Lecture 2 Project Financing & Evaluation

7/28/2019 Lecture 2 Project Financing & Evaluation

1/116

1.040/1.4011.040/1.401

Project ManagementProject ManagementSpring 2007Spring 2007

Project Financing & EvaluationProject Financing & Evaluation

Dr. SangHyun Lee

[email protected]@mit.edu

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental Engineering

Massachusetts Institute of TechnologyMassachusetts Institute of Technology


2/116

PreliminariesPreliminaries

STELLAR access: to be announcedSTELLAR 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


3/116

AS 2: StudentAS 2: Student

PresentationPresentation 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 haveYour past project experience (strongly recommended if you haveany)any) 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 Reality,Emerging construction technologies (e.g., 4D CAD, Virtual Reality,

Sensing, )Sensing, )

Volunteers for next week?Volunteers for next week?


4/116


STELLAR access: to be announcedSTELLAR 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 Dont memorize course content.Dont memorize course content.

Understand it.Understand it.


5/116

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


6/116

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


7/116

Project Management PhaseProject Management Phase

FEASIBILITY DESIGNPLANNING

CLOSEOUTDEVELOPMENT OPERATIONS

Financing &Evaluation

Risk


8/116

Context: FeasibilityContext: Feasibility

PhasesPhases 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


9/116

Lecture 2 - ReferencesLecture 2 - References

More details on:More details on: Hendrickson PM for Construction on-lineHendrickson PM for Construction on-linetextbooktextbook Chapter 7Chapter 7


10/116

OutlineOutline






11/116

Financing GrossFinancing 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 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 $0

contractor 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

wner investment = contractor revenue


12/116


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






Design/Preliminary Construction


13/116


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






Early expenditure Takes time to get revenu

Design/Preliminary Construction


14/116

Project FinancingProject Financing

Aims to bridge this gap in the mostAims to bridge this gap in the most

beneficial way!beneficial way!


15/116

Critical Role of FinancingCritical Role of Financing

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

Riskiness of constructionRiskiness of construction ClaimsClaims Prices offered by contractors (e.g., high bid pricePrices offered by contractors (e.g., high bid price

for late payment)for late payment)

Difficulty of Financing is a major driverDifficulty of Financing is a major drivertowards alternate delivery methods (e.g.,towards alternate delivery methods (e.g.,Build-Operate-Transfer)Build-Operate-Transfer)


16/116

How Does Owner Finance aHow Does Owner Finance a

Project?Project?

PublicPublic PrivatePrivate

Project financingProject financing


17/116

OutlineOutline






18/116

Public FinancingPublic Financing

Sources of fundsSources of funds General purpose or special-purpose bondsGeneral purpose or special-purpose 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,Benefits to region, quality of life, unemployment relief,

etc.etc.

Important consideration: exemption from taxesImportant consideration: exemption from taxes Public owners face restrictions (e.g. bondingPublic owners face restrictions (e.g. bonding

caps)caps) Major motivation for public/private partnershipsMajor motivation for public/private partnerships

MARR (Minimum Attractive Rate of Return) muchMARR (Minimum Attractive Rate of Return) muchlower (e.g. 8-10%), often standardizedlower (e.g. 8-10%), often standardized


19/116

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 ofMust entice investors with sufficiently high rate of

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

ownership)ownership) DebtDebt

Borrow moneyBorrow money BondsBonds

Because higher costs and risks, requireBecause higher costs and risks, require

higher returnshigher returns

P i t O /C ll t lP i t O /C ll t l


20/116

Private Owners w/CollateralPrivate Owners w/Collateral

Facility Distinct FinancingFacility Distinct Financing

PeriodsPeriods Short-term construction loanShort-term 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)

Long-term mortgageLong-term 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

timeconstruction

w/o tangible

operation

w/ tangible


21/116

OutlineOutline






22/116

Project FinancingProject Financing

Investment is paid back from the project profitInvestment is paid back from the project profitrather than the general assets or creditworthinessrather than the general assets or creditworthinessof the project ownersof 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 purposeInvestment in project through special purposecorporationscorporations 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 (directExternal investors: reduced agency cost (direct

investment in project)investment in project)


