1.040/1.401 Project Management › bitstream › handle › 1721.1 › 53709 › 1...1.040/1.401 Project Management Spring 2007 Project Financing & Evaluation Dr. SangHyun Lee Department

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 EngineeringMassachusetts Institute of Technology Massachusetts Institute of Technology

AS 2: Student PresentationAS 2: Student Presentation

10 minute presentation followed by 5 minute discussion10 minute presentation followed by 5 minute discussion1 or 2 presentations from Feb. 20 to Mar. 191 or 2 presentations from Feb. 20 to Mar. 19TopicsTopics

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 figuresMain managerial aspectsMain managerial aspectsProject management practicesProject management practicesProblems, strengths, weaknesses, risksProblems, strengths, weaknesses, risksYour learning Your 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?

PreliminariesPreliminaries

MIT Server access: to be announcedMIT Server access: to be announcedAS1 Survey due by tonight 12 pmAS1 Survey due by tonight 12 pmTP1 and AS2 are outTP1 and AS2 are outPictures will be taken before you leavePictures will be taken before you leaveWho we areWho we areDonDon’’t memorize course content. Understand it.t memorize course content. Understand it.

OutlineOutline

Session Objective & ContextSession Objective & Context

Project FinancingProject FinancingOwnerOwnerProjectProjectContractorContractorAdditional IssuesAdditional Issues

Financial EvaluationFinancial EvaluationTime value of moneyTime value of moneyPresent valuePresent valueRatesRatesInterest FormulasInterest FormulasNPV NPV IRR & payback periodIRR & payback period

Missing factorsMissing factors

Session ObjectiveSession Objective

The role of project financing The role of project financing

Mechanisms for project financingMechanisms for project financing

Measures of project profitability Measures of project profitability

Project Management PhaseProject Management Phase

FEASIBILITY DESIGNPLANNING

DEVELOPMENT CLOSEOUT OPERATIONS

Financing & Evaluation

Risk

Context: Feasibility PhasesContext: Feasibility Phases

Project ConceptProject ConceptLand Purchase & Sale ReviewLand Purchase & Sale ReviewEvaluation (scope, size, etc.)Evaluation (scope, size, etc.)Constraint surveyConstraint survey

Site constraintsSite constraintsCost modelsCost modelsSite infrastructural issuesSite infrastructural issuesPermit requirementsPermit requirements

Summary Report Summary Report Decision to proceedDecision to proceedRegulatory process (obtain permits, etc)Regulatory process (obtain permits, etc)Design PhaseDesign Phase

Lecture 2 Lecture 2 -- ReferencesReferences

More details on:More details on:Hendrickson PM for Construction onHendrickson PM for Construction on--line textbookline textbook

Chapter 7Chapter 7

OutlineOutline





Financing Financing –– Gross Gross 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 cashflowcontractor 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


($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





Design/Preliminary Construction


($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





• Early expenditure• Takes time to get revenue

Design/Preliminary Construction

Project FinancingProject Financing

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

Critical Role of FinancingCritical Role of Financing

Makes projects possibleMakes projects possibleHas major impact on Has major impact on

RiskinessRiskiness of constructionof constructionClaimsClaimsPrices offered by contractors (e.g., high bid price for late Prices offered by contractors (e.g., high bid price for late payment)payment)

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

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

PublicPublic

PrivatePrivate

““ProjectProject”” financingfinancing

OutlineOutline





Public FinancingPublic Financing

Sources of fundsSources of fundsGeneral purpose or specialGeneral purpose or special--purpose bondspurpose bondsTax revenuesTax revenuesCapital grants subsidiesCapital grants subsidiesInternational subsidized loansInternational subsidized loans

Social benefits important justificationSocial benefits important justificationBenefits 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 taxesPublic 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 partnershipsMARR (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

Private FinancingPrivate Financing

Major mechanismsMajor mechanismsEquity Equity

Invest corporate equity and retained earningsInvest corporate equity and retained earningsOffering 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 returnMay be too limited to support the full investmentMay be too limited to support the full investmentMay be strategically wrong (e.g., source of money, ownership)May be strategically wrong (e.g., source of money, ownership)

