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1.040/1.401 Project Management Spring 2007 Project Financing & Evaluation Dr. SangHyun Lee lsh@mit.edu Department of Civil and Environmental Engineering Massachusetts Institute of Technology

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Preliminaries STELLAR access: to be announced STELLAR access: to be announced AS1 Survey due by tonight 12 pm AS1 Survey due by tonight 12 pm TP1 and AS2 are out TP1 and AS2 are out

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AS 2: Student Presentation 10 minute presentation followed by 5 minute discussion 10 minute presentation followed by 5 minute discussion 1 or 2 presentations from Feb. 20 to Mar. 19 1 or 2 presentations from Feb. 20 to Mar. 19 Topics Topics Your past project experience (strongly recommended if you have any) Your past project experience (strongly recommended if you have any) Size of project is not important! Size of project is not important! Project main figures Project main figures Main managerial aspects Main managerial aspects Project management practices Project management practices Problems, strengths, weaknesses, risks Problems, strengths, weaknesses, risks Your learning Your learning Emerging construction technologies (e.g., 4D CAD, Virtual Reality, Sensing, …) Emerging construction technologies (e.g., 4D CAD, Virtual Reality, Sensing, …) Volunteers for next week? Volunteers for next week?

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Preliminaries STELLAR access: to be announced STELLAR access: to be announced AS1 Survey due by tonight 12 pm AS1 Survey due by tonight 12 pm TP1 and AS2 are out TP1 and AS2 are out Pictures will be taken before you leave Pictures will be taken before you leave Who we are Who we are Don’t memorize course content. Understand it. Don’t memorize course content. Understand it.

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Outline Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Session Objective The role of project financing The role of project financing Mechanisms for project financing Mechanisms for project financing Measures of project profitability Measures of project profitability

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Project Management Phase FEASIBILITY DESIGN PLANNING CLOSEOUT DEVELOPMENT OPERATIONS Financing & Evaluation Risk

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Context: Feasibility Phases Project Concept Project Concept Land Purchase & Sale Review Land Purchase & Sale Review Evaluation (scope, size, etc.) Evaluation (scope, size, etc.) Constraint survey Constraint survey Site constraints Site constraints Cost models Cost models Site infrastructural issues Site infrastructural issues Permit requirements Permit requirements Summary Report Summary Report Decision to proceed Decision to proceed Regulatory process (obtain permits, etc) Regulatory process (obtain permits, etc) Design Phase Design Phase

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Lecture 2 - References More details on: Hendrickson PM for Construction on-line textbook Hendrickson PM for Construction on-line textbook Chapter 7 Chapter 7

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Outline Session Objective & Context Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Financing – Gross Cashflows Owner investment = contractor revenue

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Financing – Gross Cashflows Owner investment = contractor revenue Design/Preliminary Construction

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Financing – Gross Cashflows Owner investment = contractor revenue Early expenditure Takes time to get revenue Design/Preliminary Construction

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

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Critical Role of Financing Makes projects possible Makes projects possible Has major impact on Has major impact on Riskiness of construction Riskiness of construction Claims Claims Prices offered by contractors (e.g., high bid price for late payment) Prices offered by contractors (e.g., high bid price for late payment) Difficulty of Financing is a major driver towards alternate delivery methods (e.g., Build-Operate-Transfer) Difficulty of Financing is a major driver towards alternate delivery methods (e.g., Build-Operate-Transfer)

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How Does Owner Finance a Project? Public Public Private Private “Project” financing “Project” financing

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Outline Session Objective & Context Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Public Financing Sources of funds Sources of funds General purpose or special-purpose bonds General purpose or special-purpose bonds Tax revenues Tax revenues Capital grants subsidies Capital grants subsidies International subsidized loans International subsidized loans Social benefits important justification Social benefits important justification Benefits to region, quality of life, unemployment relief, etc. Benefits to region, quality of life, unemployment relief, etc. Important consideration: exemption from taxes Important consideration: exemption from taxes Public owners face restrictions (e.g. bonding caps) Public owners face restrictions (e.g. bonding caps) Major motivation for public/private partnerships Major motivation for public/private partnerships MARR (Minimum Attractive Rate of Return) much lower (e.g. 8- 10%), often standardized MARR (Minimum Attractive Rate of Return) much lower (e.g. 8- 10%), often standardized

