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Essential formulae in project appraisal 2 tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả...
Fin650:Project Appraisal Lecture Essential Formulae in Project Appraisal Benefits and Cost Realized at Different Times Benefits and costs realized in different times are not comparable Some benefits and costs are recurrent, while some are realized only for a temporary period Examples: Roads, built now at heavy costs, to generate benefits later, Dams, entail environmental costs long after their economic benefits have lapsed, A life lost now entails cost for at least as long into the future as the person would have lived Fundamentals in Financial Evaluation Money has a time value: a $ or £ or € or Tk today, is worth more than a $ or £ or € or Tk next year A risk free interest rate may represent the time value of money Inflation too can create a difference in money value over time It is NOT the time value of money It is a decline in monetary purchasing power Moving Money Through Time Investment projects are long lived, so we usually use annual interest rates With compound interest rates, money moved forward in time is ‘compounded’, whilst money moved backward in time is ‘discounted’ Financial Calculations Time value calculations in capital budgeting usually assume that interest is annually compounded ‘Money’ in investment projects is known as ‘cash flows’: the symbol is: Ct is Cash flow at end of period t Financial Calculations The present value of a single sum is: PV = FV (1 + r)-t the present value of a dollar to be received at the end of period t, using a discount rate of r The present value of series of cash flows is: PV = t ∑ CFt (1 + r ) t Financial Calculations: Cash Flow Series A payment series in which cash flows are Equally sized and Equally timed is known as an annuity There are four types: Ordinary annuities; the cash flows occur at the end of each time period (Workbook 5.10 and 5.11) Annuities due; the cash flows occur at the start of each time period Deferred annuities; the first cash flow occurs later than one time period into the future (Workbook 5.10 and 5.11) Perpetuities; the cash flows begin at the end of the first period, and go on forever Evaluation of Project Cash Flows Cash flows occurring within investment projects are assumed to occur regularly, at the end of each year Since they are unlikely to be equal, they will not be annuities Annuity calculations apply more to loans and other types of financing All future flows are discounted to calculate a Net Present Value, NPV; or an Internal Rate of Return, IRR Decision Making With Cash Flow Evaluations If the Net Present Value is positive, then the project should be accepted The project will increase the present wealth of the firm by the NPV amount If the IRR is greater than the required rate of return, then the project should be accepted The IRR is a relative measure, and does not measure an increase in the firm’s wealth Calculating NPV and IRR With Excel Basics Ensure that the cash flows are recorded with the correct signs: -$, +$, -Tk, +Tk etc Make sure that the cash flows are evenly timed: usually at the end of each year Enter the discount rate as a percentage, not as a decimal: e.g 15.6%, not 0.156 Check your calculations with a hand held calculator to ensure that the formulae have been correctly set up 10 Difficulties With The Internal Rate of Return Criterion (Cont’d) Fourth difficulty: Same project but started at different times Project A: Investment costs = 1,000 in year Benefits = 1,500 in year Project B: Investment costs = 1,000 in year Benefits = 1,600 in year NPV A : -1,000 + 1,500/(1.08) = 388.88 NPV B : -1,000/(1.08) + 1,600/(1.08) = 327.68 0 Hence, NPV A> NPV B IRR A : -1,000 + 1,500/(1+K A) = which implies that K A = 0.5 IRR B : -1,000/(1+K B) 5+ 1,600/(1+K B) 6= which implies that K B = 0.6 Hence, K B >KA 46 IRR FOR IRREGULAR CASHFLOWS For Example: Look at a Private BOT Project from the perspective of the Government Year Project A IRR A 1000 1200 800 3600 -8000 3600 -6400 10% Compares Project A and Project B ? Project B IRR B 1000 1200 800 -2% Project B is obviously better than A, yet IRR A > IRR B Project C IRR C 1000 1200 800 3600 -4800 -16% Project C is obviously better than B, yet IRR B > IRR C Project D -1000 IRR D 4% 1200 800 3600 -4800 Project D is worse than C, yet IRR D > IRR C Project E IRR E -1325 1200 800 3600 -4800 20% Project E is worse than D, yet IRR E > IRR D 47 The Social Discount Rate: Main Issues How much current consumption society is willing to give up now in order to obtain a given increase in future Consumption? It is generally accepted that society’s choices, including the choice of weights be based on individuals’ choices Three unresolved issues Whether market interest rates can be used to represent how individuals weigh future consumption relative to present consumption? Whether to include unborn future generation in addition to individuals alive today? Whether society attaches the same value to a unit of investment as to a unit of consumption Different assumptions will lead to choice of different discount rate 48 Does the Choice of Discount Rate Matter? Generally a low discount rate favors projects with highest total benefits, irrespective of when they occur, e.g project C Increasing the discount rate applies smaller weights to benefits or (costs) that occur further in the future and, therefore, weakens the case for projects with benefit that are back-end loaded (such as project C), strengthens the case for projects with benefit that are front-end loaded (such as project B) 49 NPV for Three Alternative Projects Year Project A Project B Project C -80,000 -80,000 -80,000 25,000 80,000 25,000 10,000 25,000 10,000 25,000 10,000 25,000 10,000 140,000 Total benefits 45,000 40,000 