Debt Debt Borrow moneyBorrow moneyBondsBonds

Because higher costs and risks, require higher returnsBecause higher costs and risks, require higher returnsMARR varies per firm, often high (e.g. 20%)MARR varies per firm, often high (e.g. 20%)

Private Owners w/Collateral Facility Private Owners w/Collateral Facility Distinct Financing PeriodsDistinct Financing Periods

ShortShort--term construction loanterm construction loanBridge 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 mortgageSenior DebtSenior Debt

Typically facility is collateralTypically facility is collateralPays for operations and Construction financing debtsPays for operations and Construction financing debtsTypically much lower interestTypically much lower interest

Loans often negotiated as a packageLoans often negotiated as a package

timeconstructionw/o tangible

operationw/ tangible

OutlineOutline





““ProjectProject”” FinancingFinancing

Investment is paid back from the project profit rather than the Investment is paid back from the project profit rather than the general assets or creditworthiness of the project owners general 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 benefitInvestment in project through special purpose corporationsInvestment in project through special purpose corporations

Often joint venture between several partiesOften joint venture between several partiesNeed capacity for independent operationNeed capacity for independent operationBenefitsBenefits

Off balance sheet (liabilities do not belong to parent)Off balance sheet (liabilities do not belong to parent)Limits riskLimits riskExternal investors: reduced agency cost (direct investment in prExternal investors: reduced agency cost (direct investment in project)oject)

DrawbackDrawbackTensions among stakeholdersTensions among stakeholders

OutlineOutline





Contractor Financing IContractor Financing I

Payment schedule Payment schedule Break out payments into componentsBreak out payments into components

Advance paymentAdvance paymentPeriodic/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 ownerArchitect certifies progressArchitect certifies progressAgreed-upon payments

retention on payments (usually, about 10%)retention on payments (usually, about 10%)

Often must cover deficit during construction Often must cover deficit during construction Can be many months before payment receivedCan be many months before payment received

SS--curvecurve WorkWork

Man-hours

months

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

Cum

ulat

ive

cost

s$K

Daily costCum. costs

Expense & PaymentExpense & Payment

Contractor'sexpenses

Owner's paymentsAm

ount

(D

olla

rs)

Cum

ulat

ive

net c

ash

flow

(D

olla

rs)

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.

Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out forFrontFront--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

Rev

enue

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

Rev

enue

Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out forFrontFront--end loaded bids (discounting)end loaded bids (discounting)Unbalanced bidsUnbalanced bids

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

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

Help secure lowerHelp secure lower--priced loan for contractorpriced loan for contractorSometimes assist owners in funding!Sometimes assist owners in funding!

Big construction company, small municipalityBig construction company, small municipalityBOTBOT

Agreed upon in contractAgreed upon in contractOften structure proposed by ownerOften structure proposed by ownerShould be checked by owner (fairShould be checked by owner (fair--cost estimate)cost estimate)Often based on Often based on ““MasterformatMasterformat”” Cost Breakdown Structure Cost 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





Latent CreditLatent Credit

Many people forced to serve as lenders to owner due Many people forced to serve as lenders to owner due to delays in paymentsto delays in payments

DesignersDesignersContractors Contractors ConsultantsConsultantsCMCMSuppliersSuppliers

ImplicationsImplicationsGood in the shortGood in the short--termtermMajor concern on long run effectsMajor concern on long run effects

Role of TaxesRole of Taxes

Tax deductions forTax deductions forDepreciation Depreciation

the process of recognizing the using up of an asset through the process of recognizing the using up of an asset through wear and obsolescence and of subtracting capital expenses wear and obsolescence and of subtracting capital expenses from the revenues that the asset generates over time in from the revenues that the asset generates over time in computing taxable incomecomputing taxable income

OthersOthers

OutlineOutline


Project FinancingProject FinancingOwnerProjectContractorAdditional Issues



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 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


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

Sale Value=$8.5MSale Value=$8.5M


Profit?Profit?

Quantitative MethodQuantitative Method

ProfitabilityProfitabilityCreate value for the companyCreate value for the company

ProfitProfitTOTAL TOTAL

EQUIVAL. $EQUIVAL. $

REVENUESREVENUES 5,500,000.005,500,000.00COSTSCOSTS 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??