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Private Financing Major mechanisms Major mechanisms Equity Equity Invest corporate equity and retained earnings Invest corporate equity and retained earnings Offering equity shares Offering equity shares Stock Issuance (e.g. in capital markets) Stock Issuance (e.g. in capital markets) Must entice investors with sufficiently high rate of return Must entice investors with sufficiently high rate of return May be too limited to support the full investment May be too limited to support the full investment May be strategically wrong (e.g., source of money, ownership) May be strategically wrong (e.g., source of money, ownership) Debt Debt Borrow money Borrow money Bonds Bonds Because higher costs and risks, require higher returns Because higher costs and risks, require higher returns MARR varies per firm, often high (e.g. 20%) MARR varies per firm, often high (e.g. 20%)

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Private Owners w/Collateral Facility Distinct Financing Periods Short-term construction loan Short-term construction loan Bridge Debt Bridge 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 mortgage Long-term mortgage Senior Debt Senior Debt Typically facility is collateral Typically facility is collateral Pays for operations and Construction financing debts Pays for operations and Construction financing debts Typically much lower interest Typically much lower interest Loans often negotiated as a package Loans often negotiated as a package time construction w/o tangible operation w/ tangible

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Outline Session Objective & Context Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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“Project” Financing Investment is paid back from the project profit rather than the general assets or creditworthiness of the project owners Investment is paid back from the project profit rather than the general assets or creditworthiness of the project owners For larger projects due to fixed cost to establish For larger projects due to fixed cost to establish Small projects not much benefit Small projects not much benefit Investment in project through special purpose corporations Investment in project through special purpose corporations Often joint venture between several parties Often joint venture between several parties Need capacity for independent operation Need capacity for independent operation Benefits Benefits Off balance sheet (liabilities do not belong to parent) Off balance sheet (liabilities do not belong to parent) Limits risk Limits risk External investors: reduced agency cost (direct investment in project) External investors: reduced agency cost (direct investment in project) Drawback Drawback Tensions among stakeholders Tensions among stakeholders

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Outline Session Objective & Context Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Contractor Financing I Payment schedule Payment schedule Break out payments into components Break out payments into components Advance payment Advance payment Periodic/monthly progress payment (itemized breakdown structure) Periodic/monthly progress payment (itemized breakdown structure) Milestone payments Milestone payments Often some compromise between contractor and owner Often some compromise between contractor and owner Architect certifies progress Architect certifies progress Agreed-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 received Can be many months before payment received

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S-curve Work Man-hours months

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S-curve Cost Daily cost Cum. costs

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Expense & Payment

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Contractor Financing II Owner keeps an eye out for Owner keeps an eye out for Front-end loaded bids (discounting) Front-end loaded bids (discounting) Unbalanced bids Unbalanced bids

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Contractor Financing II Owner keeps an eye out for Owner keeps an eye out for Front-end loaded bids (discounting) Front-end loaded bids (discounting) Unbalanced bids Unbalanced bids Contractors frequently borrow from Contractors frequently borrow from Banks (Need to demonstrate low risk) Banks (Need to demonstrate low risk) Interaction with owners Interaction with owners Some owners may assist in funding Some owners may assist in funding Help secure lower-priced loan for contractor Help secure lower-priced loan for contractor Sometimes assist owners in funding! Sometimes assist owners in funding! Big construction company, small municipality Big construction company, small municipality BOT BOT

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Agreed upon in contract Agreed upon in contract Often structure proposed by owner Often structure proposed by owner Should be checked by owner (fair-cost estimate) Should be checked by owner (fair-cost estimate) Often based on “Masterformat” Cost Breakdown Structure (Owner standard CBS) Often based on “Masterformat” Cost Breakdown Structure (Owner standard CBS) Certified by third party (Architect/engineer) Certified by third party (Architect/engineer) Contractor Financing III

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Outline Session Objective & Context Session Objective & Context Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Latent Credit Many people forced to serve as lenders to owner due to delays in payments Many people forced to serve as lenders to owner due to delays in payments Designers Designers Contractors Contractors Consultants Consultants CM CM Suppliers Suppliers Implications Implications Good in the short-term Good in the short-term Major concern on long run effects Major concern on long run effects

