Lecture Notes ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS Lecture Five

1. Lecture Notes ECON 437/837: ECONOMIC COST-BENEFIT ANALYSIS Lecture Five

2. DEVELOPMENT OF CASH FLOW (RESOURCE) STATEMENT

3. (+) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Benefits Less Costs Year of Project Life (-) Initial Investment Period Operating Stage Residual Value Project Life Project Cash Flow Profile

4. Components of Cash Flow Analysis A. Investment Plan • Need to reconcile timing of technical construction plans with the financing plan, demand module, and manpower availability B. Operating Plan • Need to reconcile market module with manpower module and minimum cash flows for operation of project

5. What Is the Total Cost of a Three Year Investment? Bt - Ct t0 t1 t2 t3 Time NPV010%=182.23 50 50 NPV310%=242.35 100 Opportunity Cost of Funds = 10% Investment Costs: a. Simple Sum = $200 b. At t0 = 50 + 100/(1.1)1 + 50/(1.1)2 =50 + 90.91 + 41.32 =$182.23 c. At t3 = 50(1.1)3 + 100(1.1)2 + 50(1.1)1 = $242.35 Accrued capital cost (i.e., interest during construction) is equal to $42.35 (Assumption that all expenditures are made at beginning of the period.)

6. Accrued Capital Cost during Construction • Concept of opportunity cost when investment covers more than one period. • It is not the nominal interest expenses required to serve debt. • Applies to the actual amount of investments made whether financed by equity or by debt. • Capitalized interests during construction are included in estimates of total investment cost.

7. Treatment of Depreciation • Concepts of depreciation expense used in calculating cash flow profile: • Tax depreciation or capital cost allowances (to estimate taxes) • Economic depreciation (to estimate residual values of assets)

8. Cash Receipts versus Sales Sales for Period + Accounts Receivable for Beginning of Period - Accounts Receivable for End of Period Cash Receipts for Period (Inflow) For Example: Sales1 = 10,000 Accounts Receivable0 = 5,000 Accounts Receivable1 = 8,000 Receipts = 10,000+(5,000-8,000) = 7,000

9. Uncollectable Receivables (Bad Debts) versus Sales • Uncollectable receivables are calculated as a percentage of the accounts receivable at the beginning of the period. Sales for Period + (Accounts Receivable for Beginning of Period -Accounts Receivable for End of Period) - Uncollectable Receivables Cash Receipts for Period (Inflow)

10. Uncollectable Receivables versus Sales (Cont’d) • Suppose, the accounts receivable are 20% of sales of current year and the uncollectable receivables are 10% of accounts receivable of previous year. Years 2000 2001 2002 2003 Sales (S) 4000 5000 6000 6000 Accounts Receivable (AR) 800 1000 1200 1200 Uncollectable Receivables (UR) - 80 100 120 Change in AR (ARt-1–ARt–URt) - -280 -300 -120 For Example, Year 2001: Sales2001 = 5,000 Accounts Receivable2000 = 800 Accounts Receivable2001 = 1,000 Uncollectable Receivables2001 = 80 Receipts = 5,000+(800-1,000)-80 = 4,720 For Example, Year 2002: Sales2002 = 6,000 Accounts Receivable2001 = 1,000 Accounts Receivable2002 = 1,200 Uncollectable Receivables2002 = 100 Receipts = 6,000+(1,000-1,200)-100 = 5,700

11. Cash Expenditures versus Purchases Purchases for Period + Accounts Payable at Beginning of Period - Accounts Payable at End of Period = Cash Expenditures for Period (Outflow) For Example: Purchases1 = 11,000 Accounts Payable0 = 6,000 Accounts Payable1 = 4,000 Expenditures = 11,000+(6,000-4,000) = 13,000

12. Accounting for Working Capital • Working Capital = Cash for Transactions + Accounts Receivables - Accounts Payables + Inventories + Prepaid Expenses - Accrued Liabilities • Very important part of investment in most projects • In Canada and USA, proportion of the Total Investment (Fixed Assets + Working Capital) that is working capital (WC) is about 30%: Proportion of WC in Total Investment =  0.30 WC FA + WC

