute) a discount rate.IRR does not require you to assume (or compute) a discount rate.

IRR ignores capacity to reinvestIRR ignores capacity to reinvest

IRR may not be uniqueIRR may not be unique

Use both NPV (Use both NPV (sizesize) and IRR together () and IRR together (raterate))

However,However,

Trust the NPV: It is the only criterion that ensuresTrust the NPV: It is the only criterion that ensures

wealth maximization. It measures how much richer one willwealth maximization. It measures how much richer one willbecome by undertaking the investment opportunity.become by undertaking the investment opportunity.

Payback PeriodPayback Period


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Payback period (Payback period (Time to returnTime to return)) Minimal length of time over which benefits repay costsMinimal length of time over which benefits repay costs

Typically only used as secondary assessmentTypically only used as secondary assessment

Payback PeriodPayback Period


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Payback period (Payback period (Time to returnTime to return)) Minimal length of time over which benefits repay costsMinimal length of time over which benefits repay costs

Typically only used as secondary assessmentTypically only used as secondary assessment

Important for selection when the risk is extremely highImportant for selection when the risk is extremely high

DrawbacksDrawbacks

Ignores what happens after payback periodIgnores what happens after payback period

Does not take into account discountingDoes not take into account discounting

Comparing ProjectsComparing Projects


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Financing has major impact on project selectionFinancing has major impact on project selection Suppose that one had to choose between 2 investmentSuppose that one had to choose between 2 investment

projectsprojects

How can one compare them?How can one compare them?

Comparing ProjectsComparing Projects


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Financing has major impact on project selectionFinancing has major impact on project selection Suppose that one had to choose between 2 investmentSuppose that one had to choose between 2 investment

projectsprojects

How can one compare them?How can one compare them? Use NPVUse NPV

Verify IRRVerify IRR

Check payback periodCheck payback period

Other MethodsOther Methods


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BenefitBenefit--Cost ratio (benefits/costs)Cost ratio (benefits/costs)

Discounting still generally appliedDiscounting still generally applied Accept if >1 (benefits > costs)Accept if >1 (benefits > costs)

Common for public projectsCommon for public projects

Does not consider the absoluteDoes not consider the absolute sizesizeof the benefitsof the benefits CostCost--effectivenesseffectiveness

Looking at nonLooking at non--economic factorseconomic factors

Discounting still often applied for nonDiscounting still often applied for non--economiceconomic

$/Life saved$/Life saved

$/Life quality$/Life quality

Inflation & DeflationInflation & Deflation


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Inflation means that the prices of goods and services increaseInflation means that the prices of goods and services increase

over time either imperceptibly or in leaps and bounds. Inflationover time either imperceptibly or in leaps and bounds. Inflationeffects need to be included in investment because cost andeffects need to be included in investment because cost and

benefits are measured in money and paid in current dollars,benefits are measured in money and paid in current dollars,

francs or pesos. An inflationary trend makes future dollars havefrancs or pesos. An inflationary trend makes future dollars have

less purchasing power than present dollars.less purchasing power than present dollars.

Deflation means the opposite of inflation. Prices of goods &Deflation means the opposite of inflation. Prices of goods &services decrease as time passes.services decrease as time passes.


ijjii ++=' discount rate excluding inflationdiscount rate excluding inflationi

'


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ijjii ++=

If i, A(y=0)will be A*(1+i) after one year.Then, if j, A will be A*(1+i)*(1+j).

discount rate including inflationdiscount rate including inflation

annual inflation rateannual inflation rate

'i

j


ijjii ++=' discount rate excluding inflationdiscount rate excluding inflationi

'


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ijjii ++

If i, A(y=0)will be A*(1+i) after one year.Then, if j, A will be A*(1+i)*(1+j).

discount rate including inflationdiscount rate including inflation

annual inflation rateannual inflation rate

'i

j

t

n

t

tiAANPV )1(/

1

0 ++= =

t

n

t

tiAANPV )1(/ '

1

'