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Role of Taxes Tax deductions for Tax deductions for Depreciation - Link Depreciation - LinkLink the process of recognizing the using up of an asset through wear and obsolescence and of subtracting capital expenses from the revenues that the asset generates over time in computing taxable income the process of recognizing the using up of an asset through wear and obsolescence and of subtracting capital expenses from the revenues that the asset generates over time in computing taxable income Others Others

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional Issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Develop or Not Develop Is any individual project worthwhile? Is any individual project worthwhile? Given a list of feasible projects, which one is the best? Given a list of feasible projects, which one is the best? How does each project rank compared to the others on the list? How does each project rank compared to the others on the list?

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Project Evaluation Example: Project A Project A Construction=3 years Construction=3 years Cost = $1M/year Cost = $1M/year Sale Value=$4M Sale Value=$4M Total Cost? Total Cost? Profit? Profit? Project B Construction=6 years Cost=$1M/year Sale Value=$8.5M Total Cost? Profit?

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Quantitative Method Profitability Profitability Create value for the company Create value for the company

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Profit TOTAL EQUIVAL. $ REVENUES5,500,000.00 COSTS4,600,000.00 Project management 400,000.00 Engineering800,000.00 Material & transport 2,200,000.00 Construction/commissioning1,300,000.00 Contingencies200,000.00 GROSS MARGIN 900,000.00 Time factor?

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Quantitative Method Profitability Profitability Create value for the company Create value for the company Opportunity Cost Opportunity Cost Time Value of Money Time Value of Money A dollar today is worth more than a dollar tomorrow A dollar today is worth more than a dollar tomorrow Investment relative to best-case scenario Investment relative to best-case scenario E.g. Project A - 8% profit, Project B - 10% profit E.g. Project A - 8% profit, Project B - 10% profit

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Money Is Not Everything Social Benefits Social Benefits Hospital Hospital School School Highway built into a remote village Highway built into a remote village Intangible Benefits (E.g, operating and competitive necessity) Intangible Benefits (E.g, operating and competitive necessity) New warehouse New warehouse New cafeteria New cafeteria

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Basic Compounding Suppose we invest $x in a bank offering interest rate i Suppose we invest $x in a bank offering interest rate i If interest is compounded annually, asset will be worth If interest is compounded annually, asset will be worth $x(1+i) after 1 year $x(1+i) after 1 year $x(1+i) 2 after 2 years $x(1+i) 2 after 2 years $x(1+i) 3 after 3 years …. $x(1+i) 3 after 3 years …. $x(1+i) n after n years $x(1+i) n after n years $x 0 1$x(1+i)2 2 $x(1+i) 2 n n $x(1+i) n …

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Time Value of Money If we assume If we assume That money can always be invested in the bank (or some other reliable source) now to gain a return with interest later That money can always be invested in the bank (or some other reliable source) now to gain a return with interest later That as rational actors, we never make an investment which we know to offer less money than we could get in the bank That as rational actors, we never make an investment which we know to offer less money than we could get in the bank Then Then Money in the present can be thought as of “equal worth” to a larger amount of money in the future Money in the present can be thought as of “equal worth” to a larger amount of money in the future Money in the future can be thought of as having an equal worth to a lesser “present value” of money Money in the future can be thought of as having an equal worth to a lesser “present value” of money

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Equivalence of Present Values Given a source of reliable investments, we are indifferent between any cash flows with the same present value – they have “equal worth” Given a source of reliable investments, we are indifferent between any cash flows with the same present value – they have “equal worth” This indifferences arises because we can convert one to the other with no extra expense This indifferences arises because we can convert one to the other with no extra expense

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Preliminaries STELLAR access: http://stellar.mit.edu/S/course/1/sp07/1.040/ 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 Part I Next Tuesday Recitation: Skyscraper Part I Please set up an appointment to discuss your AS2 if you choose emerging technologies (MF preferred) Please set up an appointment to discuss your AS2 if you choose emerging technologies (MF preferred) Office: 1-174 Office: 1-174 TA (50%) for our class TA (50%) for our class Send your resume (or brief your experience) by this Sunday Send your resume (or brief your experience) by this Sunday