23/116

OutlineOutline






24/116

Contractor Financing IContractor Financing I

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

Advance paymentAdvance payment

Periodic/monthly progress payment (itemizedPeriodic/monthly progress payment (itemizedbreakdown structure)breakdown structure)

Milestone paymentsMilestone payments

Often some compromise between contractorOften some compromise between contractor

and ownerand 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


25/116

S-curve WorkS-curve Work

Man-hours

months


26/116

S-curve CostS-curve Cost

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


27/116

Expense & PaymentExpense & Payment


28/116

Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out for Front-end loaded bids (discounting)Front-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

Revenue

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

Reven

ue


29/116

Contractor Financing IIContractor Financing II

Owner keeps an eye out forOwner keeps an eye out for Front-end loaded bids (discounting)Front-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 lower-priced loan for contractorHelp secure lower-priced loan for contractor

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


30/116

Agreed upon in contractAgreed upon in contract

Often structure proposed by ownerOften structure proposed by owner Should be checked by owner (fair-costShould be checked by owner (fair-cost

estimate)estimate)

Often based on Masterformat CostOften based on Masterformat Cost

Breakdown Structure (Owner standard CBS)Breakdown Structure (Owner standard CBS)

Certified by third partyCertified by third party

(Architect/engineer)(Architect/engineer)

Contractor Financing IIIContractor Financing III


31/116

OutlineOutline






32/116

Latent CreditLatent Credit

Many people forced to serve as lenders toMany people forced to serve as lenders to

owner due to delays in paymentsowner due to delays in payments DesignersDesigners

ContractorsContractors ConsultantsConsultants

CMCM

SuppliersSuppliers

ImplicationsImplications Good in the short-termGood in the short-term

Major concern on long run effectsMajor concern on long run effects


33/116

Role of TaxesRole of Taxes

Tax deductions forTax deductions for

Depreciation -Depreciation - LinkLink the process of recognizing the using up of anthe process of recognizing the using up of an

asset through wear and obsolescence and ofasset through wear and obsolescence and of

subtracting capital expenses from thesubtracting capital expenses from the

revenues that the asset generates over timerevenues that the asset generates over timein computing taxable incomein computing taxable income

OthersOthers
http://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/Depreciation%20Example.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/Depreciation%20Example.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/Depreciation%20Example.xls


34/116

OutlineOutline


Project FinancingProject Financing Owner Project Contractor Additional Issues




35/116

Develop or Not DevelopDevelop or Not Develop

Is any individual project worthwhile?Is any individual project worthwhile?

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

How does each project rank compared toHow does each project rank compared tothe others on the list?the others on the list?

Project EvaluationProject Evaluation


36/116

Project EvaluationProject EvaluationExample:Example:

Project AProject A

Construction=3Construction=3

yearsyears

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

Sale Value=$4MSale Value=$4M Total Cost?Total Cost?

Profit?Profit?

Project BProject B


yearsyears

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

Sale Value=$8.5MSale Value=$8.5M Total Cost?Total Cost?

Profit?Profit?


37/116

Quantitative MethodQuantitative Method

ProfitabilityProfitability

Create value for the companyCreate value for the company


38/116


39/116

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 best-case scenarioInvestment relative to best-case scenario E.g. Project A - 8% profit, Project B - 10% profitE.g. Project A - 8% profit, Project B - 10% profit


40/116

Money Is NotMoney Is NotEverythingEverything

Social BenefitsSocial Benefits

HospitalHospital

SchoolSchool

Highway built into a remote villageHighway built into a remote village

Intangible Benefits (E.g, operating andIntangible Benefits (E.g, operating and

competitive necessity)competitive necessity) New warehouseNew warehouse

New cafeteriaNew cafeteria

O liO tli


41/116

OutlineOutline


Project FinancingProject Financing Owner Project Contractor Additional issues

Financial EvaluationFinancial EvaluationTime value of moneyTime value of money Present valuePresent value

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



42/116

Basic CompoundingBasic Compounding

Suppose we invest $x in a bank offeringSuppose we invest $x in a bank offering

interest rate iinterest rate i

If interest is compounded annually, assetIf interest is compounded annually, assetwill be worthwill 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


