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

1

Lecture Ten

FINA 522: Project Finance and Risk Management

Updated: 7 May 2007

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 InformationThe 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 ParametersInflation Rate 5.50%Expected Inflation Rate 5.50%

Price of Quick fix in Year 0 Po= 18 $/10 kg containerGrowth Rate of Real Price rp= 2.00% per yearQuantity of Quickfix in Year 0 Qo= 5 million unitsGrowth Rate in Q g= 4.00% per yearUnit Cost in Year 0 co= 9 $/unitsGrowth Rate of Real Unit Cost rc= 3.00% per year

Capital Assets Purchased Ao= 300 $millionEconomic Depreciation Rate de=1/20 or 5.00% per yearTax Depreciation Rate (Straight Line Depreciation) dtax=1/12 or 8.33% per year

LoanInitial Investment Loan Do= 160 $millionReal Interest Rate ir= 6.00% per yearRisk Premium on Debt R= 2.00% per yearReal Supply Price of Equity re= 10.00% per yearCorporate Tax Rate Tc= 25.00% per year

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Cash Flows: Total Investment Perspectives

Year 0 1 2 3 4 5 6 7 8 9 10 11Inflation 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

LiquidationValues 270.31

Expenses

Investment 300

OperatingExpenses 50.86 57.47 64.95 73.40 82.95 93.75 105.94 119.73 135.31 152.91Before TaxNet 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 netCash FlowNominal -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 NetCash FlowReal -300.00 41.38 48.55 49.00 49.55 50.18 50.90 51.71 53.80 56.00 58.32 150.00

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Cash Flows: Equity Holders’ Perspective

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

Net Cash FlowAfter Taxes

-300.00 43.65 54.04 57.54 61.38 65.59 70.19 75.22 82.56 90.67 99.61 270.31

Loan

PV of Loan

160

0.00

-53.03-47.641

-53.03-45.1573

-53.03-42.8

-53.03-40.57

-53.03-38.46

Equity NetCash FlowNominal -140.00 43.65 1.02 4.52 8.36 12.56 17.16 75.22 82.56 90.67 99.61 270.31

Equity NetCash FlowReal -140.00 41.38 0.91 3.85 6.75 9.61 12.45 51.71 53.80 56.00 58.32 150.00

Net PresentValue at10% D.R. 69.30

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Sensitivity Case(10% Change in Varible)

NPV to Equity(Owner’s Perspective)

Percentage Change fromBase Case

Base Case $69.30 0.0%

Inflation = 6.05% $69.03 -0.4%

Po = $19.80 $124.88 80.2%

rp = 2.2% $75.00 8.2%

Qo = 5.5 M $95.63 38.0%

g = 4.4% $74.53 7.5%

co = $9.90 $40.02 -42.0%

rc = 3.3% $64.76 -6.6%

Ao = $330.00 $47.57 -31.4%

de = 5.5% $64.04 -7.6%

dtax = 9.163% $72.31 4.3%

Do = $176.00 $71.62 3.3%

ir = 6.6% $66.86 -3.5%

R = 2.2% $68.49 -1.2%

re = 11.0% $55.90 -19.3%

Tc = 27.5% $64.80 -6.5%

SENSITIVITY ANALYSIS FOR CEMENT ADDITIVES PLANT (QUICKFIX)

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Risk Analysis

Risk Type of Variables Distribution Probability

StepInflation Rate Rectangular <3% 0%

From: 3% 4% 10%4% 5% 20%5% 6% 40%6% 7% 25%7% 8% 5%

Risk Type of Variables Distribution Maximum

Growth Rate in RealPrice of Quickfix

rp Normal 3.0%Growth Rate inSales of Quickfix

g Rectangular 5.0%unit Costs in Year 0co ($/unit) Rectangular 16Growth Rate in RealUnit Cost

rc Normal 5.0%

7

2.0%

Value

Minimim

-1.5%

2.5%

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

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Expected Value of NPV = -28.19Standard Deviation = 61.26

-200 -150 -100 -50 0 50 100 150

P(NPV<0) = 71.00%

Cumulative NPV DistributionEquity Capital: Owner’s View

1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

Expected loss from accepting = 40.96Expected loss from rejecting = 12.77

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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

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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

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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

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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

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RISK SHIFTINGThe 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

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CENSORED DISTRIBUTIONCase of a floor price, Pf

PfP P contract

Price

Prob.of Price

The result is that projectrevenues and hence the expected NPV will have(a) a higher expected value,and (b) a lower variance

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.

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Example: Risk Under Conditions of Limited Liability

Probability

- Equity Liability Limit N.P.V.

+Ev (0)0

Adjusted probability distribution to reflect liability limits

Expected value increases

Ev (1)

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Re: Quickfix Projectcontract that specifies that unit costs (co) will not rise above $12

Cumulative NPV Distribution

-100 -50 0 50 100 150

P(NPV<0) = 63%

Owner’s View with a Ceiling on Initial Costs (Co)1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

Expected value of NPV = - $0.74Srd. Deviation = $44.41Expected loss from accepting = 18.28Expected loss from rejecting = 17.54

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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.