Quantitative MethodQuantitative Method

ProfitabilityProfitabilityCreate value for the companyCreate value for the company

Opportunity CostOpportunity CostTime 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 scenarioE.g. Project A E.g. Project A -- 8% profit, Project B 8% profit, Project B -- 10% profit 10% profit

Money Is Not EverythingMoney Is Not Everything

Social BenefitsSocial BenefitsHospitalHospitalSchoolSchoolHighway 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 warehouseNew cafeteriaNew cafeteria

OutlineOutline


Project FinancingProject FinancingOwnerProjectContractorAdditional issues



Basic CompoundingBasic Compounding

Suppose we invest $x in a bank offering interest rate iSuppose we invest $x in a bank offering interest rate iIf 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 years after 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…

Time Value of MoneyTime Value of Money

If we assume If we assume That money can always be invested in the bank (or some That 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 laterThat as rational actors, we never make an investment which That as rational actors, we never make an investment which we know to offer less money than we could get in the bankwe know to offer less money than we could get in the bank

Then Then Money in the Money in the presentpresent can be thought as of can be thought as of ““equal worthequal worth”” to to a larger amount of money in the futurea larger amount of money in the futureMoney in the Money in the future future can be thought of as having an equal can be thought of as having an equal worth to a lesser worth to a lesser ““present valuepresent value”” of moneyof money

Equivalence of Present ValuesEquivalence of Present Values

Given a source of reliable investments, we are Given a source of reliable investments, we are indifferent between any cash flows with the indifferent between any cash flows with the same present value same present value –– they have they have ““equal worthequal worth””

This indifferences arises because we can This indifferences arises because we can convert one to the other with no extra expenseconvert one to the other with no extra expense

OutlineOutline



Financial EvaluationFinancial EvaluationTime value of moneyPresent valuePresent valueRatesRatesInterest FormulasInterest FormulasNPV NPV IRR & payback periodIRR & payback period


Time Value of Money: RevisitTime Value of Money: Revisit

If we assume If we assume That money can always be invested in the bank (or some That 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 laterThat as rational actors, we never make an investment which That as rational actors, we never make an investment which we know to offer less money than we could get in the bankwe know to offer less money than we could get in the bank

Then Then Money in the Money in the presentpresent can be thought as of can be thought as of ““equal worthequal worth”” to to a larger amount of money in the futurea larger amount of money in the futureMoney in the Money in the future future can be thought of as having an equal can be thought of as having an equal worth to a lesser worth to a lesser ““present valuepresent value”” of moneyof money

Present Value (Revenue)Present Value (Revenue)

How is it that some future revenue How is it that some future revenue r r at time at time tt has a has a ““present present valuevalue””??Answer: Given that we are sure that we will be gaining revenue Answer: Given that we are sure that we will be gaining revenue rrat time at time tt, we can take and spend an immediate loan from the , we can take and spend an immediate loan from the bank bank

We choose size of this loan We choose size of this loan ll so that at time so 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 loan The loan ll is the present value of is the present value of r r ll = = PV(PV(rr))

Future to Present RevenueFuture to Present Revenue

x

t

-x

tPV(x)

0 I’ll 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 x at time tinto a (smaller) PV(x) now!

Present Value (Cost)Present Value (Cost)

How is it that some future cost How is it that some future cost c c at time at time tt has a has a ““present valuepresent value””??Answer: Given that we are Answer: Given that we are suresure that we will bear cost that we will bear cost cc at time at time tt, , we immediately deposit a sum of money we immediately deposit a sum of money xx into the bank yielding into the bank yielding a known returna known return

We choose size of deposit We choose size of deposit xx so that at time so that at time tt, the total size of the , the total size of the investment (including accrued interest) is investment (including accrued interest) is ccWe can then pay off We can then pay off cc at time at time tt by 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) xx is the is the present valuepresent value of of cc..

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 x at time tinto a (smaller) cost of PV(x) now!