60,000 NPV (i=2%) 37,838 35,762 46,802 NPV (i=10%) 14,770 21,544 6,929 50 Appropriate Social Discount Rate in Perfect Markets • As individuals, we prefer to consume immediate benefits to ones occurring in the future (marginal rate of time preference) • We also face an opportunity cost of forgone interest when we spend money today rather than invest them for future use (marginal rate of return on private investment) • In a perfectly competitive market: rate of return on private investment = the market interest rates = marginal rate of time preference (MRTP) • The rate at which an individual makes marginal trade-offs is called an individuals MRTP Therefore, we may use the market interest rate as the social discount rate 51 Equality of MRTP and Market Interest Rate 52 Alternative Social Discount Rate in Imperfect Markets Six potential discounting methods Social discount rate equal to marginal rate of return on private investment, rz Social discount rate equal to marginal rate of time preference, pz Social discount rate equal to weighted average of pz, rz and i , where i is the government’s real long-term borrowing rate Social discount rate is the shadow price of capital A discount rate that declines over the time horizon of the project A discount rate SG, based on the growth in real per capita consumption 53 Alternative Social Discount Rate in Imperfect Markets Using the Marginal Rate of Return on Private Investment The government takes resources out of the private sector Society must receive a higher rate of return compared to the return in the private sector Criticism Too high Return on private sector investment incorporates a risk premium Government project might be financed by taxes, displaces consumption rather than investment Project may be financed by low cost foreign loans Private sector return may be high because of monopoly or negative externalities Government investment sometimes raises the private return on capital 54 Alternative Social Discount Rate in Imperfect Markets Using the Marginal Social Rate of Time Preference, pz Numerical values of pz Real after-tax return on savings, around percent for the US economy Criticisms Individuals have different MRTP How to aggregate such individual MRTP Market interest rate reflects MRTP of individuals currently alive Using the Weighted Social Opportunity Cost of Capital WSOC= arz + bi + (1-a-b)pz Numerical Value, percent for the US economy 55 Harberger’s Social Discount Rate Social discount rate should be obtained by weighting rz and pz by the relative size of the relative contributions that investment and consumption would make toward funding the project s = arz + (1-a)pz, where a = ΔI/(ΔI+ ΔC) and (1-a) = ΔC/(ΔI+ ΔC) Savings are not very responsive to changes in the interest rate, ΔC is close to zero The value of the parameter a is close to one The marginal rate of return on private investment rz is a good approximation of true social discount rate 56 Alternative Social Discount Rate in Imperfect Markets Criticisms of WSOC Criticisms applicable to use of rz and pz applies Different discount rates for different projects based on source of financing Use the Shadow Price of Capital Strong theoretical appeal Discounting be done in four steps Costs and benefits in each period are divided into those that directly affect consumption and those affect investment Flows into and out of investment are multiplied by the shadow price of capital θ, to convert them into consumption equivalents Changes in consumption are added to changes in consumption equivalents Discounting the resultant flow by pz 57 Alternative Social Discount Rate in Imperfect Markets Shadow Price of Capital θ= (rz + δ )(1 − f ) p z − rz f + δ (1 − f ) Where rz is the net return on capital after depreciation, δ is the depreciation rate of capital, f is the fraction of gross return that is reinvested, and pz is the marginal social rate of time preference Numerical Values for the economy Applying SPC in Practice θ,SPC, 1.5-2.5 for the US Criticism of calculation and use of the SPC 58 Alternative Social Discount Rate in Imperfect Markets Using Time-Declining Discount Rates Conclusion, Social Discounting in Imperfect Markets If all costs and benefits are measured as increments to consumption, use MSRTP, pz, Boardman et Al suggests a value of percent, sensitivity 0-4 percent If all costs and benefits are measured as increments to private sector investment, use MRROI, rz, Boardman et Al suggests a value of percent, sensitivity 6-10 percent If all costs and benefits are measured as increments to both consumption and private sector investment, use SPOC, θ, to increments in investment and then discount at MSRTP, Boardman et Al suggests for SPOC, a value of 1.65 percent, sensitivity 1.3-2.7 percent; and ΔI = 15 percent and, ΔC= 85 percent, in the absence of information 59 The Social Discount Rate in Practice Many Government Agencies not discount at all Shadow Price of Capital is rarely used Governments not use time-varying discount rates Constant positive rate that varies from country to country US, 7-10 percent Canada, 10 percent, sensitivity 5-15 percent 0-3 percent for Health and Environment Projects ADB, EIRR of 10-12 percent 60 ... 1)(1+r) 2+ (B 2- C 2) (1+r)+(B 3-C 3)+ (B n-C n)/(1+r) n-3 Then NPV r = (1+r) NPV r 22 Examples of Discounting Year Net Cash Flow -1000 20 0 300 350 1440 20 0 300 350 1440 NPV = −1000 + + + + = 676 .25 ... NPVA Project B: PV of Benefits = $7.0 M = $2. 0 M RA = 7/5 = 1.4 0 PV of Costs = $20 .0 M, PV of Benefits = $24 .0 M NPVB = $4.0 M RB = 24 /20 = 1 .2 According to the Benefit-Cost Ratio criterion, project. .. Private BOT Project from the perspective of the Government Year Project A IRR A 1000 120 0 800 3600 -8000 3600 -6400 10% Compares Project A and Project B ? Project B IRR B 1000 120 0 800 -2% Project