Lecture Ten

1. Updated: 7 May 2007 FINA 522: Project Finance and Risk Management Lecture Ten

2. PRINCIPLES OF CONTRACTING, RISK SHARING AND RISK REDUCTION

3. Risk Management • Problem: • Many projects have • large investment outlays • long periods of project payout • incomplete sharing of information and technology, especially with foreign investors • differences in the ability of the parties to bear risks • unstable contracts • Projects may be attractive in aggregate but are unattractive to one or more parties due to uncertainties about sharing risks and returns • The result is that attractive projects are not being undertaken

4. DESIGNING CONTRACTS FOR CLIENT SPECIFIC PROJECTS • EXAMPLES: • Solid Waste Disposal Plants • Water Supply Projects • Power Purchase Agreements • Road Concessions Contracts are required before investors will be willing to undertake projects.

5. The Special Role of Information Perfect Information No Incentive Problem Incomplete Information Use Incentive Contracts

6. RISK ANALYSIS EVALUATION OF A CEMENT ADDITIVES PLANT IN INDONESIA

7. Existing Information The existing financial evaluation of the project over a 12-year time horizon: * Basic Parameters * Revenues * Formulas for estimating revenues, unit costs and taxes * Costs * Investment Costs and Depreciation * Loan Schedule for Long-Term Debt * Income Tax Schedule * Cash Flows - Total Investment perspective * Cash Flows - Equity Holders Perspective Table 1: Basic Parameters Inflation Rate 5.50% Expected Inflation Rate 5.50% Price of Quick fix in Year 0 Po= 18 $/10 kg container Growth Rate of Real Price rp= 2.00% per year Quantity of Quickfix in Year 0 Qo= 5 million units Growth Rate in Q g= 4.00% per year Unit Cost in Year 0 co= 9 $/units Growth Rate of Real Unit Cost rc= 3.00% per year Capital Assets Purchased Ao= 300 $million Economic Depreciation Rate de=1/20 or 5.00% per year Tax Depreciation Rate (Straight Line Depreciation) dtax=1/12 or 8.33% per year Loan Initial Investment Loan Do= 160 $million Real Interest Rate ir= 6.00% per year Risk Premium on Debt R= 2.00% per year Real Supply Price of Equity re= 10.00% per year Corporate Tax Rate Tc= 25.00% per year

8. Year 0 1 2 3 4 5 6 7 8 9 10 11 Inflation Index 1.000 1.055 1.113 1.174 1.239 1.307 1.379 1.455 1.535 1.619 1.708 1.802 Revenues 0.00 100.72 112.72 126.15 141.18 158.01 176.83 197.90 221.48 247.87 277.40 Liquidation Values 270.31 Expenses Investment 300 Operating Expenses 50.86 57.47 64.95 73.40 82.95 93.75 105.94 119.73 135.31 152.91 Before Tax Net Cash Flow -300.00 49.87 55.25 61.20 67.78 75.05 83.09 91.96 101.75 112.56 124.48 270.31 Tax Payments 0.00 6.22 1.21 3.66 6.40 9.47 12.90 16.74 19.19 21.89 24.87 0.00 After Tax net Cash Flow Nominal -300.00 43.65 54.04 57.54 61.38 65.59 70.19 75.22 82.56 90.67 99.61 270.31 After Tsx Net Cash Flow Real -300.00 41.38 48.55 49.00 49.55 50.18 50.90 51.71 53.80 56.00 58.32 150.00 Cash Flows: Total Investment Perspectives

9. Cash Flows: Equity Holders’ Perspective

10. SENSITIVITY ANALYSIS FOR CEMENT ADDITIVES PLANT (QUICKFIX)

11. Risk Analysis Evaluation of a Cement Additives Plant Risk Variables, Probability Distribution, and Correlation

12. Expected Value of NPV = -28.19 Standard Deviation = 61.26 Expected loss from accepting = 40.96 Expected loss from rejecting = 12.77 Cumulative NPV Distribution Equity Capital: Owner’s View 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -200 -150 -100 -50 0 50 100 150 P(NPV<0) = 71.00%

13. HOW TO REDUCE THE COST OF RISK • Use Capital and Futures Markets • Use forward, futures, and option markets to hedge specific project risks • Use the capital market to diversify the risk to equity owners; ideally, diversification will eliminate unique or unsystematic risk and reduce the cost of equity capital • If there is no well-developed capital market then risks can be reduced by spreading them over more investors; however, risk spreading works only if project income (cash flow) is independent of other investor income • Use Contractual Arrangements to Reallocate Risks and Returns • Risk Shifting • Risk Management

