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

2. 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

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

4. 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’

5. 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

6. 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)

7. 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.

8. 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.

9. 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.

10. 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

11. 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.

12. 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”

13. 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) = 4.329 zP = 1000*4.329 = $4,329 zRelevance for loans?

14. 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

15. 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 )

16. 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

17. 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

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

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

20. 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

21. 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

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

23. 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

24. 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

25. Depreciation zDecline in value of assets over time yBuildings, equipment, etc. yAccounting entry - no actual cash flow ySystematic cost allocation over time yMain emphasis is to reduce our tax burden 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

26. 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

27. 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 )

28. 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

29. 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 sell asset for salvage value, no further tax implications (IN THIS COURSE WE ASSUME THIS TO SIMPLIFY) yIf we sell asset for higher than salvage value, we pay taxes since we received depreciation expense benefits (but we will generally ignore this since its not the focus of the course) yWe show salvage value on separate lines to emphasize this.

30. 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 (where r is rate) yB t =P*(1-r) t, D t = P*r*(1-r) t-1 yRequires us to keep an eye on B yTypically r=2/N - aka double dec. balance

31. 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**

32. Notes on Example zLast year would need to be adjusted to consider salvage, D 7 =$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

33. 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

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

35. 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”

36. 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%

37. 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

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

39. 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