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

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Admin Issues zHW 1 Solutions zHW 2 Due Wednesday yAll Office hours this week zPipeline case later today

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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

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

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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

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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

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

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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

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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

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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

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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

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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 )

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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

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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.

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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

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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**

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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

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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

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

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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”

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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%

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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

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

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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

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Show of Hands Example zChoice #1: y$50 today or $100 paid 1 year from now? yWhy? zChoice #2: y$50 to be paid in 5 years or $100 in 6 years? yWhy?

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Hyperbolic Discounting zBehavioral economics: yWe generally prefer smaller, sooner payoffs to larger, later payoffs when the smaller payoffs would be imminent; yWhen same payoffs are distant in time, we tend to prefer the larger, even though the time lag (e.g., 1 year) would be the same

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Hyperbolic Discounting zOur “preferences” follow a hyperbolic curve rather than the conventional, exponential curve that would produce consistent choice over time zWe are time inconsistent (we don’t perceive the same tradeoff values today vs. in 5+ years) Recall: Continuous P=F * e -in zP=F /(1+kn) yWhere k is still the steepness of our tradeoff

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Hyperbolic versus standard

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Hyperbolic Discounting- Implications zIf we actually have hyperbolic preferences zWhat do our discount rates look like? zHow would that affect our preferences for social projects, especially those with long time horizons? yTime inconsistency known in advance

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Pipeline Case zHand them In zDiscussion / Overview zModels Built zSample Model zWhat is Missing in these models? zDid they build it?

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