43/116

Time Value of MoneyTime Value of Money

If we assumeIf we assume That money can always be invested in theThat money can always be invested in the

bank (or some other reliable source) now tobank (or some other reliable source) now togain a return with interest latergain a return with interest later That as rational actors, we never make anThat as rational actors, we never make an

investment which we know to offer less moneyinvestment which we know to offer less moneythan we could get in the bankthan we could get in the bank

ThenThen Money in theMoney in the presentpresent can be thought as ofcan be thought as ofequal worth to a larger amount of money inequal worth to a larger amount of money inthe futurethe future

Money in theMoney in the futurefuture can be thought of ascan be thought of as

having an equal worth to a lesser presenthaving an equal worth to a lesser presentvalue of monevalue of mone

E i l f PE i l f P t


44/116

Equivalence of PresentEquivalence of Present

ValuesValues

Given a source of reliableGiven a source of reliable

investments, we are indifferentinvestments, we are indifferentbetween any cash flows with thebetween any cash flows with the

same present value they havesame present value they have

equal worthequal worth

This indifferences arises because weThis indifferences arises because we

can convert one to the other with nocan convert one to the other with no


45/116


STELLAR access:STELLAR access:

http://stellar.mit.edu/S/course/1/sp07/1.040/http://stellar.mit.edu/S/course/1/sp07/1.040/

Next Tuesday Recitation: Skyscraper PartNext Tuesday Recitation: Skyscraper Part

II

Please set up an appointment to discussPlease set up an appointment to discuss

your AS2 if you choose emergingyour AS2 if you choose emerging

technologies (MF preferred)technologies (MF preferred)

Office: 1-174Office: 1-174

TA (50%) for our classTA (50%) for our class

O tliO tli
http://stellar.mit.edu/S/course/1/sp07/1.040/http://stellar.mit.edu/S/course/1/sp07/1.040/http://stellar.mit.edu/S/course/1/sp07/1.040/


46/116

OutlineOutline


Project FinancingProject Financing Owner Project Contractor Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present valuePresent value



i l fTi V l f M


47/116

Time Value of Money:Time Value of Money:

RevisitRevisit

If we assumeIf we assume That money can always be invested in theThat money can always be invested in the

bank (or some other reliable source) now tobank (or some other reliable source) now togain a return with interest latergain a return with interest later That as rational actors, we never make anThat as rational actors, we never make an

investment which we know to offer less moneyinvestment which we know to offer less moneythan we could get in the bankthan we could get in the bank

ThenThen Money in theMoney in the presentpresent can be thought as ofcan be thought as ofequal worth to a larger amount of money inequal worth to a larger amount of money inthe futurethe future

Money in theMoney in the futurefuture can be thought of ascan be thought of as

having an equal worth to a lesser presenthaving an equal worth to a lesser presentvalue of monevalue of mone


48/116

Present Value (Revenue)Present Value (Revenue)

How is it that some future revenueHow is it that some future revenue rrat timeat time tthashas

a present value?a present value?

Answer: Given that we are sure that we will beAnswer: Given that we are sure that we will begaining revenuegaining revenue rrat timeat time tt, we can take and, we can take and

spend an immediate loan from the bankspend an immediate loan from the bank We choose size of this loanWe choose size of this loan ll so that at timeso that at time tt, the total, the total

size of the loan (including accrued interest) issize of the loan (including accrued interest) is rr

The loanThe loan ll is the present value ofis the present value ofrr ll = PV(= PV(rr))

F t t P tF t t P t


49/116

Future to PresentFuture to Present

RevenueRevenue

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 x at timinto a (smaller) PV(x) now!


50/116

Present Value (Cost)Present Value (Cost)

How is it that some future costHow is it that some future cost cc at timeat time tthas ahas a

present value?present value?