13. Accounting for Working Capital (cont’d) Example: Estimation of the adequate working capital for an expansion project • Proposed expansion project: - FA for expansion project = $750 - WC proportion from the balance sheet of the existing firm = 25% • Find adequate working capital = $250: WC/(FA + WC) = 25%

14. Year 0 1 2 3 4 Operating Expenses Desired Cash Impact on Net Cash Flow 2000 400 -400 2500 500 -100 3200 640 -140 5000 1000 -360 0 0 +1000 Accounting for Working Capital (cont’d) • Cash held to carry out transactions is a use of cash • Increases in cash holdings is a cash outflow • Decreases in cash holdings is a cash inflow For Example: Desired stock of cash = 20% of Operating Expenses

15. Moving from Financial to Economic Analysis Restate financial revenues or physical outputs into their economic venues – willingness to pay or economic value of resources saved. Restate financial costs to economic opportunity costs. Identify and quantify externalities both positive and negative of project. Estimate economic values of externalities and include them as part of resource flows of the project. Identify sources and magnitudes of risks that affect economic outcomes. Adjust resource flows for the cost of managing such risks. Apply the economic opportunity cost of capital to determine the net economic resource flows to the economic NPV of project.

16. Integration of Movements in Prices, Inflation, and Exchange Rates

17. 1. Nominal Prices (Current prices) P1t, P2t, P3t……….. Pnt 2. Price Level PLt = in (Pit Wi) Where: i = Individual good or service included in the market basket; Pit= Price of the good or service (i) at a point in time (t); Wi= Weight given to the price of a particular good or service (i); and wi = 1 Note: it is generally useful to express the price level of a basket of goods and services at a specific point in time in terms of a price index (P ) P = P / P Where P = Price level in period (t) P = Price level for the base period (B) t I t I tL BL tL BL

18. t iR t-1 iR P - P t-1 iR P PtiR = Real price of good (i) as of a specific period 3. Changes in Price Level (Inflation) • Measured in terms of a price index: gPeI = ((PtI - PIt-1)/(PIt-1)) * 100 4. Real Prices PtiR = Pti / PtI Where Pti = nominal price of good or service (i) as of a point in time (t) PtI = Price level index at time period (t) 5. Changes in Real Prices Change in PtiR =

19. Example 1: Nominal Prices and Changes in Price level Assume Year 1 is base year Goods 1 2 3 Weights 0.2 0.5 0.3 Nominal Prices Year 1: P11 = 30P21 = 100 P31 = 50 PL1 = 0.2(30) + 0.5(100) + 0.3(50) PL1 = 71 PLB = 71 Price Index P I1 =1.00 Nominal Prices Year 2: P12 = 40P22 = 110 P32 = 40 PL2 = 0.2(40) + 0.5(110) + 0.3(40) PL2 = 75 P LB = 71 Price Index PI2 = 1.056

20. Example 1:Nominal Prices and Changes in Price Level (cont’d) • Assume Year 1 is base year • Goods 1 2 3 • Weights 0.2 0.5 0.3 • Nominal Prices Year 3: P13 =35P23=108 P33=60 • P L3 =0.2(35)+0.5(108)+0.3 (60) • P L3 =79 • Price Index P I3 =1.113 • INFLATION RATE • Changes in Price Level : Measured in terms of a price index • gPI2 = ((PI2 – PI1)/(PI1)) * 100 = ((1.056-1.00)/1.00))*100 = 5.63% • gPI3 = ((PI3 – PI2)/(PI2)) * 100 = ((1.113-1.056)/1.056)*100 = 5.33%

21. EXAMPLE 2: Real Prices and Changes in Real Prices Goods 1 2 3 Weights 0.2 0.5 0.3 Nominal Prices Year 1: P11 =30P21=100 P31=50 Price Index PI1 =1 Real Prices Year 1: P1R1=30/1 P2R1=100/1 P3R1=50/1 P1R1=30 P2R1=100 P3R1=50 Nominal Prices Year 2: P12 =40P22=110 P32=40 Price Index PI2 =1.056 Real Prices Year 2:P1R2=40/1.056 P2R2=110/1.056 P3R2=40/1.056 P1R2=37.87 P2R2=104.13 P3R2=37.87