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Time Value of Money: Revisit If we assume If we assume That money can always be invested in the bank (or some other reliable source) now to gain a return with interest later That money can always be invested in the bank (or some other reliable source) now to gain a return with interest later That as rational actors, we never make an investment which we know to offer less money than we could get in the bank That as rational actors, we never make an investment which we know to offer less money than we could get in the bank Then Then Money in the present can be thought as of “equal worth” to a larger amount of money in the future Money in the present can be thought as of “equal worth” to a larger amount of money in the future Money in the future can be thought of as having an equal worth to a lesser “present value” of money Money in the future can be thought of as having an equal worth to a lesser “present value” of money

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Present Value (Revenue) How is it that some future revenue r at time t has a “present value”? How is it that some future revenue r at time t has a “present value”? Answer: Given that we are sure that we will be gaining revenue r at time t, we can take and spend an immediate loan from the bank Answer: Given that we are sure that we will be gaining revenue r at time t, we can take and spend an immediate loan from the bank We choose size of this loan l so that at time t, the total size of the loan (including accrued interest) is r We choose size of this loan l so that at time t, the total size of the loan (including accrued interest) is r The loan l is the present value of r The loan l is the present value of r l = PV(r) l = PV(r)

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Future 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 t into a (smaller) PV(x) now!

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Present Value (Cost) How is it that some future cost c at time t has a “present value”? How is it that some future cost c at time t has a “present value”? Answer: Given that we are sure that we will bear cost c at time t, we immediately deposit a sum of money x into the bank yielding a known return Answer: Given that we are sure that we will bear cost c at time t, we immediately deposit a sum of money x into the bank yielding a known return We choose size of deposit x so that at time t, the total size of the investment (including accrued interest) is c We choose size of deposit x so that at time t, the total size of the investment (including accrued interest) is c We can then pay off c at time t by retrieving this money from the bank We can then pay off c at time t by retrieving this money from the bank The size of the deposit (immediate cost) x is the present value of c. The size of the deposit (immediate cost) x is the present value of c.

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Future to Present Cost x t PV(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 t into a (smaller) cost of PV(x) now! PV(x) -x t 0 If I know this cost is coming…

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Summary Because we can flexibly switch from one such value to another without cost, we can view these values as equivalent Because we can flexibly switch from one such value to another without cost, we can view these values as equivalent FV t v v’ 0 PV

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Summary Because we can flexibly switch from one such value to another without cost, we can view these values as equivalent Because we can flexibly switch from one such value to another without cost, we can view these values as equivalent FV t v v’ 0 PV Given a reliable source offering annual return i (i.e., interest) we can shift without additional costs between cash v at time 0 and v(1+i) t at time t Given a reliable source offering annual return i (i.e., interest) we can shift without additional costs between cash v at time 0 and v(1+i) t at time t = v(1+i) t

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Rates Difference between PV (v) and FV ( =v(1+i) t ) depends on i and t. Difference between PV (v) and FV ( =v(1+i) t ) depends on i and t.

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Rates Interest Rate Interest Rate Contractual arrangement between a borrower and a lender Contractual 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 + Risk Worth 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 the risks of a project (i.e., minimum standard of desirability) Minimum discount rate accepted by the market corresponding to the risks of a project (i.e., minimum standard of desirability)

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Choice of Discount Rate GDP = Gross Domestic Product

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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Interest Formulas i = Effective interest rate per interest period (discount rate or MARR) i = Effective interest rate per interest period (discount rate or MARR) n = Number of compounding periods n = Number of compounding periods PV = Present Value PV = Present Value FV = Future Value FV = Future Value A = Annuity (i.e., a series of payments of set size) at end-of-period A = Annuity (i.e., a series of payments of set size) at end-of-period

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Interest Formulas: Payment Single Payment Compound Amount Factor (F=P×Factor) Single Payment Compound Amount Factor (F=P×Factor) Factor that will make your present value future value in single payment Factor that will make your present value future value in single payment (F/P, i, n) = (1 + i ) n (F/P, i, n) = (1 + i ) n P n0 F 12…

