Social Discount Rate

1. Social Discount Rate 12-706 / 19-702

2. Admin Issues • Schedule changes: • No Friday recitation – will do in class Monday • Pipeline case study writeup – still Monday • Format expectations: • Framing of problem (see p. 7!), • Answer/justify with preliminary calculations • Don’t just estimate the answer! • Do not need to submit an excel printout, but feel free to paste a table into a document • Length: Less than 2 pages.

3. Real and Nominal Values • Nominal: ‘current’ or historical data • Real: ‘constant’ or adjusted data • Use deflator or price index for real • Generally “Real” has had inflation/price changes factored in and nominal has not • For investment problems: • If B&C in real dollars, use real disc rate • If B&C in nominal dollars, use nominal rate • Both methods will give the same answer

4. Similar to Real/Nominal : Foreign Exchange Rates / PPP • Big Mac handout • Common Definition of inputs • Should be able to compare cost across countries • Interesting results? Why? • What are limitations?

5. Is it worth to spend $1 million today to save a life 10 years from now? • How about spending $1 million today so that your grandchildren can have a lifestyle similar to yours?

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

7. Social Discount Rate • Rate used to make investment decisions for society • Most people tend to prefer current, rather than future, consumption • Marginal rate of time preference (MRTP) • Face opportunity cost (of foregone interest) when we spend not save • Marginal rate of investment return

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

9. Government Discount Rates • US Government Office of Management and Budget (OMB) Circular A-94 • http://www.whitehouse.gov/omb/circulars/a094/a094.html • Discusses how to do BCA and related performance studies • What discount, inflation, etc. rates to use • Basically says “use this rate, but do sensitivity analysis with nearby rates”

10. OMB Circular A-94, Appendix C • Provides the current suggested values to use for federal government analyses • http://www.whitehouse.gov/omb/circulars/a094/a94_appx-c.html • Revised yearly, usually “good until January of the next year” • How would the government decide its discount rates? • What is the government’s MARR?

11. Historic Nominal Interest Rates (from OMB A-94)

12. Real Discount Rates (from A-94)

13. What do people think • Cropper et al surveyed 3000 homes • Asked about saving lives in the future • Found a 4% discount rate for lives 100 years from now

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

15. If future generations will be better off than us anyway • Then we might have no reason to make additional sacrifices • There might be ‘special standing’ in addition to ‘equal standing’ • Immediate relatives vs. distant relatives • Different discount rates over time • Why do we care so much about future and ignore some present needs (poverty)

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

17. Comprehensive Everglades Restoration Project • Comprehensive project to restore natural water flow to the Florida Everglades. • Enhance water supply to South Florida region. • Provide continuous flood protection. See more info at http://www.evergladesplan.org/

18. Indian River Lagoon-South (IRLS) • Part of Everglades Restoration Project. • Total Cost of $1.21 billion. • Annual Benefits of $159 million after project is completed in 2015. • Find NPV of first 25 years of project.

19. $159 per year 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 $0.425 $2.043 $12.62 All values are in millions $447.3 $748.3 IRLS Cash Schedule

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

21. NPV of Project

22. Borrowing, Depreciation, Taxes in Cash Flow Problems H. Scott Matthews 12-706 / 19-702

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

24. Without taxes, cash flows simple • A = B - C • Cash flow = benefits - costs • Or.. Revenues - expenses

25. Notes on Tax deductibility • Reason we care about financing and depreciation: they affect taxes owed • For personal income taxes, we deduct items like IRA contributions, mortgage interest, etc. • Private entities (eg businesses) have similar rules: pay tax on net income • Income = Revenues - Expenses • There are several types of expenses that we care about • Interest expense of borrowing • Depreciation (can only do if own the asset) • These are also called ‘tax shields’

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

27. Investment types • Debt financing: using a bank or investor’s money (loan or bond) • DFD:disbursement (payments) • DFR:receipts (income) • DFI: portion tax deductible (only non-principal) • Equity financing: using own money (no borrowing)

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

29. Borrowing • Numerous arrangements possible: • bonds and notes (pay dividends) • bank loans and line of credit (pay interest) • municipal bonds (with tax exempt interest) • Lenders require a real return - borrowing interest rate exceeds inflation rate.

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

31. Issues (cont.) • Flexibility of loan - can loan be repaid early (makes re-finance attractive when interest rates drop). Issue of contingencies. • Up-front expenses: lawyer fees, taxes, marketing bonds, etc.- 10% common • Term of loan • Source of funds

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

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

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

35. Borrowing • Sometimes we don’t have the money to undertake - need to get loan • i=specified interest rate • At=cash flow at end of period t (+ for loan receipt, - for payments) • Rt=loan balance at end of period t • It=interest accrued during t for Rt-1 • Qt=amount added to unpaid balance • At t=n, loan balance must be zero

36. Equations • i=specified interest rate • At=cash flow at end of period t (+ for loan receipt, - for payments) • It=i * Rt-1 • Qt= At + It • Rt= Rt-1 + Qt <=>Rt= Rt-1 + At + It • Rt= Rt-1 + At + (i * Rt-1)

37. Annual, or Uniform, payments • Assume a payment of U each year for n years on a principal of P • Rn=-U[1+(1+i)+…+(1+i)n-1]+P(1+i)n • Rn=-U[((1+i)n-1)/i] + P(1+i)n • Uniform payment functions in Excel • Same basic idea as earlier slide

38. Example • Borrow $200 at 10%, pay $115.24 at end of each of first 2 years • R0=A0=$200 • A1= -$115.24, I1=R0*i = (200)*(.10)=20 • Q1=A1 + I1 = -95.24 • R1=R0+Qt = 104.76 • I2=10.48; Q2=-104.76; R2=0

39. Various Repayment Options • Single Loan, Single payment at end of loan • Single Loan, Yearly Payments • Multiple Loans, One repayment

40. Notes • Mixed funds problem - buy computer • Below: Operating cash flows At • Four financing options (at 8%) in At section below

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

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

43. Effect of other MARRs (e.g. 6%) • Now reverse is true • Why? Internal funds only earn 6% ! • First option now worst