PV(x)

-x

t0

If I know this cost is coming…

SummarySummary

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

v’0

PV

SummarySummary

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

v’0

PV

Given a reliable source offering annual return Given a reliable source offering annual return ii (i.e., interest) we (i.e., interest) we can shift without additional costs between cash can shift without additional costs between cash vv at time at time 00 and and v(1+i)v(1+i)tt at time at time tt

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

OutlineOutline



Financial EvaluationFinancial EvaluationTime value of moneyPresent valueRatesRatesInterest FormulasInterest FormulasNPV NPV IRR & payback periodIRR & payback period


RatesRates

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

RatesRates

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

Interest RateInterest RateContractual 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 Rate Discount 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 risks e 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

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 bondRate of inflation. It is measured by either by consumer priceindex or GDP deflatorRisk factor consisting of market risk, industry risk, firmspecific risk and project risk

Market RiskIndustry RiskFirm Specific RiskProject Risk

Figure by MIT OCW.

OutlineOutline



Financial EvaluationFinancial EvaluationTime value of moneyPresent valueRatesInterest FormulasInterest FormulasNPV NPV IRR & payback periodIRR & payback period


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

Single Payment Compound Amount Factor (F=Single Payment Compound Amount Factor (F=PP××FactorFactor))

Factor that will make your present value future value in single Factor 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 …

Interest Formulas: PaymentInterest Formulas: Payment

Single Payment Present Value Factor (P=Single Payment Present Value Factor (P=FF××FactorFactor))

Factor that will make your future value present value in single Factor that will make your future value present value in single paymentpayment

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

P

n0

F

1 … n-1

Interest Formulas: PaymentInterest Formulas: Payment-- ExampleExample

If you wish to have $100,000 at the end of five years If you wish to have $100,000 at the end of five years in an account that pays 12 percent annually, how in an account that pays 12 percent annually, how much would you need to deposit now? much would you need to deposit now?



(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



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

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

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

Interest Formulas: SeriesInterest Formulas: Series

Uniform Series Compound Amount Factor (F=Uniform Series Compound Amount Factor (F=AA××FactorFactor))

Factor that will make your annuity value future value in series Factor 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 1F

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

2 …




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

A A A A

n0 1F

F = A

2 …




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

A A A A

n0 1F

F = A+A(1+i)

2 …




(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--1 1

2 …


Uniform Series Sinking Fund Factor (A=Uniform Series Sinking Fund Factor (A=FF××FactorFactor))

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

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

A A A A

n0 1

F

2 …


A A A A

n0 1P

Uniform Series Present Value Factor (P=Uniform Series Present Value Factor (P=AA××FactorFactor))

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 …


A A A A

n0 1




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

2 …


A A A A

n0 1




P = A/(1 + (1 + ii ) + A/(1 + ) + A/(1 + ii ))2 2

2 …


A A A A

n0 1




P = A/(1 + (1 + ii ) + A/(1 + ) + A/(1 + ii ))2 2 + … + A/(1 + 1 + ii ))nn

Verify it!

2 …


Uniform Series Capital Recovery Factor (A=Uniform Series Capital Recovery Factor (A=PP××FactorFactor))

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 ))nn –– 1] = 1 / (P/A, 1] = 1 / (P/A, ii, n), n)

Verify it!

A A A A

n0 1

P

2 …

Interest Formulas: SeriesInterest Formulas: Series-- ExampleExample

A ranch is offered for sale in Mexico with a 15 year mortgage A ranch is offered for sale in Mexico with a 15 year mortgage rate 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 ranch Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required?is 5 million pesos. What yearly payment is required?



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

P = P = 5,000,000 5,000,000 –– 1,000,000 = 4,000,0001,000,000 = 4,000,000

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



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

P = P = 5,000,000 5,000,000 –– 1,000,000 = 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

$ 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?

A A -- Annual Equivalent Annual Equivalent

P P -- Present Equivalent Present Equivalent


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.


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



Financial EvaluationFinancial EvaluationTime value of moneyPresent valueRateInterest FormulasNPVNPVIRR & payback periodIRR & payback period


Net Present ValueNet Present Value

Suppose we had a collection (or stream, flow) of costs Suppose 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 present The 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 ValueTotal 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

Accept a project which has 0 or positive NPVAccept a project which has 0 or positive NPVAlternatively,Alternatively,

Use NPV to choose the best among a set of Use 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 precludes es 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 Example Project Evaluation Example Revisit: Which one is better?Revisit: Which one is better?