Answer: Given that we areAnswer: Given that we are suresure that we will bearthat we will bearcostcost cc at timeat time tt, we immediately deposit a sum of, we immediately deposit a sum of

moneymoneyxxinto the bank yielding a known returninto the bank yielding a known return We choose size of depositWe choose size of depositxxso that at timeso that at time tt, the total, the total

size of the investment (including accrued interest) issize of the investment (including accrued interest) is

cc

We can then pay offWe can then pay offcc at timeat time ttby retrieving this moneyby retrieving this money

from the bankfrom the bank

The size of the deposit (immediate cost)The size of the deposit (immediate cost)xxis theis the

present valuepresent value ofofcc..


51/116

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

PV(x)

-x

t0

If I know this cost is coming


52/116


53/116

SummarySummary

Because we can flexibly switch from one suchBecause we can flexibly switch from one such

value to another without cost, we can view thesevalue to another without cost, we can view these

values as equivalentvalues as equivalent

FV

tv

v0

PV

Given a reliable source offering annual returnGiven a reliable source offering annual return ii(i.e., interest) we can shift without additional(i.e., interest) we can shift without additional

costs between cashcosts between cash vvat timeat time 00 andand v(1+i)v(1+i)ttatat

timetime tt

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

OutlineOutline


54/116

OutlineOutline


Project FinancingProject Financing Owner Project Contractor

Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present value




55/116

RatesRates

Difference between PV (Difference between PV (vv) and FV () and FV ( ==v(1+i)v(1+i)tt)) dependsdepends

onon ii andand tt..


56/116

RatesRates

Difference between PV (Difference between PV (vv) and FV () and FV ( ==v(1+i)v(1+i)tt))

depends ondepends on ii andand tt..

Interest RateInterest Rate Contractual arrangement between a borrower and aContractual arrangement between a borrower and a

lenderlender

Discount Rate (real change in value to a person orDiscount Rate (real change in value to a person or

group)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 acce ted b the marketMinimum discount rate acce ted b the market


57/116

Choice of Discount RateChoice of Discount Rate

r = rf + ri + rr

Where:

r is the discount rate

rf

the risk free interest rate. Normally government bond

ri Rate of inflation. It is measured by either by consumer price

index or GDP deflator.

rr Risk factor consisting of market risk, industry risk, firm

specific risk and project riskMarket Risk

rr = Industry RiskFirm specific Risk

Project Risk

GDP = Gross Domestic Product

OutlineOutline


58/116

OutlineOutline



Additional issues

Financial EvaluationFinancial Evaluation Time value of money Present value

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



59/116

Interest FormulasInterest Formulas

ii = Effective interest rate per interest period (discount= Effective interest rate per interest period (discountrate or MARR)rate or 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) atA = Annuity (i.e., a series of payments of set size) at

end-of-periodend-of-period

Interest Formulas:Interest Formulas:


60/116


PaymentPayment

Single Payment Compound Amount FactorSingle Payment Compound Amount Factor(F=PFactor)(F=PFactor)

Factor that will make your present value future value in singleFactor that will make your present value future value in singlepaymentpayment

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

P

n0

F

1 2



61/116


PaymentPayment

Single Payment Present Value Factor (P=FFactor)Single Payment Present Value Factor (P=FFactor)

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



62/116

Interest Formulas:Interest Formulas:PaymentPayment

- Example- Example If you wish to have $100,000 at the endIf you wish to have $100,000 at the end

of five years in an account that pays 12of five years in an account that pays 12

percent annually, how much would youpercent annually, how much would youneed to deposit now?need to deposit now?



63/116





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

P=?

n0

F=$100,000



64/116





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

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

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



65/116


SeriesSeries

Uniform Series Compound Amount FactorUniform Series Compound Amount Factor(F=AFactor)(F=AFactor)

Factor that will make your annuity value future value in serieFactor that will make your annuity value future value in serie

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



66/116


SeriesSeries




A A A A

n0 1

F

F = A

2



67/116


SeriesSeries




A A A A

n0 1

F

F = A+A(1+i)

2



68/116


SeriesSeries




A A A A

n0 1

F = A + A(1+i) + + A(1 +1 +

ii ))n-1n-1

2



69/116

Interest Formulas:e es o u as

SeriesSeries

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

Factor that will make your future value annuity value in serieFactor that will make your future value annuity value in seriepaymentpayment