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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)

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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 belower than it was without the agreement

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Expected Value of NPV = 23.72Standard Deviation = 34.53Expected loss from accepting = 2.82Expected loss from rejecting = 26.53

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

P(NPV<0) = 26%

Cumulative NPV Distribution Owner’s View: Cost Ceiling & Correlated Selling Price

-40 -20 0 20 40 60 80 100 120 140

1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

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Expected Value of NPV = $48.73Standard Deviation = $28.24Expected loss from accepting = 0.09Expected loss from rejecting = 48.82

Re: Quickfix Project- cost ceiling of $12-contract for selling price linked to initial costs (Co)If Co < 9, Po = 16; otherwise Po = 20

Cumulative NPV Distribution Owner’s View: Cost Ceiling & Contract for Selling Price

-40 -20 0 20 40 60 80 100 120 140

1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

P(NPV<0) = 3%

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Expected Value of NPV = $41.45Standard Deviation = 27.28Expected loss from accepting = 0.19Expected loss from rejecting = 41.64

Re: Quickfix Project- cost ceiling of $12-Revised contract for selling priceIf Co < 9, Po = $169 < Co < 11, Po = $19; otherwise Po = $20

-40 -20 0 20 40 60 80 100 120 140

P(NPV) < 0 = 3%

Cumulative NPV Distribution Owner’s View: Cost Ceiling & First Revised Sales Contract

1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

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Expected Value of NPV = $28.52Standard Deviation = 23.82Expected loss from accepting = 0.71Expected loss from rejecting = 29.23

P(NPV) < 0 = 8%

Cumulative NPV Distribution Owner’s View: Cost Ceiling & Second Revised Sales Contract

-40 -20 0 20 40 60 80 100

1.0

Cum

ulat

ive

Prob

abil

ity 0.8

0.6

0.4

0.2

0.0

0.1

0.3

0.5

0.7

0.9

Re: Quickfix Project- cost ceiling of $12-Revised contract for selling priceIf Co < 9, Po = $16.509 < Co < 11, Po = $18.50; otherwise Po = $19.50

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Restructuring Intra-Project Correlation

- Adding another product line will decrease thevariance of revenues provided that the revenues form the newproduct 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.

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Diversification Reduces Risk

• Example A:

– An island economy trying to develop its tourist industry

– The chief source of uncertainty is the weatherRate of return from manufacturing activities

Weather Probability Suntan Lotion Umbrellas

RainySeason 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%

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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

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4. Risk Pooling Reduces Risk• Let yi = possible returns from a risky project

Assume 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

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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

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• 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

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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

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Taking Account of Contracting Risks in Estimating Expected Cash Flows

Return

Contractual return

Return adjusted for contracting risks

Expected alteration of contract

O

Risk-Bearing and Contract Forms for Oil Exploration

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.

Pro

babi

lity

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Applications of Monte Carlo Simulation

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Mexican Cheese Operation Queso OAXACA Inc.

1. Project to build cheese processing plant in Mexico.

2. Product sold 70 percent in the U.S. and 30 percent in Mexico

3. Investment of $2.0 million pesos, financed by 23% equity and 77% debt

4. Initially loans and equity all from Mexican sources

5. Investment during first year, operations for a ten-year period.

6. No imported inputs

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QUESO OXACA Inc.

TABLE 1: TABLE OF PARAMETERS

PRICES (as of year 0) WORKING CAPITALOutput: 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 10Indirect 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 10Fuel 0.0110 0.0106 0.0102Labor (number of workers) 32 40 45 INFLATION AND EXCHANGE RATES

Domestic inflation 30.0%INVESTMENT COST Year 0 Year 1 Year 6 Foreign inflation 3.0% (in yr. 0 Pesos) Exchange rate in Yr 0 7.8Land 160,000 Yearly apprec. of Mex. Peso 0.20%Buildings 800,000Machinery 750,000 COST OF CAPITALUtilities 50,600 Return to equity, real 10.0%Mechanical installation 103,000Electrical installation 60,700 PRODUCTION AND INVENTORYFurniture and equipment 28,000 Starting production in Year 2 (Kg) (in year 1 Pesos)Vehicles 9,450 9,450 Year 3Pre-operating expenses 46,095 % increase in production 40.0%

FISCAL DEPRECIATION Useful life for tax purp. (years) Ending inventory as %Buildings 25 of gross salesVehicles 5 Operating daysMachinery, Utilities, Installation costs 15Furniture and equipment 7 EXPORTS

Exports as a % of sales

35.0%35.0%

330330

70.0%

Ps/$

<<Risk V.

<<Risk V.