Project AProject A



Sale Value = $4MSale Value = $4M


Profit?Profit?

Project BProject B



Sale Value = $8.5MSale Value = $8.5M


Profit?Profit?

Drawing out the examplesDrawing out the examples

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

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

The cash flow profiles of four independent projects are shown The cash flow profiles of four independent projects are shown below. Using a MARR of 20%, determine the acceptability of below. Using a MARR of 20%, determine the acceptability of each of the projects on the basis of the net present value each of the projects on the basis of the net present value criterion for accepting independent projects. criterion for accepting independent projects.

[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

SolutionSolution

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 = 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

[NPV1] = 17.4[NPV2] = 8.4[NPV3] = 0.4[NPV4] = -1.6


Discount Rate in NPVDiscount Rate in NPV

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 the ate of the ““reliable reliable 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, projects gh, 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 accept ill 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

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

2 pieces of equipment: one needs a human operator (initial cost 2 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 the equipment 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 of There is a critical value of ii that 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 early ulation 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 was ould 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 made halt 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 less t while requiring less

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

OutlineOutline



Financial EvaluationFinancial EvaluationTime value of moneyPresent valueRateInterest FormulasNPVIRR & payback periodIRR & payback period


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

Defined as the rate of return that makes the NPV of the project Defined 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 project’’s rate of return is equal to or higher s 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

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 $20,0005 years$4,000

$10,000$4,400

LifeSalvage ValueAnnual ReceiptsAnnual Disbursements

Image by MIT OCW.

Relationship between NPV & IRRRelationship between NPV & IRR

2520151050

-1,000

1,000(15, 730)

(20, -1,196)

IRR

Interest Rate, i (%)

Net

Pre

sent

Val

ue ($

)

(10, 3,713)

2,000

3,000

4,000

Image by MIT OCW.

IRR Investment RuleIRR Investment Rule

““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 < Reject

r = IRR, r = MARR*-

Oftentimes, IRR and NPV give the same decision/ranking among Oftentimes, IRR and NPV give the same decision/ranking among projects.projects.IRR only looks at IRR only looks at raterate of gain of gain –– not not sizesize of gainof gainIRR 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 reinvestIRR may not be uniqueIRR may not be unique

IRR vs. NPVIRR vs. NPV

NPV

Discount Rate

Oftentimes, IRR and NPV give the same decision/ranking among Oftentimes, IRR and NPV give the same decision/ranking among projects.projects.IRR only looks at IRR only looks at raterate of gain of gain –– not not sizesize of gainof gainIRR 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 reinvestIRR 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 ensures Trust the NPV: It is the only criterion that ensures wealth maximization. It measures how much richer one will wealth maximization. It measures how much richer one will become by undertaking the investment opportunity.become by undertaking the investment opportunity.

IRR vs. NPVIRR vs. NPV

Payback PeriodPayback Period

Payback period (Payback period (““Time to returnTime to return””))Minimal length of time over which benefits repay costs Minimal length of time over which benefits repay costs Typically only used as secondary assessmentTypically only used as secondary assessment

Payback PeriodPayback Period

Payback period (Payback period (““Time to returnTime to return””))Minimal length of time over which benefits repay costs Minimal length of time over which benefits repay costs Typically only used as secondary assessmentTypically only used as secondary assessmentImportant for selection when the risk is extremely highImportant for selection when the risk is extremely highDrawbacksDrawbacks

Ignores what happens after payback periodIgnores what happens after payback periodDoes not take into account discountingDoes not take into account discounting

Comparing ProjectsComparing Projects

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

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

Comparing ProjectsComparing Projects

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

BenefitBenefit--Cost ratio (benefits/costs)Cost ratio (benefits/costs)Discounting still generally appliedDiscounting still generally appliedAccept if >1 (benefits > costs)Accept if >1 (benefits > costs)Common for public projectsCommon for public projectsDoes not consider the absolute Does not consider the absolute sizesize of the benefitsof the benefits