(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


70/116

Interest Formulas: SeriesInterest Formulas: Series

A A A A

n0 1

P

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

Factor that will make your annuity value present value inFactor that will make your annuity value present value inseries paymentseries payment

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

2


71/116


A A A A

n0 1




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

2


72/116


A A A A

n0 1




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

2


73/116


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


74/116


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

Factor that will make your present value annuity value in seriesFactor that will make your present value annuity value in seriespaymentpayment

(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



75/116

SeriesSeries

- Example- Example A ranch is offered for sale in Mexico with a 15A ranch is offered for sale in Mexico with a 15

year mortgage rate at 40% compoundedyear mortgage rate at 40% compoundedannually, and 20% down payment. Annualannually, and 20% down payment. Annualpayments are to be made. The first cost of thepayments are to be made. The first cost of theranch is 5 million pesos. What yearly paymentranch is 5 million pesos. What yearly paymentis required?is required?



76/116

SeriesSeries



Down Payment = 5,000,000 * 0.2 =Down Payment = 5,000,000 * 0.2 =1,000,0001,000,000

P = 5,000,000 1,000,000 = 4,000,000P = 5,000,000 1,000,000 = 4,000,000

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



77/116

SeriesSeries



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

P = 5,000,000 1,000,000 = 4,000,000P = 5,000,000 1,000,000 = 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


78/116


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

$ 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 - Annual EquivalentA - Annual Equivalent

P - Present EquivalentP - Present Equivalent

E i t E lEquipment Example


79/116




80/116


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

0.15, 5)0.15, 5)

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

= -5,373= -5,373

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

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

= -18,011= -18,011

OutlineOutline


81/116

OutlineOutline



Additional issues Financial EvaluationFinancial Evaluation

Time value of money Present value

Rate Interest Formulas NPVNPV IRR & payback periodIRR & payback period


lN t P t V l


82/116

Net Present ValueNet Present Value

Suppose we had a collection (or stream,Suppose we had a collection (or stream,

flow) of costs and revenues in the futureflow) of costs and revenues in the future The net present value (NPV) is the sum ofThe net present value (NPV) is the sum of

the present values for all of these coststhe present values for all of these costs

and revenuesand revenues Treat revenues as positive and costs asTreat revenues as positive and costs as

negativenegative

Calculation of NetCalculation of Net


83/116

Calculation of NetCalculation of Net

Present ValuePresent ValueTotal Revenue (R)

(+)Various Costs (C)

(-)

Calculate GrossReturn

Calculate NetReturn

PV of Net Return

NPV of the Project

Tax (-)

Discount Rate (r)

Initial Invest (-I)



84/116


Decision RuleDecision Rule

Accept a project which has 0 orAccept a project which has 0 or

positive NPVpositive NPV

Alternatively,Alternatively, Use NPV to choose the best among aUse NPV to choose the best among a

set of (mutually exclusive) alternativeset of (mutually exclusive) alternative

projectsprojects

> Accept the project

NPV = 0 Indifferent to the project

< Reject the project

Project EvaluationPro ect Eva uat onExample Revisit: WhichExample Revisit: Which


85/116

Example Revisit: WhichExample Revisit: Whichone is better?one is better?

Project AProject A


yearsyears


Sale Value = $4MSale Value = $4M

Total Cost?Total Cost?

Profit?Profit?

Project BProject B


yearsyears


Sale Value = $8.5MSale Value = $8.5M

Total Cost?Total Cost?

Profit?Profit?

Drawing out theDrawing out the


86/116

examplesexamples

Project AProject A

Project BProject B

$1M

$4M

$1M

1

$8.5M

6

$1M $1M $1M

$1M

$1M$1M

Assume 10% discount rate

Link

0 32

$1M

0 1

Or Using InterestOr Using Interest
http://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/NPV%20example-lecture%202.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/NPV%20example-lecture%202.xls


87/116

FormulasFormulas

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

6)6)

