Social Discount Rate /

Admin Issues zSchedule changes: yNo Friday recitation – will do in class Monday zPipeline case study writeup – still Monday zFormat expectations: yFraming of problem (see p. 7!), yAnswer/justify with preliminary calculations yDon’t just estimate the answer! yDo not need to submit an excel printout, but feel free to paste a table into a document zLength: Less than 2 pages.

Real and Nominal Values zNominal: ‘current’ or historical data zReal: ‘constant’ or adjusted data yUse deflator or price index for real zGenerally “Real” has had inflation/price changes factored in and nominal has not zFor investment problems: yIf B&C in real dollars, use real disc rate yIf B&C in nominal dollars, use nominal rate yBoth methods will give the same answer

Similar to Real/Nominal : Foreign Exchange Rates / PPP zBig Mac handout zCommon Definition of inputs zShould be able to compare cost across countries zInteresting results? Why? zWhat are limitations?

zIs it worth to spend $1 million today to save a life 10 years from now? zHow about spending $1 million today so that your grandchildren can have a lifestyle similar to yours?

RFF Discounting Handout zHow much do/should we care about people born after we die? zEthically, no one’s interests should count more than another’s: “Equal Standing”

Social Discount Rate zRate used to make investment decisions for society zMost people tend to prefer current, rather than future, consumption yMarginal rate of time preference (MRTP) zFace opportunity cost (of foregone interest) when we spend not save yMarginal rate of investment return

Intergenerational effects zWe have tended to discuss only short term investment analyses (e.g. 5 yrs) zEconomists agree that discounting should be done for public projects yDo not agree on positive discount rate

Government Discount Rates zUS Government Office of Management and Budget (OMB) Circular A-94 yhttp:// 4/a094.html yDiscusses how to do BCA and related performance studies yWhat discount, inflation, etc. rates to use yBasically says “use this rate, but do sensitivity analysis with nearby rates”

OMB Circular A-94, Appendix C zProvides the current suggested values to use for federal government analyses yhttp:// c.htmlhttp:// c.html yRevised yearly, usually “good until January of the next year” yHow would the government decide its discount rates? yWhat is the government’s MARR?

Historic Nominal Interest Rates (from OMB A-94)

Real Discount Rates (from A-94)

What do people think zCropper et al surveyed 3000 homes yAsked about saving lives in the future yFound a 4% discount rate for lives 100 years from now

Hume’s Law zDiscounting issues are normative vs. positive battles zHume noted that facts alone cannot tell us what we should do yAny recommendation embodies ethics and judgment yE.g. focusing on ‘highest NPV’ implies net benefits is only goal for society

zIf future generations will be better off than us anyway yThen we might have no reason to make additional sacrifices zThere might be ‘special standing’ in addition to ‘equal standing’ yImmediate relatives vs. distant relatives yDifferent discount rates over time yWhy do we care so much about future and ignore some present needs (poverty)

A Few More Questions zCurrent government discount rates are ‘effectively zero’ zWhat does this mean for projects and project selection decisions? zWhat does it say about intergenerational effects? zWhat are implications of zero or negative discount rates?

Comprehensive Everglades Restoration Project zComprehensive project to restore natural water flow to the Florida Everglades. zEnhance water supply to South Florida region. zProvide continuous flood protection. See more info at

Indian River Lagoon-South (IRLS) zPart of Everglades Restoration Project. zTotal Cost of $1.21 billion. zAnnual Benefits of $159 million after project is completed in zFind NPV of first 25 years of project.

IRLS Cash Schedule $0.425 $748.3 $2.043 $447.3 $12.62 $159 per year All values are in millions

NPV of Project What would NPV be if we used a negative discount rate?

NPV of Project

Borrowing, Depreciation, Taxes in Cash Flow Problems H. Scott Matthews /

Theme: Cash Flows zStreams of benefits (revenues) and costs over time => “cash flows” zWe need to know what to do with them in terms of finding NPV of projects zDifferent perspectives: private and public yWe will start with private since its easier yWhy “private..both because they are usually of companies, and they tend not to make studies public zCash flows come from: operation, financing, taxes

Without taxes, cash flows simple zA = B - C yCash flow = benefits - costs yOr.. Revenues - expenses

Notes on Tax deductibility zReason we care about financing and depreciation: they affect taxes owed zFor personal income taxes, we deduct items like IRA contributions, mortgage interest, etc. zPrivate entities (eg businesses) have similar rules: pay tax on net income yIncome = Revenues - Expenses zThere are several types of expenses that we care about yInterest expense of borrowing yDepreciation (can only do if own the asset) yThese are also called ‘tax shields’