CostCost--effectivenesseffectivenessLooking at nonLooking at non--economic factorseconomic factorsDiscounting still often applied for nonDiscounting still often applied for non--economiceconomic

$/Life saved$/Life saved$/Life quality$/Life quality

Inflation & DeflationInflation & Deflation

Inflation means that the prices of goods and services increase Inflation 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 and effects 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 haveless 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 ++='

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 excluding inflationdiscount rate excluding inflation→→ discount rate including inflationdiscount rate including inflation→→ annual inflation rateannual inflation rate

i'ij


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 excluding inflationdiscount rate excluding inflation→→ discount rate including inflationdiscount rate including inflation→→ annual inflation rateannual inflation rate

i'ij

tn

tt iAANPV )1(/

10 ++= ∑

=

tn

tt iAANPV )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

A company plans to invest $55,000 initially in a piece of equipment 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 in constant dollars at the end of 5 years and the depreciation allowance is computed on the basis of the straight line depreciation method (i.e., $10,000 during next five years). The marginal income tax rate for this company is 34%. The inflation expectation is 5% per year, and the after-tax MARR specified by the company is 8% excluding inflation. Determine whether the investment is worthwhile.

SolutionSolution

With 5% inflation, the investment is no longer worthwhile because the value of 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 by the U.S. Internal Revenue Service.

Impact of Inflation: Boston Central Artery Impact of Inflation: Boston Central Artery YearYear

ttPricePrice

IndexIndex1982 $1982 $

Price Price IndexIndex2002 $2002 $

ProjectProjectExpensesExpenses

($ K)($ K)

Project Project ExpensesExpenses

(1982 $ k)(1982 $ k)

Project Project ExpensesExpenses(2002 $ K)(2002 $ K)

19821982198319831984198419851985198619861987198719881988198919891990199019911991199219921993199319941994199519951996199619971997199819981999199920002000200120012002 2002 20032003200420042005200520062006SumSum

100100104104111111118118122122123123130130134134140140144144146146154154165165165165165165175175172172176176181181183183189 189 195195202202208208215215

53535555595962626565656569697171747476767777828288888888878793939191949496969797100 100 103103107107110110114114

33,00033,00082,00082,000131,000131,000164,000164,000214,000214,000197,000197,000246,000246,000574,000574,000854,000854,000852,000852,000764,000764,000

1,206,0001,206,0001,470,0001,470,0001,523,0001,523,0001,329,0001,329,0001,246,0001,246,0001,272,000 1,272,000 1,115,0001,115,000779,000779,000441,000441,000133,000133,000

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

27,00027,00067,00067,000101,000101,000122,000122,000153,000153,000137,000137,000169,000169,000372,000372,000517,000517,000515,000515,000464,000464,000687,000687,000853,000853,000863,000863,000735,000735,000682,000682,000674,000 674,000 572,000572,000386,000386,000212,000212,00062,00062,000

8,370,0008,370,000

51,00051,000126,000126,000190,000190,000230,000230,000289,000289,000258,000258,000318,000318,000703,000703,000975,000975,000973,000973,000877,000877,000

1,297,0001,297,0001,609,0001,609,0001,629,0001,629,0001,387,0001,387,0001,288,0001,288,0001,272,000 1,272,000 1,079,0001,079,000729,000729,000399,000399,000117,000117,000

15,797,00015,797,000


OutlineOutline





Certainty about future cash flowsMain uncertainties:

Financial concernsCurrency fluctuations (international projects)Inflation/deflationTaxes variations

Project risks

What are we Assuming Here?

That only quantifiable monetary benefits matter

Project Management PhaseProject Management Phase

FEASIBILITY DESIGNPLANNING

DEVELOPMENT CLOSEOUT OPERATIONS

Financing & Evaluation

Risk

Risk ManagementRisk Management

Case Study Case Study

Documents

1.040/1.401 Project Management › bitstream › handle › 1721.1 › 53709 › 1...1.040/1.401 Project Management Spring 2007 Project Financing & Evaluation Dr. SangHyun Lee Department