1. Borrowing, Depreciation, Taxes in Cash Flow Problems H. Scott Matthews 12-706 / 19-702 /73-359 Lecture 5

2. Admin Issues zWho bought Boardman book? Can return. zCampbell Textbook due today. First 20 names will be sent zTA Office Hours in CEE Lounge (PH 118 hallway near my office) yJoe and Paulina will swap coverage next week (i.e, go to office hours in lounge, but look for Joe instead)

3. 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’

4. Goal: Find Cash Flows after taxes 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

5. After-tax cash flows zD t = Depreciation allowance in t zI t = Interest accrued in t y+ on unpaid balance, - overpayment yQ t = available for reducing balance in t zW t = taxable income in t; X t = tax rate zT t = income tax in t zY t = net after-tax cash flow

6. Equations zD t = Depreciation allowance in t zI t = Interest accrued in t yQ t = available for reducing balance in t ySo A t = Q t - I t zW t = A t -D t -I t (Operating - expenses) zT t = X t W t zY t = A* t - X t W t (pre tax flow - tax) OR zY t = A t + A t - X t (A t -D t -I t )

7. Simple example zFirm: $500k revenues, $300k expense yDepreciation on equipment $20k yNo financing, and tax rate = 50% zY t = A t + A t - X t (A t -D t -I t ) zY t =($500k-$300k)+0-0.5 ($200k-$20k) zY t = $110k

8. Notes zMixed funds problem - buy computer zBelow: Operating cash flows At zFour financing options in At

9. 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

10. Effect of other MARRs (e.g. 10%) z‘Total’ NPV higher than operation alone for all options yAll preferable to ‘internal funding’ (equity financing) yWhy? Internal funds could earn 10%, we’re only paying 8% yFirst option ‘gets most of loan’, is best

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

12. First Complex Example zFirm will buy $46k equipment yYr 1: Expects pre-tax benefit of $15k yYrs 2-6: $2k less per year ($13k..$5k) ySalvage value $4k at end of 6 years yNo borrowing, tax=50%, MARR=6% yUse SOYD and SL depreciation

13. Results - SOYD zD1=(6/21)*$42k = $12,000 zSOYD really reduces taxable income!

14. Results - Straight Line Dep. zNPV negative - shows effect of depreciation (why lower?) yNegative tax? Typically treat as credit not cash back yProjects are usually small compared to overall size of company - this project would “create tax benefits”

15. Let’s Add in Interest - Computer Again zPrice $22k, $6k/yr benefits for 5 yrs, $2k salvage after year 5 yBorrow $10k of the $22k price yConsider single payment at end and uniform yearly repayments yDepreciation: Double-declining balance yIncome tax rate=50% yMARR 8%

16. Single Repayment zHad to ‘manually adjust’ D t in yr. 5 zNote loan balance keeps increasing yOnly additional interest noted in I t as interest expense

17. Uniform payments zNote loan balance keeps decreasing zNPV of this option is lower - should choose previous (single repayment at end).. not a general result

18. Leasing z‘Make payments to owner’ instead of actually purchasing the asset ySince you do not own it, you can not take depreciation expense yLease payments are just a standard expense (i.e., part of the C t stream) yA t = B t - C t ; Y t = A t - A t X t yTradeoff is lower expenses vs. loss of depreciation/interest tax benefits

19. Social Discount Rate zRate used to make investment decisions for society zDiscounting rooted in consumer preference zWe 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

20. Intergenerational effects zWe have tended to discuss only short term investment analyses (e.g. 5 yrs) yWhat about effects in distant future? yCalled intergenerational effects zEconomists agree that discounting should be done for public projects yDo not agree on positive discount rate

21. Discounting handout zHow much do/should we care about people born after we die? yHigher the discount rate, the less future values will count compared to today zEthically, no one’s interests should count more than another’s yImplies there is no justification for discounting across long time periods yCalled ‘equal standing’

22. Climate Change zDiscussions ongoing about how best to manage global CO2 emissions to limit effects of global change zShould we sacrifice short-run economic growth to do something to improve environment and leave resources for the future? yReally asking 2 separate questions!

23. Two Questions zWhat duty do we have to make sacrifices for future generations? zIf we sacrifice, what is the optimal policy to maximize benefit? ySo we should compare global change proposals with alternatives yPerhaps higher R&D spending on science or medicing would have higher benefits!

24. Hume’s Law zThus discounting 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

25. Some evidence zCropper et al surveyed 3000 homes yAsked about saving lives in the future yFound a 4% discount rate for lives 100 years per now zEqual standing does not imply different generations have equal claims to present resources! yHarsanyi says only do so if their marginal gain is higher than our loss

26. More evidence 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) zBased on these arguments, what discount rates should we use for policy problems (eg climate)

27. Government Discount Rates zUS Government Office of Management and Budget (OMB) Circular A-94 yhttp://www.whitehouse.gov/omb/circulars/a094/a094.html yDiscusses how to do BCA and related performance studies yMatch real values with real discount rates, etc yHow to do sensitivity analysis / which inputs to vary yWhat discount, inflation, etc. rates to use yBasically says “use this rate, but do sensitivity analysis with nearby rates”

28. OMB Circular A-94, Appendix C zProvides the current suggested values to use for federal government analyses yhttp://www.whitehouse.gov/omb/circulars/a094/a94_appx-c.htmlhttp://www.whitehouse.gov/omb/circulars/a094/a94_appx-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?

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

30. Real Discount Rates (from A-94)

31. Effect of these Discount Rates zThese 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?

32. Next Up: Sensitivity Analysis zSkim Clemen Chapter 5 Refers to decision/trees, etc that we have not done yet.