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Interest Formulas: Payment Single Payment Present Value Factor (P=F×Factor) Single Payment Present Value Factor (P=F×Factor) Factor that will make your future value present value in single payment Factor that will make your future value present value in single payment (P/F, i, n) = 1/ (1 + i ) n = 1/ (F/P, i, n) (P/F, i, n) = 1/ (1 + i ) n = 1/ (F/P, i, n) P n0 F 1…n-1

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

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

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Interest Formulas: Payment - Example If you wish to have $100,000 at the end of five years in an account that pays 12 percent annually, how much would you need to deposit now? If you wish to have $100,000 at the end of five years in an account that pays 12 percent annually, how much would you need to deposit now? 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 = $56,740 P = 100,000 × 0.5674 = $56,740

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Interest Formulas: Series Uniform Series Compound Amount Factor (F=A×Factor) Uniform Series Compound Amount Factor (F=A×Factor) Factor that will make your annuity value future value in series payment Factor that will make your annuity value future value in series payment (F/A, i, n) =[(1+i) n - 1]/ i (F/A, i, n) =[(1+i) n - 1]/ i AAAA n01 F Annuity occurs at the end of the interest period Annuity occurs at the end of the interest period 2…

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Interest Formulas: Series Uniform Series Compound Amount Factor (F=A×Factor) Uniform Series Compound Amount Factor (F=A×Factor) Factor that will make your annuity value future value in series payment Factor that will make your annuity value future value in series payment (F/A, i, n) =[(1+i) n - 1]/ i (F/A, i, n) =[(1+i) n - 1]/ i AAAA n01 F F = A 2…

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Interest Formulas: Series Uniform Series Compound Amount Factor (F=A×Factor) Uniform Series Compound Amount Factor (F=A×Factor) Factor that will make your annuity value future value in series payment Factor that will make your annuity value future value in series payment (F/A, i, n) =[(1+i) n - 1]/ i (F/A, i, n) =[(1+i) n - 1]/ i AAAA n01 F F = A+A(1+i) 2…

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Interest Formulas: Series Uniform Series Compound Amount Factor (F=A×Factor) Uniform Series Compound Amount Factor (F=A×Factor) Factor that will make your annuity value future value in series payment Factor that will make your annuity value future value in series payment (F/A, i, n) =[(1+i) n - 1]/ i (F/A, i, n) =[(1+i) n - 1]/ i AAAA n01 1 + i ) n-1 F = A + A(1+i) + … + A(1 + i ) n-1 2…

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Interest Formulas: Series Uniform Series Sinking Fund Factor (A=F×Factor) Uniform Series Sinking Fund Factor (A=F×Factor) Factor that will make your future value annuity value in series payment Factor that will make your future value annuity value in series payment (A/F, i, n) = i / [ (1 + i ) n – 1] = 1 / (F/A, i, n) (A/F, i, n) = i / [ (1 + i ) n – 1] = 1 / (F/A, i, n) AAAA n01 F 2…

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Interest Formulas: Series AAAA n01 P Uniform Series Present Value Factor (P=A×Factor) Uniform Series Present Value Factor (P=A×Factor) Factor that will make your annuity value present value in series payment Factor that will make your annuity value present value in series payment (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] 2…

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Interest Formulas: Series AAAA n01 Uniform Series Present Value Factor (P=A×Factor) Uniform Series Present Value Factor (P=A×Factor) Factor that will make your annuity value present value in series payment Factor that will make your annuity value present value in series payment (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (1 + i ) P = A/ (1 + i ) 2…

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Interest Formulas: Series AAAA n01 Uniform Series Present Value Factor (P=A×Factor) Uniform Series Present Value Factor (P=A×Factor) Factor that will make your annuity value present value in series payment Factor that will make your annuity value present value in series payment (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (1 + i ) + A/(1 + i ) 2 P = A/(1 + i ) + A/(1 + i ) 2 2…

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Interest Formulas: Series AAAA n01 Uniform Series Present Value Factor (P=A×Factor) Uniform Series Present Value Factor (P=A×Factor) Factor that will make your annuity value present value in series payment Factor that will make your annuity value present value in series payment (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (P/A, i, n) = [ (1 + i ) n -1 ] / [ i (1 + i ) n ] (1 + i ) + A/(1 + i ) 2 1 + i ) n P = A/(1 + i ) + A/(1 + i ) 2 + … + A/(1 + i ) n Verify it! 2…

