1. Project Finance (part 2) H. Scott Matthews 12-706/73-359 Lecture 12 - Oct. 8, 2003

2. Admin Issues zPipeline case out - read for Monday yBrief discussion on preparing cases zHW 2 back today zProject groups/ideas due today yShort (1/2 page) description of project, client zMidterm

3. Notes on Notation zPV = $FV / (1+i) n = $FV * [1 / (1+i) n ] yBut [1 / (1+i) n ] is only function of i,n y$1, i=5%, n=5, [1/(1.05) 5 ]= 0.784 = (P|F,i,n) yWould see tables like this in ‘old’ textbooks zAs shorthand: yFuture value of Present: (P|F,i,n) xSo PV of $500, 5%,5 yrs = $500*0.784 = $392 yPresent value of Future: (F|P,i,n) yWe’ll see similar notations for other types

4. Timing of Future Values zNoted last time that we assume ‘end of period’ values zWhat is relative difference? zConsider comparative case: y$1000/yr (uniform) Benefit for 5 years @ 5% yAssume case 1: received beginning yAssume case 2: received end

5. Timing of Benefits zDraw 2 cash flow diagrams zNPV 1 = 1000 + 1000/1.05 + 1000/1.05 2 + 1000/1.05 3 + 1000/1.05 4 yNPV 1 =1000 + 952 + 907 + 864 + 823 = $4,545 zNPV 2 = 1000/1.05 + 1000/1.05 2 + 1000/1.05 3 + 1000/1.05 4 + 1000/1.05 5 yNPV 2 = 952 + 907 + 864 + 823 + 784 = $4,329 zNPV 1 - NPV 2 ~ $216 zNotation: (P|U,i,n)

6. Relative NPV Analysis zIf comparing, can just find ‘relative’ NPV compared to a single option yE.g. beginning/end timing problem yNet difference was $216 zAlternatively consider ‘net amounts’ yNPV 1 =1000 + 952 + 907 + 864 + 823 = $4,545 yNPV 2 = 952 + 907 + 864 + 823 + 784 = $4,329 y‘Cancel out’ intermediates, just find ends yNPV 1 is $216 greater than NPV 2

7. Uniform Values - Theory zAssume ‘end of period’ values zA = U/(1+i) +U/(1+i) 2 +..+ U/(1+i) n zA = U*[(1+i) -1 +(1+i) -2 +..+ (1+i) -n ] zA(1+i)=U*[1+(1+i) -1 +(1+i) -2 +..+ (1+i) 1-n ] zA(1+i) - A = U*[1 - (1+i) -n ] zA = U*[1 - (1+i) -n ] / i = U*(P|U,i,n)

8. Uniform Values - Application zRecall $1000 / year for 5 years example zStream = U*(P|U,i,n) = U*[1 - (1+i) -n ] / i z(P|U,5%,5) = 4.329 zStream = 1000*4.329 = $4,329 = NPV 2

9. 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.

10. Borrowing zNumerous arrangements possible: ybonds and notes ybank loans and line of credit ymunicipal bonds (with tax exempt interest) zLenders require a real return - borrowing interest rate exceeds inflation rate.

11. 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.

12. 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

13. 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

14. 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 )

15. Option: 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

16. 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

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

18. Note on Taxes zCompanies pay tax on net income zIncome = Revenues - Expenses zThere are several types of expenses that we care about yInterest expense of borrowing yDepreciation (can only do if you own asset) yThese are also called ‘tax shields’

19. 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

20. 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

21. 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

22. 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**

23. 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

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 =net pre-tax operating cash flow zA,B,C: financing cash flows zA*,B*,C*: pre-tax totals / all sources

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

26. 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

27. 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

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

29. 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

30. 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 )

31. 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

32. 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

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

34. Results - Straight Line Dep. zNow NPV is negative - shows effect of depreciation method on decision yNegative tax? Typically a credit not cash back

35. 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%

36. 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

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