Assume 10% discount rate

Four IndependentFour Independent


88/116

Four Independentou depe de

ProjectsProjects

The cash flow profiles of four independentThe cash flow profiles of four independent

projects are shown below. Using a MARR of 20%,projects are shown below. Using a MARR of 20%,

determine the acceptability of each of thedetermine the acceptability of each of theprojects on the basis of the net present valueprojects on the basis of the net present value

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

SolutionSolution


89/116

[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 CashFlow

SolutionSolution


90/116

[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


91/116

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

Source: Hendrickson and Au, 1989/2003

Di t R t i NPVDiscount Rate in NPV


92/116

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 interestIn the absence of risk or inflation, this is just the interest

rate of the reliable source (opportunity cost)rate of the reliable source (opportunity cost) Correct selection of the discount rate is fundamental. If tooCorrect selection of the discount rate is fundamental. If too

high, projects that could be profitable can be rejected. If toohigh, projects that could be profitable can be rejected. If too

low, the firm will accept projects that are too risky withoutlow, the firm will accept projects that are too risky without

proper compensation.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:Selection of Discount Rate:


93/116

ExampleExample

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 labor); the second is fully automated$10,000, annual $4,200 for labor); the second is fully automated

(initial cost $18,000, annual #3,000 for power). n=10years.(initial cost $18,000, annual #3,000 for power). 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 $1,200 annual savings? (discount rate: 5 orequipment worthy the $1,200 annual savings? (discount rate: 5 or

10%)10%)

Link

Selection of Discount Rate:Selection of Discount Rate:
http://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/NPV%20selection%20of%20discount%20rate.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/NPV%20selection%20of%20discount%20rate.xls


94/116

ExampleExample

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 labor); the second is fully automated$10,000, annual $4,200 for labor); the second is fully automated

(initial cost $18,000, annual #3,000 for power). n=10years.(initial cost $18,000, annual #3,000 for power). 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 $1,200 annual savings? (discount rate: 5 orequipment worthy the $1,200 annual savings? (discount rate: 5 or

10%)10%)

There is a critical value ofThere is a critical value ofii that changes the equipment choicethat changes the equipment choice

(approximately 8.15%)(approximately 8.15%)

Example: The US Federal Highway Administration promulgated aExample: The US Federal Highway Administration promulgated a

regulation in the early 1970s that the discount rate for all federallyregulation in the early 1970s that the discount rate for all federally

funded highways would be zero. This was widely interpreted as afunded highways would be zero. This was widely interpreted as a

victory for the cement industry over asphalt industry. Roads made ofvictory for the cement industry over asphalt industry. Roads made of

OutlineOutline


95/116




Time value of money Present value

Rate Interest Formulas NPV IRR & payback periodIRR & payback period


Internal Rate of ReturnInternal Rate of Return


96/116

(IRR)(IRR)

Defined as the rate of return that makes the NPVDefined as the rate of return that makes the NPVof the project equal to zeroof the project equal to zero

To see whether the projects rate of return isTo see whether the projects rate of return is

equal to or higher than the rate of the firm toequal to or higher than the rate of the firm to

expect to get from the projectexpect to get from the project

IRR Calculation ExampleIRR Calculation Example


97/116

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

LinkLink

Relationship between NPVRelationship between NPV& IRR& IRR
http://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/IRR%20example.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/IRR%20example.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/IRR%20example.xls


98/116

& IRR& IRR

IRRIRR

IRR Investment RuleIRR Investment Rule


99/116

IRR Investment RuleIRR Investment Rule

Accept a project with IRR larger thanAccept a project with IRR larger than

MARRMARR

Alternatively,Alternatively,

Maximize IRR across mutually exclusiveMaximize IRR across mutually exclusive

> Accept

r- =

r*

Indifferent

< Reject

r = IRR, r = MARR- *

IRR vs NPVIRR vs NPV


100/116

Oftentimes, IRR and NPV give the sameOftentimes, IRR and NPV give the samedecision/ranking among projects.decision/ranking among projects.