22. EXAMPLE 2: Real Prices and Changes in Real Prices (Cont’d) Goods 1 2 3 Weights 0.2 0.5 0.3 Nominal Prices Year 3: P13 =35P23=108 P33=60 Price Index PI3 =1.113 Real Prices Year 3:P1R3=35/1.113 P2R3=108/1.113 P3R3=60/1.113 P1R3=31.46 P2R3=97.06 P3R3=53.92 Changes in Real Prices Year 2 Change in P1R2 = (P1R2 – P1R1) / (P1R1) = ((37.80-30)/30) ( (104.13-100)/100)((37.80-50)/50) = 0.26 = 0.04 = -0.24 Changes in Real Prices in Year 3 Change in P1R3 = (P1R3 - P1R2) / (P1R2) = ((31.46-37.87)/37.87) ((97.06-104.13)/104.13) ((53.92-37.87)/37.87) = - 0.17 = - 0.07 = 0.42

23.  P t+1 i  P = estimated nominal price of good i in year t+1 t+1 i t i = nominal price of good i in year t P t iR = estimated growth in real price of good i gP eI = assumed growth in price level index from year t to t+1 gP 6. Inflation Adjusted Values = Pti*(1 + gPtiR)*(1 + gPeI)

24. Example: Telephone charges over time: Satellite ProjectDue to changes in Technology and Deregulation real price of telephone calls are falling at 8% per year

25. Market vs Real Exchange Rates

26. EtM = 8 Rand / $US ItD = 1.0 ItUS = 1.0 I 1.0 EtR = E  = 8.0  = 8.0 Rand/$ I 1.0 US t M t D t Example • Initial year prices indexes in both countries assumed in project analysis to be equal to 1.0.

27. Germany France Italy Real effective Exchange Rates IF/IDItaly Real effective Exchange Rates IF/IDFrance Real effective Exchange Rates IF/IDGermany

28. Market vs Real Exchange Rates (cont’d)

29. Market vs Real Exchange Rates (cont’d) where K is a random variable with a mean of zero.

30. I + M R t 5 = * E E + + t 5 t 5 f I + t 5 (1.47) ´ = 8.0 10.65 (1.10) What is market exchange rate going to be in 5 years time ? Suppose that in the current year: Domestic Price Index = 1 and Foreign Price Index = 1 Using year 0 as the base year, E0M = E0R. Suppose E0M is 8 Rand/$US, E0R is also 8 Rand/$US. Now, assume that the real exchange rate remains constant. If gPf = 2%/p.a. Foreign rate of inflation If gPd = 8%/p.a. Domestic rate of inflation Idt+5= 1 (1.08)5 = 1.47 Ift+5= 1 (1.02)5 = 1.10 ERt+5 = 8 Rand/$ Therefore, if then: EMt+5= Rand/$US d

31. Inflation and Nominal Interest Rates • Nominal Interest Rate = i • Real Interest Rate = r • Risk Premium = R • Expected Growth (inflation) in Prices = gPe Given the factors above, nominal interest rate is calculated as: i = r + R + (1 + R + r) gPe

32. By using following information: Inflation rate (gPe) = 20% Risk Premium (R) = 0 Real Interest Rate (r) = 0.05 i = r + R + (1 + R + r) gPe = 0.05 + 0 + (1 + 0 + 0.05)* 0.20 = 0.26 Example Determination of Nominal Interest Rate:

33. Period 0 1.0 -1000 -1000 0 1 1.0 50 50 2 1.0 50 50 3 1.0 50 50 4 1.0 50 1000 1050 2. $1000 Loan @5% Interest & 20% Inflation Price index Loan Interest Loan Payment Cash Flow in Current Prices Cash Flow in year 0 Prices Net Present Value (Dis-Equilibrium Situation) 1.0 -1000 -1000 -1000 -487.24 1.20 50 50 41.67 1.44 50 50 34.72 1.728 50 50 28.94 2.074 50 1000 1050 506.37 3. $1000 Loan @ 26.0% Interest & 20% Inflation Price Index Loan Interest Loan Payment Cash Flow in Current Prices Cash Flow in year 0 Prices Net Present Value (Equilibrium Situation) 4. Undiscounted Change in Cash Flow =Case 1 - Case 3 in Year 0 Prices 1.0 -1000 -1000 -1000 0 0 1.2 260 260 216.67 -166.67 1.44 260 260 180.56 -130.56 1.728 260 260 150.46 -100.46 2.074 260 1000 1260 607.64 +442.36 Inflation and its Impact on Interest and Principal Payments 1. $1000 Loan @5% Interest & No Inflation Price Index Loan Interest Loan Payment Cash Flow in Year 0 Prices Net Present Value (Equilibrium Situation)

34. Steps for Undertaking Financial Analysis 1. Estimate Real Prices, (Pit /Pt level) for project life 2. Make Assumptions about Future Inflation Rate 3. Calculate Changes in Inflation-Adjusted Prices 4. Calculate estimated Nominal Interest Rate 5. Determine Cash Requirements (Nominal) 6. Determine Financing Requirements (Nominal) 7. Estimate Taxable Income and Income Taxes (Nominal) 8. Construct Pro-Forma Cash Flow Statement in Nominal Values 9. Calculate Nominal Net Cash Flows from Different Points of View 10. Deflate Nominal Value by General Price Index for Each Year to Obtain Real Cash Flow Statements 11. Calculate Debt Service Ratios (ADSCR, LLCR) for Total Investment (Banker’s) Point of View 12. Calculate NPV and IRR for Owner’s Point of View

35. Impact of Expected Change in Real Exchange Rate on Real Interest Rates • US ($) LoanYen (Y) Loan Nominal interest rate: iUS = rUS + (1+rUS)gPUS iJ = rJ + (1+rJ)gPJ • Market exchange rate: E0M = (#$/Y) E0M = E0R (I0US/I0J) E1M = E1R (I1US/I1J)

36. Define the price indices in US and Japan so that

37. In equilibrium the nominal return of giving a loan to Japan in Yen must be same as making a loan in US$ in the US.

38. The return in dollars from a loan you make to Japan is given by the real rate of interest you earn in Japan plus any addition (or reduction) in dollars you receive when you convert the Yen repayments into dollars. • In equilibrium the nominal and real return of giving a loan to Japan in Yen must be same as making a loan in US $ in the US.

39. An Example Assume that Yen is appreciating at an annual rate of 3%. E1R = E0R (1.03) The $ is devaluing 3% a year relative to the Yen. Alternatively, the Yen is appreciating 3% a year.

40. Example $ 1,000 loan • iUS = rUS + (1+rUS)gPUS • Market exchange rate: • E0M = 0.01 $/Y • rUS = 0.05 • Expected rate of inflation in US (gPUS) = 0.04/year • iUS = rUS + (1+rUS)gPUS • iUS = 0.05 + (1+0.05)0.04 • iUS = 0.092 • If one year loan made to US borrower: • Year 0 1 • Loan -1000 • Repayment +1000 • Interest 92 • Total -1000 +1092

41. Real Interest Rate in Yen (1+rUS) = ($1/ E0R)(1 + rJ) (E1R) (1+rUS) = (1 + rJ) (E1R/E0R) where E0R is the real exchange rate in year zero and E1R is real exchange rate in year 1. Let us assume E1R/E0R = 1.03, i.e. the dollar is devaluing at 3 percent a year relative to the Yen. Hence, if rUS = 0.05, 1.05 = (1 + rJ) (1.03) rJ = (1.05/1.03) – 1 rJ = 0.019417476