14. Elements of Contracting • General Form • Exchange of x for y • Additional Considerations • Timing of x and y (when) • Contingency of x and y (under what circumstances) • Penalties in case on non-performance or bonus for good performance

15. Contracting Criteria • Contract with lowest cost (highest return if investment occurs) not necessarily best contract • Efficient contracts may provide: • better risk shifting - better distribution of cost across circumstances • i.e. Given probabilities, change the allocation of risk between participants • better risk management - higher project returns or lower total project risk as result of incentive • i.e. Change the incentive structure to change the probabilities of outcomes

16. Risk ReallocationSources of Contracting Benefits • Risk Shifting • Differing risk preferences. e.g., less risk averse investor willing to accept a lower return on a risky asset • Differing capacity to diversify. e.g., foreign investors may be able to diversify risk in more efficient capital markets • Differing outlooks or predictions of future. e.g., some investors are more tolerant and some are more optimistic • Risk Management • Differing ability to influence project outcomes

17. RISK SHIFTING • The following options are available: • Contracts that limit the range of values of a particular cash flow item, or of net cash flow. • For example, a purchaser may agree to purchase a minimum quantity or to pay a minimum price in order to be sure of delivery; these measures would put a lower bound on the sales revenue. • Similar measures would include: • limited liability • a limited product price range • a fixed price growth path • an undertaking to pay a long-run average price • specific price escalator clauses that would maintain the competitiveness of the product, e.g. indexing price to the price of a close substitute

18. Prob. of Price The result is that project revenues and hence the expected NPV will have (a) a higher expected value, and (b) a lower variance Price Pf P P contract Contract offers price equal to market price unless market falls below Pf when it pays guaranteed floor price of Pf. P = mean or expected market price without floor price guarantee. P contract = expected price project will receive with floor price guarantee. CENSORED DISTRIBUTIONCase of a floor price, Pf

19. Probability Expected value increases Adjusted probability distribution to reflect liability limits - + 0 Ev (0) Ev (1) Equity Liability Limit N.P.V. Example: Risk Under Conditions of Limited Liability

20. Re: Quickfix Project contract that specifies that unit costs (co) will not rise above $12 Expected value of NPV = - $0.74 Srd. Deviation = $44.41 Expected loss from accepting = 18.28 Expected loss from rejecting = 17.54 Cumulative NPV Distribution Owner’s View with a Ceiling on Initial Costs (Co) 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -100 -50 0 50 100 150 P(NPV<0) = 63%

21. Restructuring Intra-project Correlations • Risk-sharing contracts that reduce the risk borne by investors by increasing the correlation between sales revenue and some cost items, e.g., • profit sharing contract with labor • bonds with interest rates indexed to the product’s sales price • Risk-sharing contracts that decrease the correlation between benefit items or alternatively between cost items.

22. Restructuring Intra-Project Correlations (cont’d) • The benefits from restructuring correlations are based on the formula for the variance of the sum of two random variables (x and y) • v (ax + by) = a2v (x) + b2v (y) + 2ab cov (x,y) • where a and b are parameters or constants. • For example, let: • x = revenues (R); y = costs (C); and a = 1, b = -1 • v(net profit) = v(R-C) = v(R) + v(C) - 2 cov(R,C) • Any measure that will increase the positive correlation between R and C will increase cov(R,C) and reduce the variance of the net profit (provided, of course, that the measure does not increase the variance of a cost item by more than twice the cov)

23. Example: A Profit-Sharing Agreement • Assume that wages are the only cost • Without the agreement: total cost = C • With the agreement: • Let g = proportion of the costs that is still paid to workers • as a wage, • h = labor’s share of profit after wages have been paid. • Thus, total cost = gC + h(R - gC) • Net profit = R - gC - h(R - gC) • = (1-h)R - g(1 - h)C • v(net profit) = (1-h)2v(R) + g2(1-h)2v(C) - 2g(1-h)2cov(R,C) • If 0< g < 1 and 0< h < 1, then the variance of net profit will be • lower than it was without the agreement

24. Cumulative NPV Distribution Owner’s View: Cost Ceiling & Correlated Selling Price 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -40 -20 0 20 40 60 80 100 120 140 P(NPV<0) = 26% Re: Quickfix Project - contract with supplier that establishes a cost ceiling of $12 - correlated initial selling price (po) and unit cost (Co) such that 18<Po<20 and correlation between Co & Po = +0.6 Expected Value of NPV = 23.72 Standard Deviation = 34.53 Expected loss from accepting = 2.82 Expected loss from rejecting = 26.53