IRR only looks atIRR only looks at raterate of gain notof gain not sizesize of gainof gain IRR does not require you to assume (or compute) aIRR does not require you to assume (or compute) a

discount rate.discount rate. IRR ignores capacity to reinvestIRR ignores capacity to reinvest IRR may not be uniqueIRR may not be unique

IRR vs. NPVIRR vs. NPV

NPV

Discount Rate

Link

IRR vs NPVIRR vs NPV
http://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/Multiple%20IRRs.xlshttp://c/Documents%20and%20Settings/labi/My%20Documents/MIT-1.401/2007/Lecture/2.%20Financing&Evaluation/Multiple%20IRRs.xls


101/116

Oftentimes, IRR and NPV give the sameOftentimes, IRR and NPV give the samedecision/ranking among projects.decision/ranking among projects.

IRR only looks atIRR only looks at raterate of gain notof gain not sizesize of gainof gain IRR does not require you to assume (or compute) aIRR does not require you to assume (or compute) a

discount rate.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 thatTrust the NPV: It is the only criterion thatensures wealth maximization. It measures howensures wealth maximization. It measures howmuch richer one will become by undertaking themuch richer one will become by undertaking theinvestment opportunity.investment opportunity.

IRR vs. NPVIRR vs. NPV

Payback PeriodPayback Period


102/116


Payback period (Time to return)Payback period (Time to return) Minimal length of time over which benefitsMinimal length of time over which benefits

repay costsrepay costs

Typically only used as secondary assessmentTypically only used as secondary assessment



103/116


Payback period (Time to return)Payback period (Time to return) Minimal length of time over which benefitsMinimal length of time over which benefits

repay costsrepay costs

Typically only used as secondary assessmentTypically only used as secondary assessment

Important for selection when the risk isImportant for selection when the risk is

extremely highextremely 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


104/116


Financing has major impact on projectFinancing has major impact on project

selectionselection

Suppose that one had to choose between 2Suppose that one had to choose between 2investment projectsinvestment projects

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



105/116


Financing has major impact on projectFinancing has major impact on project

selectionselection

Suppose that one had to choose between 2Suppose that one had to choose between 2investment projectsinvestment projects

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

Use NPVUse NPV Verify IRRVerify IRR

Check payback periodCheck payback period

Other MethodsOther Methods


106/116

Other MethodsOther Methods

Benefit-Cost ratio (benefits/costs)Benefit-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 sizesize of theof the

benefitsbenefits

Cost-effectivenessCost-effectiveness Looking at non-economic factorsLooking at non-economic factors

Discounting still often applied for non-Discounting still often applied for non-

economiceconomic $/Life saved$/Life saved

Inflation & DeflationInflation & Deflation


107/116


Inflation means that the prices of goods andInflation means that the prices of goods and

services increase over time either imperceptiblyservices increase over time either imperceptibly

or in leaps and bounds. Inflation effects need toor in leaps and bounds. Inflation effects need to

be included in investment because cost andbe included in investment because cost andbenefits are measured in money and paid inbenefits are measured in money and paid in

current dollars, francs or pesos. An inflationarycurrent dollars, francs or pesos. An inflationary

trend makes future dollars have less purchasingtrend makes future dollars have less purchasing

power than present dollars.power than present dollars.

Deflation means the opposite of inflation. PricesDeflation means the opposite of inflation. Prices

of goods & services decrease as time passes.of goods & services decrease as time passes.



108/116


ijjii ++='

discount rate excludingdiscount rate excludinginflationinflation

discount rate includingdiscount rate includinginflationinflation

annual inflation rateannual inflation rate

i

'i

j

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



109/116


ijjii ++='

discount rate excludingdiscount rate excludinginflationinflation

discount rate includingdiscount rate includinginflationinflation

annual inflation rateannual inflation rate

i

'i

j

t

n

t

tiAANPV )1(/

1

0 ++= =

AAtt cash flow in year t expressed in terms of constant cash flow in year t expressed in terms of constant

(base year) dollars(base year) dollars

A'A'tt cash flow in year t expressed in terms of inflated cash flow in year t expressed in terms of inflated-

t

n

t

tiAANPV )1(/ '

1

'

0 ++= =

jii +='

jii = 'or

When the inflation rate is small, these relations can be

approximated by:

j

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

Inflation ExampleInflation Example


110/116

Inflation ExampleInflation Example

A company plans to invest $55,000 initially in apiece of equipment which is expected to producea uniform annual constant dollars net revenuebefore tax of $15,000 over the next five years.