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Interest Formulas: Series Uniform Series Capital Recovery Factor (A=P×Factor) Uniform Series Capital Recovery Factor (A=P×Factor) Factor that will make your present value annuity value in series payment Factor that will make your present value annuity value in series payment (A/P, i, n) = [i (1 + i ) n / [(1 + i ) n – 1] = 1 / (P/A, i, n) (A/P, i, n) = [i (1 + i ) n / [(1 + i ) n – 1] = 1 / (P/A, i, n) Verify it! AAAA n01 P 2…

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Interest Formulas: Series - Example A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required? A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required?

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Interest Formulas: Series - Example A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required? A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required? Down Payment = 5,000,000 * 0.2 = 1,000,000 Down Payment = 5,000,000 * 0.2 = 1,000,000 P = 5,000,000 – 1,000,000 = 4,000,000 P = 5,000,000 – 1,000,000 = 4,000,000 A = P * (which factor?) A = P * (which factor?)

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Interest Formulas: Series - Example A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required? A ranch is offered for sale in Mexico with a 15 year mortgage rate at 40% compounded annually, and 20% down payment. Annual payments are to be made. The first cost of the ranch is 5 million pesos. What yearly payment is required? Down Payment = 5,000,000 * 0.2 = 1,000,000 Down Payment = 5,000,000 * 0.2 = 1,000,000 P = 5,000,000 – 1,000,000 = 4,000,000 P = 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/year A = 4,000,000 * 0.40259 = 1,610,400 pesos/year

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Equipment 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 - Annual Equivalent A - Annual Equivalent P - Present Equivalent P - Present Equivalent

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Equipment Example

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A = -20,000 * (A/P, 0.15, 5) + 4,000 * (A/F, 0.15, 5) A = -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) = -5,373 = -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

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rate Interest Formulas NPV IRR & payback period Missing factors

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Net Present Value Suppose we had a collection (or stream, flow) of costs and revenues in the future Suppose we had a collection (or stream, flow) of costs and revenues in the future The net present value (NPV) is the sum of the present values for all of these costs and revenues The net present value (NPV) is the sum of the present values for all of these costs and revenues Treat revenues as positive and costs as negative Treat revenues as positive and costs as negative

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Calculation of Net Present Value Total Revenue (R) (+)Various Costs (C) (-) Calculate Gross Return Calculate Net Return PV of Net Return NPV of the Project Tax (-) Discount Rate (r) Initial Invest (-I)

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Net Present Value Decision Rule Accept a project which has 0 or positive NPV Accept a project which has 0 or positive NPVAlternatively, Use NPV to choose the best among a set of (mutually exclusive) alternative projects Use NPV to choose the best among a set of (mutually exclusive) alternative projects Mutually exclusive projects: the acceptance of a project precludes the acceptance of one or more alternative projects. Mutually exclusive projects: the acceptance of a project precludes the acceptance of one or more alternative projects.

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Project Evaluation Example Revisit: Which one is better? Project A Project A Construction=3 years Construction=3 years Cost = $1M/year Cost = $1M/year Sale Value = $4M Sale Value = $4M Total Cost? Total Cost? Profit? Profit? Project B Construction=6 years Cost = $1M/year Sale Value = $8.5M Total Cost? Profit?

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Drawing out the examples Project A Project A Project B Project B $1M $4M $1M 1 $8.5M 6 $1M Assume 10% discount rate Link 03 2 $1M 0 1

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Or Using Interest Formulas Project A Project 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 B Project 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

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

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[NPV1]20% = -77 + (235)(P/F, 0.2, 5) = -77 + 94.4 = 17.4 [NPV2]20% = -75.3 + (28)(P/A, 0.2, 5) = -75.3 + 83.7 = 8.4Solution 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

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Solution [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

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Solution [NPV1] = 17.4 [NPV2] = 8.4 [NPV3] = 0.4 [NPV4] = -1.6 Source: Hendrickson and Au, 1989/2003