0 ++= =

AAtt

cash flow in year t expressed in terms of constant (base year)cash flow in year t expressed in terms of constant (base year) dollarsdollarsA'A'tt cash flow in year t expressed in terms of inflated (thencash flow in year t expressed in terms of inflated (then--current) dollarscurrent) dollars

jii +=' jii = '

When the inflation rate is small, these relations can be approximated by:j

or

Inflation ExampleInflation Example


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A company plans to invest $55,000 initially in a piece ofequipment which is expected to produce a uniform annual

constant dollars net revenue before tax of $15,000 over the nextfive years. The equipment has a salvage value of $5,000 inconstant dollars at the end of 5 years and the depreciation

allowance is computed on the basis of the straight linedepreciation method (i.e., $10,000 during next five years). Themarginal income tax rate for this company is 34%. The inflation

expectation is 5% per year, and the after-tax MARR specified bythe company is 8% excluding inflation. Determine whether theinvestment is worthwhile.

SolutionSolution


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With 5% inflation, the investment is no longer worthwhile because the valueof the depreciation tax reduction is not increased to match the inflation rate.

Verify that the use of MARR including inflation gives the same result (credit

by next Monday send me one-page excel sheet) Whether taking into account inflation or not, NPV could be different.

Depreciation costs are not inflated to current dollars in conformity with the practice recommended bythe U.S. Internal Revenue Service.

Impact of Inflation: Boston Central ArteryImpact of Inflation: Boston Central Artery

YearYear

tt

PricePriceIndexIndex

1982 $1982 $

PricePriceIndexIndex

2002 $2002 $

ProjectProjectExpensesExpenses

($ K)($ K)


(1982 $ k)(1982 $ k)


(2002 $ K)(2002 $ K)

19821982 100100 5353


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1982198219831983198419841985198519861986

198719871988198819891989199019901991199119921992

19931993199419941995199519961996199719971998199819991999

20002000200120012002200220032003200420042005200520062006SumSum

100100104104111111118118122122

123123130130134134140140144144146146

154154165165165165165165175175172172176176

181181183183189189195195202202208208215215

53535555595962626565

656569697171747476767777

8282888888888787939391919494

96969797100100103103107107110110114114

33,00033,000

82,00082,000131,000131,000164,000164,000214,000214,000197,000197,000246,000246,000

574,000574,000854,000854,000852,000852,000764,000764,000

1,206,0001,206,0001,470,0001,470,0001,523,0001,523,000

1,329,0001,329,0001,246,0001,246,0001,272,0001,272,0001,115,0001,115,000779,000779,000441,000441,000133,000133,000

14,625,000,00014,625,000,000

27,00027,000

67,00067,000101,000101,000122,000122,000153,000153,000137,000137,000169,000169,000

372,000372,000517,000517,000515,000515,000464,000464,000687,000687,000853,000853,000863,000863,000

735,000735,000682,000682,000674,000674,000572,000572,000386,000386,000212,000212,00062,00062,000

8,370,0008,370,000

51,00051,000

126,000126,000190,000190,000230,000230,000289,000289,000258,000258,000318,000318,000

703,000703,000975,000975,000973,000973,000877,000877,000

1,297,0001,297,0001,609,0001,609,0001,629,0001,629,000

1,387,0001,387,0001,288,0001,288,0001,272,0001,272,0001,079,0001,079,000729,000729,000399,000399,000117,000117,000

15,797,00015,797,000


OutlineOutline



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Project FinancingProject Financing Owner

Project Contractor Additional issues



What are we Assuming Here?


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Certaintyabout future cash flows

Main uncertainties: Financial concerns

Currency fluctuations (international projects)

Inflation/deflation Taxes variations

Project risks

That only quantifiable monetary benefits matter

Project Management PhaseProject Management Phase


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FEASIBILITYDESIGN

PLANNINGDEVELOPMENT CLOSEOUT OPERATIONS

Financing & Evaluation

Risk

Risk ManagementRisk Management


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Case StudyCase Study

microsoft project management - msp

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