The equipment has a salvage value of $5,000 inconstant dollars at the end of 5 years and thedepreciation allowance is computed on the basisof the straight line depreciation method (i.e.,

$10,000 during next five years). The marginalincome tax rate for this company is 34%. Theinflation expectation is 5% per year, and theafter-tax MARR specified by the company is 8%excluding inflation. Determine whether the

Link

SolutionSolution
http://c/Documents%20and%20Settings/labi/Local%20Settings/Temp/Inflation.xlshttp://c/Documents%20and%20Settings/labi/Local%20Settings/Temp/Inflation.xlshttp://c/Documents%20and%20Settings/labi/Local%20Settings/Temp/Inflation.xls


111/116

SolutionSolution

With 5% inflation, the investment is no longer worthwhilebecause the value of the depreciation tax reduction is notincreased to match the inflation rate.

Verify that the use of MARR including inflation gives thesame result (credit by next Monday send me one-pageexcel sheet)

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

Impact of Inflation: BostonImpact of Inflation: BostonCentral ArteryCentral Artery


112/116

Central ArteryCe a e yYearYear

tt

PricePrice

IndexIndex

1982 $1982 $

PricePrice

IndexIndex

2002 $2002 $

ProjectProject

ExpensesExpenses

($ K)($ K)

ProjectProject

ExpensesExpenses

(1982 $ k)(1982 $ k)

ProjectProject

ExpensesExpenses

(2002 $ K)(2002 $ K)

1982198219831983

19841984

19851985

19861986

19871987

19881988

1989198919901990

19911991

19921992

19931993

19941994

19951995

19961996

1997199719981998

19991999

20002000

20012001

20022002

20032003

20042004

20052005

100100104104

111111

118118

122122

123123

130130

134134140140

144144

146146

154154

165165

165165

165165

175175172172

176176

181181

183183

189189

195195

202202

208208

53535555

5959

6262

6565

6565

6969

71717474

7676

7777

8282

8888

8888

8787

93939191

9494

9696

9797

100100

103103

107107

110110

33,00033,000

82,00082,000

131,000131,000

164,000164,000214,000214,000

197,000197,000

246,000246,000

574,000574,000

854,000854,000

852,000852,000

764,000764,000

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

1,523,0001,523,000

1,329,0001,329,000

1,246,0001,246,000

1,272,0001,272,000

1,115,0001,115,000

779,000779,000

441,000441,000

27,00027,000

67,00067,000

101,000101,000

122,000122,000153,000153,000

137,000137,000

169,000169,000

372,000372,000

517,000517,000

515,000515,000

464,000464,000

687,000687,000853,000853,000

863,000863,000

735,000735,000

682,000682,000

674,000674,000

572,000572,000

386,000386,000

212,000212,000

51,00051,000

126,000126,000

190,000190,000

230,000230,000289,000289,000

258,000258,000

318,000318,000

703,000703,000

975,000975,000

973,000973,000

877,000877,000

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

1,629,0001,629,000

1,387,0001,387,000

1,288,0001,288,000

1,272,0001,272,000

1,079,0001,079,000

729,000729,000

399,000399,000Source: Hendrickson and Au, 1989/2003

OutlineOutline


113/116




Time value of moneyTime value of money Present valuePresent value



What are we AssumingWhat are we Assuming


114/116

Here?Here?

That only quantifiable monetaryThat only quantifiable monetary

benefits matterbenefits matter

CertaintyCertaintyabout future cash flowsabout future cash flows Main uncertainties:Main uncertainties:

Financial concernsFinancial concerns Currency fluctuations (international projects)Currency fluctuations (international projects)

Inflation/deflationInflation/deflation

Taxes variationsTaxes variations

Project risksProject risks



115/116


FEASIBILITY

DESIGN

PLANNINGCLOSEOUTDEVELOPMENT OPERATIONS

Financing &

EvaluationRisk


116/116

Lecture 2 Project Financing & Evaluation

Documents

Transcript of Lecture 2 Project Financing & Evaluation