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Discount Rate in NPV NPV (and PV) is relative to a discount rate NPV (and PV) is relative to a discount rate In the absence of risk or inflation, this is just the interest rate of the “reliable source” (opportunity cost) In the absence of risk or inflation, this is just the interest rate of the “reliable source” (opportunity cost) Correct selection of the discount rate is fundamental. If too high, projects that could be profitable can be rejected. If too low, the firm will accept projects that are too risky without proper compensation. Correct selection of the discount rate is fundamental. If too high, projects that could be profitable can be rejected. If too low, the firm will accept 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. Example Example

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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. 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%) Is the additional $8,000 in the initial investment of the second equipment worthy the $1,200 annual savings? (discount rate: 5 or 10%) Link

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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. 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%) Is the additional $8,000 in the initial investment of the second equipment worthy the $1,200 annual savings? (discount rate: 5 or 10%) There is a critical value of i that changes the equipment choice (approximately 8.15%) There is a critical value of i that changes the equipment choice (approximately 8.15%) Example: The US Federal Highway Administration promulgated a regulation in the early 1970s that the discount rate for all federally funded highways would be zero. This was widely interpreted as a victory for the cement industry over asphalt industry. Roads made of concrete cost significantly more than those of made of asphalt while requiring less maintenance and less replacement [Shtub et al., 1994] - Link Example: The US Federal Highway Administration promulgated a regulation in the early 1970s that the discount rate for all federally funded highways would be zero. This was widely interpreted as a victory for the cement industry over asphalt industry. Roads made of concrete cost significantly more than those of made of asphalt while requiring less maintenance and less replacement [Shtub et al., 1994] - LinkLink

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Time value of money Present value Rate Interest Formulas NPV IRR & payback period Missing factors

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Internal Rate of Return (IRR) Defined as the rate of return that makes the NPV of the project equal to zero Defined as the rate of return that makes the NPV of the project equal to zero To see whether the project’s rate of return is equal to or higher than the rate of the firm to expect to get from the project To see whether the project’s rate of return is equal to or higher than the rate of the firm to expect to get from the project

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IRR Calculation Example NPV = -20,000 + 5,600 (P/A, i, 5) + 4,000 (P/F, i, 5) NPV = -20,000 + 5,600 (P/A, i, 5) + 4,000 (P/F, i, 5) Link Link Link

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Relationship between NPV & IRR IRR

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IRR Investment Rule “Accept a project with IRR larger than MARR” Alternatively, “Maximize IRR across mutually exclusive projects.” r = IRR, r = MARR - *

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Oftentimes, IRR and NPV give the same decision/ranking among projects. Oftentimes, IRR and NPV give the same decision/ranking among projects. IRR only looks at rate of gain – not size of gain IRR only looks at rate of gain – not size of gain IRR does not require you to assume (or compute) a discount rate. IRR does not require you to assume (or compute) a discount rate. IRR ignores capacity to reinvest IRR ignores capacity to reinvest IRR may not be unique IRR may not be unique IRR vs. NPV NPV Discount Rate Link

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Oftentimes, IRR and NPV give the same decision/ranking among projects. Oftentimes, IRR and NPV give the same decision/ranking among projects. IRR only looks at rate of gain – not size of gain IRR only looks at rate of gain – not size of gain IRR does not require you to assume (or compute) a discount rate. IRR does not require you to assume (or compute) a discount rate. IRR ignores capacity to reinvest IRR ignores capacity to reinvest IRR may not be unique IRR may not be unique Use both NPV (size) and IRR together (rate) However, Trust the NPV: It is the only criterion that ensures wealth maximization. It measures how much richer one will become by undertaking the investment opportunity. IRR vs. NPV

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Payback Period Payback period (“Time to return”) Payback period (“Time 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 assessment Typically only used as secondary assessment

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Payback Period Payback period (“Time to return”) Payback period (“Time 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 assessment Typically only used as secondary assessment Important for selection when the risk is extremely high Important for selection when the risk is extremely high Drawbacks Drawbacks Ignores what happens after payback period Ignores what happens after payback period Does not take into account discounting Does not take into account discounting

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Comparing Projects Financing has major impact on project selection Financing has major impact on project selection Suppose that one had to choose between 2 investment projects Suppose that one had to choose between 2 investment projects How can one compare them? How can one compare them?