Goal: Cash Flows after taxes (CFAT) zMaster equation conceptually: zCFAT = -equity financed investment + gross income - operating expenses + salvage value - taxes + (debt financing receipts - disbursements) + equity financing receipts zWhere “taxes” = Tax Rate * Taxable Income zTaxable Income = Gross Income - Operating Expenses - Depreciation - Loan Interest - Bond Dividends yMost scenarios (and all problems we will look at) only deal with one or two of these issues at a time

Investment types zDebt financing: using a bank or investor’s money (loan or bond) yDF D :disbursement (payments) yDF R :receipts (income) yDF I : portion tax deductible (only non-principal) zEquity financing: using own money (no borrowing)

Why Finance? zTime shift revenues and expenses - construction expenses paid up front, nuclear power plant decommissioning at end. z“Finance” is also used to refer to plans to obtain sufficient revenue for a project.

Borrowing zNumerous arrangements possible: ybonds and notes (pay dividends) ybank loans and line of credit (pay interest) ymunicipal bonds (with tax exempt interest) zLenders require a real return - borrowing interest rate exceeds inflation rate.

Issues zSecurity of loan - piece of equipment, construction, company, government. More security implies lower interest rate. zProject, program or organization funding possible. (Note: role of “junk bonds” and rating agencies. zVariable versus fixed interest rates: uncertainty in inflation rates encourages variable rates.

Issues (cont.) zFlexibility of loan - can loan be repaid early (makes re-finance attractive when interest rates drop). Issue of contingencies. zUp-front expenses: lawyer fees, taxes, marketing bonds, etc.- 10% common zTerm of loan zSource of funds

Sinking Funds zAct as reverse borrowing - save revenues to cover end-of-life costs to restore mined lands or decommission nuclear plants. zLow risk investments are used, so return rate is lower.

Recall: Annuities (a.k.a uniform values) zConsider the PV of getting the same amount ($1) for many years yLottery pays $A / yr for n yrs at i=5% y----- Subtract above 2 equations yWhen A=1 the right hand side is called the “annuity factor”

Uniform Values - Application zNote Annual (A) values also sometimes referred to as Uniform (U).. z$1000 / year for 5 years example zP = U*(P|U,i,n) = (P|U,5%,5) = zP = 1000*4.329 = $4,329 zRelevance for loans?

Borrowing zSometimes we don’t have the money to undertake - need to get loan zi=specified interest rate zA t =cash flow at end of period t (+ for loan receipt, - for payments) zR t =loan balance at end of period t zI t =interest accrued during t for R t-1 zQ t =amount added to unpaid balance zAt t=n, loan balance must be zero

Equations zi=specified interest rate zA t =cash flow at end of period t (+ for loan receipt, - for payments) zI t =i * R t-1 zQ t = A t + I t zR t = R t-1 + Q t R t = R t-1 + A t + I t z R t = R t-1 + A t + (i * R t-1 )

Annual, or Uniform, payments zAssume a payment of U each year for n years on a principal of P zR n =-U[1+(1+i)+…+(1+i) n-1 ]+P(1+i) n zR n =-U[((1+i) n -1)/i] + P(1+i) n zUniform payment functions in Excel zSame basic idea as earlier slide

Example zBorrow $200 at 10%, pay $ at end of each of first 2 years zR 0 =A 0 =$200 zA 1 = -$115.24, I 1 =R 0 *i = (200)*(.10)=20 zQ 1 =A 1 + I 1 = zR 1 =R 0 +Q t = zI 2 =10.48; Q 2 = ; R 2 =0

Various Repayment Options zSingle Loan, Single payment at end of loan zSingle Loan, Yearly Payments zMultiple Loans, One repayment

Notes zMixed funds problem - buy computer zBelow: Operating cash flows At zFour financing options (at 8%) in At section below

Further Analysis (still no tax) zMARR (disc rate) equals borrowing rate, so financing plans equivalent. zWhen wholly funded by borrowing, can set MARR to interest rate

Effect of other MARRs (e.g. 10%) z‘Total’ NPV higher than operation alone for all options yAll preferable to ‘internal funding’ yWhy? These funds could earn 10% ! yFirst option ‘gets most of loan’, is best

Effect of other MARRs (e.g. 6%) zNow reverse is true yWhy? Internal funds only earn 6% ! yFirst option now worst