25. Cumulative NPV Distribution Owner’s View: Cost Ceiling & Contract for Selling Price 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -40 -20 0 20 40 60 80 100 120 140 P(NPV<0) = 3% Re: Quickfix Project - cost ceiling of $12 -contract for selling price linked to initial costs (Co) If Co < 9, Po = 16; otherwise Po = 20 Expected Value of NPV = $48.73 Standard Deviation = $28.24 Expected loss from accepting = 0.09 Expected loss from rejecting = 48.82

26. Cumulative NPV Distribution Owner’s View: Cost Ceiling & First Revised Sales Contract 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -40 -20 0 20 40 60 80 100 120 140 P(NPV) < 0 = 3% Re: Quickfix Project - cost ceiling of $12 -Revised contract for selling price If Co < 9, Po = $16 9 < Co < 11, Po = $19; otherwise Po = $20 Expected Value of NPV = $41.45 Standard Deviation = 27.28 Expected loss from accepting = 0.19 Expected loss from rejecting = 41.64

27. Cumulative NPV Distribution Owner’s View: Cost Ceiling & Second Revised Sales Contract 1.0 0.9 0.8 0.7 0.6 Cumulative Probability 0.5 0.4 0.3 0.2 0.1 0.0 -40 -20 0 20 40 60 80 100 P(NPV) < 0 = 8% Re: Quickfix Project - cost ceiling of $12 -Revised contract for selling price If Co < 9, Po = $16.50 9 < Co < 11, Po = $18.50; otherwise Po = $19.50 Expected Value of NPV = $28.52 Standard Deviation = 23.82 Expected loss from accepting = 0.71 Expected loss from rejecting = 29.23

28. Restructuring Intra-Project Correlation - Adding another product line will decrease the variance of revenues provided that the revenues form the new product line (Rn) are negatively correlated to existing revenues (Ro) and that the V(Rn) < 2|cov (Ro, Rn) This is evident from the variance of (Ro, Rn) V(Ro + Rn) = V(Ro) + V(Rn) + 2cov(Ro, Rn) - Also, any measure that reduces the positive correlation of costs will reduce the variance of total cost, which should also have the effect of reducing the variance of net profit.

29. Diversification Reduces Risk • Example A: • An island economy trying to develop its tourist industry • The chief source of uncertainty is the weather Rate of return from manufacturing activities Weather ProbabilitySuntan LotionUmbrellas Rainy Season 0.50 -25% 50% Sunny Season 0.50 50% -25% Expected Return 12.5% 12.5% Variance 14.06% 14.06% Covariance -0.1406 or 14.06%

30. Portfolio consisting of 50% suntan lotion shares and 50% umbrella shares Expected return: = 0.5(12.5) + 0.5(12.5) = 12.5% Variance of Portfolio Return: = (0.5)2(14.06) + (0.5)2(14.06) - 2(0.5)(0.5)(14.1) = 0 Note that in this case the Partial correlation coefficient = -1

31.  4. Risk Pooling Reduces Risk • Let yi = possible returns from a risky projectAssume that there are many such projects and that their returns are independently and identically distributed. • Without Pooling (i.e. investing in only one project)Expected Value: E(yi) = y(mean return)Variance: V(yi) = V(y) • With Pooling (e.g. buying shares in a number (n) if similar projects) • Let ai = proportion of total investment in each project = 1/n • Expected Value:aiE[y1+y2+...+yn] = ny/n = y Variance: V[ai(y1+y2+...+yn)] = V[y1/n+y2/n+...+yn/n] = nV[y/n] = nV[y]/n2 = V[y]/n n lim V[y]/n = 0

32. Example: Oil Exploration • Assume there are 100 firms in the oil exploration business • Each has $1 million invested and each drills one well, which is independent of the others Outcomes Probability Profit Rates of Return ($ mil.) (R) a) Find oil 0.50 $1.4 140% b) Do not find oil 0.50 ($1.0) -100% E[R] = 0.20 V[R] = 1.44 [R] = 1.2 0.5*1.4 + 0.5*-1.0} (1.4 - 0.20)2 * 0.5 + (-1.0 - 0.20)2 * 0.5} (1.44)1/2 

33. If an investor puts all his/her money in the shares of one company, then the risk would be very high • However, if an investor constructs a portfolio consisting of one share of each of the 100 companies, the riskiness of this portfolio will equal: E[R] = 0.20 V[R] = 1.44/100 = 0.0144 [R] = (0.0144)1/2 = 0.12

34. Contracting Risks • Potential unilateral departures from contract terms by one party that jeopardizes the other party’s position • Examples • Downside Risks • Contractor walks away from project • Government defaults on agreement if the share (of a smaller pie) going to the contractor is perceived to be too large • Upside Risks • Government reduces payment to the contractor if the return is considered exorbitant • Uncertainty about whether contract terms will be fulfilled could result in costly gaming behavior

35. Taking Account of Contracting Risks in Estimating Expected Cash Flows Risk-Bearing and Contract Forms for Oil Exploration Contractual return Probability Expected alteration of contract Return adjusted for contracting risks Return O Effect of contracting risk on total contractor returns. - The contractor may not be permitted to share in the upside returns - Hence, the contractor should evaluate the project using a “realistic” probability distribution that reflects any contracting risks.