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Comparing Projects Financing has major impact on project selection Financing has major impact on project selection Suppose that one had to choose between 2 investment projects Suppose that one had to choose between 2 investment projects How can one compare them? How can one compare them? Use NPV Use NPV Verify IRR Verify IRR Check payback period Check payback period

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Other Methods Benefit-Cost ratio (benefits/costs) Benefit-Cost ratio (benefits/costs) Discounting still generally applied Discounting still generally applied Accept if >1 (benefits > costs) Accept if >1 (benefits > costs) Common for public projects Common for public projects Does not consider the absolute size of the benefits Does not consider the absolute size of the benefits Cost-effectiveness Cost-effectiveness Looking at non-economic factors Looking at non-economic factors Discounting still often applied for non-economic Discounting still often applied for non-economic $/Life saved $/Life saved $/Life quality $/Life quality

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Inflation & Deflation Inflation means that the prices of goods and services increase over time either imperceptibly or in leaps and bounds. Inflation effects need to be included in investment because cost and benefits are measured in money and paid in current dollars, francs or pesos. An inflationary trend makes future dollars have less purchasing power than present dollars. Inflation means that the prices of goods and services increase over time either imperceptibly or in leaps and bounds. Inflation effects need to be included in investment because cost and benefits are measured in money and paid in current dollars, francs or pesos. An inflationary trend makes future dollars have less purchasing power than present dollars. Deflation means the opposite of inflation. Prices of goods & services decrease as time passes. Deflation means the opposite of inflation. Prices of goods & services decrease as time passes.

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Inflation & Deflation → discount rate excluding inflation → discount rate excluding inflation → discount rate including inflation → discount rate including inflation → annual inflation rate → annual inflation rate If i, A (y=0) will be A*(1+i) after one year. Then, if j, A will be A*(1+i)*(1+j).

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Inflation & Deflation → discount rate excluding inflation → discount rate excluding inflation → discount rate including inflation → discount rate including inflation → annual inflation rate → annual inflation rate A t → cash flow in year t expressed in terms of constant (base year) dollars A' t → cash flow in year t expressed in terms of inflated (then-current) dollars or When the inflation rate is small, these relations can be approximated by: If i, A (y=0) will be A*(1+i) after one year. Then, if j, A will be A*(1+i)*(1+j).

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Inflation 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 next five 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. Link

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Solution 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.

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Impact of Inflation: Boston Central Artery Year tPriceIndex 1982 $ PriceIndex 2002 $ ProjectExpenses ($ K) Project Expenses Project Expenses (1982 $ k) ProjectExpenses (2002 $ K) 1982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006Sum100104111118122123130134140144146154165165165175172176181183189195202208215535559626565697174767782888887939194969710010310711011433,00082,000131,000164,000214,000197,000246,000574,000854,000852,000764,0001,206,0001,470,0001,523,0001,329,0001,246,0001,272,0001,115,000779,000441,000133,00014,625,000,00027,00067,000101,000122,000153,000137,000169,000372,000517,000515,000464,000687,000853,000863,000735,000682,000674,000572,000386,000212,00062,0008,370,00051,000126,000190,000230,000289,000258,000318,000703,000975,000973,000877,0001,297,0001,609,0001,629,0001,387,0001,288,0001,272,0001,079,000729,000399,000117,00015,797,000 Source: Hendrickson and Au, 1989/2003

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Outline Session Objective & Context Session Objective & Context Project Financing Project Financing Owner Project Contractor Additional issues Financial Evaluation Financial Evaluation Time value of money Present value Rates Interest Formulas NPV IRR & payback period Missing factors

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What are we Assuming Here? That only quantifiable monetary benefits matter That only quantifiable monetary benefits matter Certainty about future cash flows Certainty about future cash flows Main uncertainties: Main uncertainties: Financial concerns Financial concerns Currency fluctuations (international projects) Currency fluctuations (international projects) Inflation/deflation Inflation/deflation Taxes variations Taxes variations Project risks Project risks

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Project Management Phase FEASIBILITY DESIGN PLANNING CLOSEOUT DEVELOPMENT OPERATIONS Financing & Evaluation Risk

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Risk Management Case Study Case Study

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