1. Borrowing, Depreciation, Taxes in Cash Flow Problems H. Scott Matthews 12-706 / 19-702 /73-359 Lecture 4

2. Admin Issues zTextbook update? 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) zHW 1 - average: 26/30 zComments - generally good. Please use “complete sources” as if writing a term paper. For websites give complete URL. yThink more about how to “present” your work. Visuals, simple tables, etc. zFor next time, read RFF Handout (posted)

3. Textbook Spreadsheets zDidn’t get to this last time: http://www.uq.edu.au/economics/bca/ z“other users”.. login: “user”, pwd: “abc2004” zYou can download spreadsheet files referenced in Campbell book chapters

4. Theme: Cash Flows zStreams of benefits (revenues) and costs over time => “cash flows” zThis is our focus for next few classes 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

5. 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’

6. 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

7. Depreciation zDecline in value of assets over time yBuildings, equipment, etc. yAccounting entry - no actual cash flow ySystematic cost allocation over time zGovernment sets dep. Allowance yP=asset cost, S=salvage,N=est. life yD t = Depreciation amount in year t yT t = accumulated (sum of) dep. up to t yB t = Book Value = Undep. amount = P - T t

8. Depreciation Example zSimple/straight line dep: D t = (P-S)/N yEqual expense for every year y$16k compressor, $2k salvage at 7 yrs. yD t = (P-S)/N = $14k/7 = $2k yB t = 16,000-2t, e.g. B 1 =$14k, B 7 =$2k zSalvage Value is an investing activity that is considered outside the context of our income tax calculation yIf we end up selling asset for salvage value, no further tax implications yIf we end up selling asset for higher than salvage value, we may pay additional taxes since we received depreciation expense benefits (but we will generally ignore this)

9. Accelerated Dep’n Methods zDepreciation greater in early years zSum of Years Digits (SOYD) yLet Z=1+2+…+N = N(N+1)/2 yD t = (P-S)[N-(t-1)]/Z, e.g. D 1 =(N/Z)*(P-S) yD 1 =(7/28)*$14k=$3,500, D 7 =(1/28)*$14k zDeclining balance: D t = B t-1 r (r is rate) yB t =P(1-r) t, D t = Pr(1-r) t-1 yRequires us to keep an eye on B yTypically r=2/N - aka double dec. balance

10. Ex: Double Declining Balance zCould solve P(1-r) N = S (find nth root) tDtBt 0-$16,000 1(2/7)*$16k=$4,571.43$11,428.57 2(2/7)*$11,428=$3265.31$8,163.26 3$2332.36$5,830.90 4$1,665.97$4,164.93 5$1,189.98$2,974.95 6$849.99$2,124.96 7$607.13**$1,517.83**

11. Notes on Example zLast year would need to be adjusted to consider salvage, D7=$124.96 zWe get high allowable depreciation ‘expenses’ early - tax benefit zWe will assume taxes are simple and based on cash flows (profits) yRealistically, they are more complex

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 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. Uniform Values - Theory zFind present value of n payment of U zAssume end of period values zP = U/(1+i) +U/(1+i) 2 +..+ U/(1+i) n y(P|U,i,n) = $1[(1+i) -1 +(1+i) -2 +..+ (1+i) -n ] z[(1+i) -1 +(1+i) -2 +..+ (1+i) -n ] = “A” z[1+(1+i) -1 +(1+i) -2 +..+ (1+i) 1-n ] = A(1+i) zA(1+i) - A = [1 - (1+i) -n ] zA = [1 - (1+i) -n ] / i, ….so zP = U*(P|U,i,n) = U*[1 - (1+i) -n ] / i

16. Uniform Values - Application zRecall $1000 / year for 5 years example zP = U*(P|U,i,n) = U*[1 - (1+i) -n ] / i z(P|U,5%,5) = 4.329 zP = 1000*4.329 = $4,329

17. 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)

18. 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.

19. 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.

20. 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.

21. 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

22. 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.

23. 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

24. 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 )

25. 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

26. Example zBorrow $200 at 10%, pay $115.24 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 = -95.24 zR 1 =R 0 +Q t = 104.76 zI 2 =10.48; Q 2 =-104.76; R 2 =0

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

28. Tax Effects of Financing zCompanies deduct interest expense zB t =total pre-tax operating benefits yExcluding loan receipts zC t =total operating pre-tax expenses yExcluding loan payments zA t = B t- C t = net pre-tax operating cash flow zA,B,C: financing cash flows zA*,B*,C*: pre-tax totals / all sources

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

30. 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

31. 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

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

33. Bonds zDone similar to loans, but mechanically different zUsually pay annual interest only, then repay interest and entire principal in yr. n ySimilar to financing option #3 in previous slides yThere are other, less common bond methods

34. 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

35. 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 )

36. 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

37. 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%

38. 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

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

40. 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