Borrowing, Depreciation, Taxes in Cash Flow Problems

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

2. 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

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

4. 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’

5. 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

6. 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)

7. 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.

8. 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.

9. 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.

10. 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

11. 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.

12. 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”

13. 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?

14. 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

15. 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)

16. 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

17. 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

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

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

20. 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

21. 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

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

23. Bonds • Done similar to loans, but mechanically different • Usually pay annual interest only, then repay interest and entire principal in yr. n • Similar to financing option #3 in previous slides • There are other, less common bond methods

24. Tax Effects of Financing • Companies deduct interest expense • Bt=total pre-tax operating benefits • Excluding loan receipts • Ct=total operating pre-tax expenses • Excluding loan payments • At= Bt- Ct = net pre-tax operating cash flow • A,B,C: financing cash flows • A*,B*,C*: pre-tax totals / all sources

25. Depreciation • Decline in value of assets over time • Buildings, equipment, etc. • Accounting entry - no actual cash flow • Systematic cost allocation over time • Main emphasis is to reduce our tax burden • Government sets dep. Allowance • P=asset cost, S=salvage,N=est. life • Dt= Depreciation amount in year t • Tt= accumulated (sum of) dep. up to t • Bt= Book Value = Undep. amount = P - Tt

26. After-tax cash flows • Dt= Depreciation allowance in t • It= Interest accrued in t • + on unpaid balance, - overpayment • Qt= available for reducing balance in t • Wt= taxable income in t; Xt= tax rate • Tt= income tax in t • Yt= net after-tax cash flow

27. Equations • Dt= Depreciation allowance in t • It= Interest accrued in t • Qt= available for reducing balance in t • So At = Qt - It • Wt= At - Dt - It (Operating - expenses) • Tt= Xt Wt • Yt= A*t - Xt Wt (pre tax flow - tax) OR • Yt= At + At - Xt (At-Dt -It)

28. Simple example • Firm: $500k revenues, $300k expense • Depreciation on equipment $20k • No financing, and tax rate = 50% • Yt= At + At - Xt (At-Dt -It) • Yt=($500k-$300k)+0-0.5($200k-$20k) • Yt= $110k

29. Depreciation Example • Simple/straight line dep: Dt= (P-S)/N • Equal expense for every year • $16k compressor, $2k salvage at 7 yrs. • Dt= (P-S)/N = $14k/7 = $2k • Bt= 16,000-2t, e.g. B1=$14k, B7=$2k • Salvage Value is an investing activity that is considered outside the context of our income tax calculation • If we sell asset for salvage value, no further tax implications (IN THIS COURSE WE ASSUME THIS TO SIMPLIFY) • If 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) • We show salvage value on separate lines to emphasize this.

30. Accelerated Dep’n Methods • Depreciation greater in early years • Sum of Years Digits (SOYD) • Let Z=1+2+…+N = N(N+1)/2 • Dt= (P-S)*[N-(t-1)]/Z, e.g. D1=(N/Z)*(P-S) • D1=(7/28)*$14k=$3,500, D7=(1/28)*$14k • Declining balance: Dt= Bt-1*r (where r is rate) • Bt=P*(1-r)t,Dt= P*r*(1-r)t-1 • Requires us to keep an eye on B • Typically r=2/N - aka double dec. balance

31. Ex: Double Declining Balance • Could solve P(1-r)N = S (find nth root) t Dt Bt 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 • Last year would need to be adjusted to consider salvage, D7=$124.96 • We get high allowable depreciation ‘expenses’ early - tax benefit • We will assume taxes are simple and based on cash flows (profits) • Realistically, they are more complex

33. First Complex Example • Firm will buy $46k equipment • Yr 1: Expects pre-tax benefit of $15k • Yrs 2-6: $2k less per year ($13k..$5k) • Salvage value $4k at end of 6 years • No borrowing, tax=50%, MARR=6% • Use SOYD and SL depreciation

34. Results - SOYD • D1=(6/21)*$42k = $12,000 • SOYD really reduces taxable income!

35. Results - Straight Line Dep. • NPV negative - shows effect of depreciation • Negative tax? Typically treat as credit not cash back • Projects are usually small compared to overall size of company - this project would “create tax benefits”

36. Let’s Add in Interest - Computer Again • Price $22k, $6k/yr benefits for 5 yrs, $2k salvage after year 5 • Borrow $10k of the $22k price • Consider single payment at end and uniform yearly repayments • Depreciation: Double-declining balance • Income tax rate=50% • MARR 8%

37. Single Repayment • Had to ‘manually adjust’ Dt in yr. 5 • Note loan balance keeps increasing • Only additional interest noted in It as interest expense

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

39. Leasing • ‘Make payments to owner’ instead of actually purchasing the asset • Since you do not own it, you can not take depreciation expense • Lease payments are just a standard expense (i.e., part of the Ct stream) • At= Bt -Ct ; Yt= At - At Xt • Tradeoff is lower expenses vs. loss of depreciation/interest tax benefits