42. Expected rate of inflation in Japan (gPJ) is 0.01/year • Hence, the nominal interest rate in Yen is, iJ = rJ + (1+rJ) gPJ iJ = 0.019417476 + (1+ 0.019417476)0.01 = 0.019417476 + 0.01019417476 = 0.02961165 Nominal interest rate in Japan is 2.961%. • If US$ 1,000 loan made to Japan in Yen, US $ 1,000 is equal to 1,000/EM = 1000/0.01 = 100,000 Yen Hence nominal interest due on 100,000 Yen loan is 2,961.165076. If one year loan made to US borrower: Year 0 1 Loan -100,000 Repayment +100,000 Interest 2,961 Total -100,000 +102,961

43. What will E1M be? • Hence, the market exchange rate in year 1 is, • E1M = E1R (I1US/I1J) • E1R = E0R (1.03) • E1R = 0.01 (1.03) = 0.0103 • E1M = E1R (I1US/I1J) = 0.0103 (1.04/1.01) • = 0.010609594 • Repayment plus interest in US$ in year 1 of Yen loan, • = (102,961 Y) (0.010609594) = 1,092 US$ • This is exactly the same as if loan made in US dollars at 9.2%.

44. Calculation of Income Tax Deduction for Foreign LoansBorrowing from Japan • Interest expense deduction if US company borrows Yen loan of 100,000 Y. Nominal interest rate in Yen = 0.02961165 Interest expense = 2,961.17 US $ equivalent in Year 1 = 2,961.17 (E1M) = 2,961.17 (0.01060594) = $31.40 • This is less than $92 interest expense that is allowed as tax deduction on an equivalent US $ loan of US $ 1,000. • Need to consider exchange rate loss in US dollars when loan paid back. • In order to pay back 100,000 Yen in year 1 the US borrower will need 100,000 (E1M) dollar or 100,000 (0.01060594) = $1060.60. • There has been a foreign exchange capital loss of $60.60 due to exchange rate devaluation. • Total tax deduction should be interest expense + foreign exchange loss or 31.40 + 60.60 = $92.00.

45. US$ 1,000 Loan made in the USA with the Real Interest of 5%

46. US$ 1,000 Loan in equivalent to 100,000 Yen made to Japan Japan

47. IMPACTS OF INFLATION

48. Impacts of Inflation:Direct Impacts • On Financing of Investments • Cost escalation due to inflation vs. • Over runs of real expenditures • Planning for cost escalation due to inflation in normal and should be part of financing plan • On Nominal Interest Expenses Paid • On Real Desired Cash Balances • On Real Accounts Receivable and Accounts Payable

49. Impacts of Inflation:Tax Impacts • Interest Expenses Deductions • Depreciation Expenses • Inventories and Cost of Goods Sold

50. Period 0 1.0 -1000 -1000 0 1 1.0 50 50 2 1.0 50 50 3 1.0 50 50 4 1.0 50 1000 1050 2. $1000 Loan @5% Interest & 20% Inflation Price index Loan Interest Loan Payment Cash Flow in Current Prices Cash Flow in year 0 Prices Net Present Value (Dis-Equilibrium Situation) 1.0 -1000 -1000 -1000 -487.24 1.20 50 50 41.67 1.44 50 50 34.72 1.728 50 50 28.94 2.074 50 1000 1050 506.37 3. $1000 Loan @ 26.0% Interest & 20% Inflation Price Index Loan Interest Loan Payment Cash Flow in Current Prices Cash Flow in year 0 Prices Net Present Value (Equilibrium Situation) 4. Undiscounted Change in Cash Flow =Case 1 - Case 3 in Year 0 Prices 1.0 -1000 -1000 -1000 0 0 1.2 260 260 216.67 -166.67 1.44 260 260 180.56 -130.56 1.728 260 260 150.46 -100.46 2.074 260 1000 1260 607.64 +442.36 Direct Impacts: Inflation and its Impact on Interest and Principal Payments 1. $1000 Loan @5% Interest & No Inflation Price Index Loan Interest Loan Payment Cash Flow in Year 0 Prices Net Present Value (Equilibrium Situation)