36. Applications of Monte Carlo Simulation

37. Mexican Cheese Operation Queso OAXACA Inc. • Project to build cheese processing plant in Mexico. • Product sold 70 percent in the U.S. and 30 percent in Mexico • Investment of $2.0 million pesos, financed by 23% equity and 77% debt • Initially loans and equity all from Mexican sources • Investment during first year, operations for a ten-year period. • No imported inputs

38. TABLE 1: TABLE OF PARAMETERS PRICES (as of year 0) WORKING CAPITAL Output: Price % real change Accounts receivable 18.0% Cheese Accounts payable 12.0% Export price ($/Kg) Risk V. >> 5.13 Cash balance 13.0% % Change in real export price -0.5% TAXES Increase in real domestic price 1.50 Ps/Kg above real export pr. Corporate income tax 32.0% Domestic sales tax 10.0% Inputs: Milk (Ps/l) Risk V. >> 7.00 2.0% LOANS (domestic) Fuel (Ps/l) Risk V. >> 2.50 1.0% Suppliers' credit: Risk premium 1.0% Wages (Ps/day/person) 60 3.0% Real interest rate 3.0% Other direct costs (Ps/Kg) 4.7 0.0% Instalments 10 Indirect costs (Ps) 2,900,000 3.0% Commercial bank loan: INPUT LEVELS Risk premium 0.5% Raw materials (liters per kg of cheese) Year 2 Year 3 Years 4-10 Real interest rate 3.0% Milk 2.660 2.530 2.470 Instalments 10 Fuel 0.0110 0.0106 0.0102 Labor (number of workers) 32 40 45 INFLATION AND EXCHANGE RATES <<Risk V. Domestic inflation 30.0% INVESTMENT COST Year 0 Year 1 Year 6 Foreign inflation 3.0% <<Risk V. Ps/$ (in yr. 0 Pesos) Exchange rate in Yr 0 7.8 Land 160,000 Yearly apprec. of Mex. Peso 0.20% Buildings 800,000 Machinery 750,000 COST OF CAPITAL Utilities 50,600 Return to equity, real 10.0% Mechanical installation 103,000 Electrical installation 60,700 PRODUCTION AND INVENTORY 500,000 Furniture and equipment 28,000 Starting production in Year 2 (Kg) (in year 1 Pesos) Year 4 Years 5-10 2.0% 1.0% Vehicles 9,450 9,450 Year 3 Pre-operating expenses 46,095 % increase in production 40.0% 35.0% FISCAL DEPRECIATION Useful life for tax purp. (years) Ending inventory as % Buildings 25 of gross sales 330 Vehicles 5 Operating days Machinery, Utilities, Installation costs 15 Furniture and equipment 7 EXPORTS 70.0% Exports as a % of sales QUESO OXACA Inc.

41. SENSITIVITY ANALYSIS

42. Risk Variable Real exchange rate (US$/Pesos) factor Probability distribution: NORMAL MIN MEAN MAX Range: -16.5% 0.0% 16.5% Standard deviation: 5.5% Degree of skewness: 0% QUESO OAXACA Inc. Risk Variables Report

45. CONTRACT: PRICE OF MILK / liter = 20.3% OF PRICE OF CHEESE / kilo Cumulative Distribution of NPV (Equity Viewpoint) Expected Value = 1,471 Standard Deviation = 2,803 Probability of Negative Outcome = 31.5% Expected Loss = 547 Expected Loss Ratio = 0.213 100% 80% 60% probability 40% 20% 0% (8,000) (6,000) (4,000) (2,000) 0 2,000 4,000 6,000 8,000 10,000 12,000

47. Risk Analysis Results DETERMINISTIC NPV (in ‘000 Pesos): 1,461

48. Input Variable Distributions • Concessions and Contracts • Impact on the expected value of outcome • Impact on the standard deviation of outcome

49. It’s all about Garbage In, Garbage Out

50. Impact of Input Specification on Output of Monte Carlo Analysis Oil Speculation Project • Buy a barrel of oil today and sell it in a year's time • Today's price (P0) is certain $20 • Next Year's price (P1) is uncertain Steps: 1) What is the RANGE of possible values? • Minimum value: Zero probability of being below $10 • Maximum value: Zero probability of being higher than $60 2) What is the PROBABILITY of finding values between these extremes?