500,000

Year 4 Years 5-10 2.0% 1.0%

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CASH FLOW STATEMENT, Real (Year 0 prices)Total Investment Point of View

(in thousands Pesos)

Years: 0 1 2 3 4 5 6 7RECEIPTS

Net foreign sales 10,229 16,855 18,743 19,272 19,451 19,539

Gross domestic sales 5,006 8,250 9,177 9,438 9,528 9,574

Change in A/R (2,742) (2,409) (1,550) (1,302) (1,241) (1,228)

Residual value:

Land

Building

Machinery

Utilities, Installation, and furniture

VehiclesCash Inflow 12,493 22,695 26,371 27,408 27,738 27,885

EXPENDITURES

Investment cost -

Land 160

Building 800

Machinery 750

Utilities, Installation, and furniture 242.30

Vehicles 9.00 9.00

Pre-operational expenses 44

Operating costs -

Milk 9,686 13,156 13,363 13,766 14,182 14,610

Fuel 14 19 18 18 19 19

Labor 672 865 1,003 1,033 1,064 1,096

Other direct costs 2,350 3,290 3,356 3,389 3,423 3,457

Indirect costs 2,900 2,987 3,077 3,169 3,264 3,362 3,463

Change in A/P (1,164) (686) (390) (419) (432) (445)

Change in cash balance 1,981 1,740 1,119 940 896 887

Cash Outflow 1,710 3,195 16,526 21,461 21,638 21,992 22,523 23,087

BEFORE-TAX NET CASHFLOW (1,710) (3,195) (4,033) 1,234 4,733 5,416 5,215 4,798

Sales tax on domestic sales 455 750 834 858 866 870

Income tax 0 1,926 2,513 2,533 2,435 2,304

AFTER-TAX NET CASHFLOW (1,710) (3,195) (4,488) (1,442) 1,385 2,024 1,914 1,624

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CASH FLOW STATEMENT, Real (Year 0 prices)Equity Holder's Point of View


Years: 0 1 2 3 4 5 6 7 8

After-tax Net Cashflow, before financing (1,710) (3,195) (4,488) (1,442) 1,385 2,024 1,914 1,624 1,266

Suppliers' credit: machinery 750 (212) (163) (126) (97) (74) (57) (44) (34)Commercial bank loan: buildings 800 (223) (171) (132) (101) (78) (60) (46) (35)

After-tax Net Cashflow, after financing (160) (3,630) (4,822) (1,699) 1,188 1,872 1,796 1,534 1,197

Net Present Value @ 12% 1,461

CASH FLOW STATEMENT, Real (Year 0 prices)Equity Holder's Point of View


9 10 11

886 492 15,184

(26) (20)(27) (21)

833 451 15,184

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SENSITIVITY ANALYSISRisk Variables Base Case

ScenarioBase Case Scenariowith 10% change

Net Prestent Value(Base Case Scenario)

Net Present Value(with 10% change in

Variable)

PoercentageChange in NPV fromBase Case Scenario

Price of cheese / kg (in US$) 5.13 4.62 1,461 -6,516 -546%

Growth rate price of cheese -0.50% -0.55% 1,461 1,226 -16%

Starting production in yr. 2 (in kg) 500,000 450,000 1,461 -588 -140%

Price of milk / liter (in Pesos) 7.00 7.70 1,461 -3,062 -310%

Growth rate cost of milk 2.00% 2.20% 1,461 922 -37%

Exchange rate (Pesos/US$) 7.80 8.58 1,461 2,177 +49%

Real Exchange rate appreciation 0.20% 0.22% 1,461 1,368 -6%

Mexican inflation rate 30.00% 33.00% 1,461 1,388 -5%

Real interest rate 3.00% 3.30% 1,461 1,452 -0.6%

Price of fuel / liter (in Pesos) 2.50 2.75 1,461 1,454 -0.5%

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QUESO OAXACA Inc.Risk Variables Report

4.60 4.80 5.00 5.20 5.40 5.60 5.80 0.00 2.00 4.00 6.00 8.00 10.00

0.00% 10.00%

20.00%

30.00%

40.00%

50.00%

0%5%

10%15%20%25%30%35%

2.0 2.5 3.0 3.5 4.5

-20.00% -10.00% 0.00% 10.00% 20.00%

Risk VariablePrice of cheese / Kg (in US$)Probability distribution: NORMAL

MIN MEAN MAX Range: 4.68 5.13 5.58 Standard deviation: 0.15 Degree of skewness: 0%

Risk VariablePrice of milk / liter (in Pesos)Probability distribution: NORMAL

MIN MEAN MAX Range: 6.25 7 7.75 Standard deviation: 0.25 Degree of skewness: 0%

Risk VariableMexican inflation rateProbability distribution: NORMAL

MIN MEAN MAX Range: 18% 30% 42% Standard deviation: 4.0% Degree of skewness: 0%

Risk VariablePrice of fuel / liter (in Pesos)Probability distribution: STEP

20% 30% 25% 25%

2.0 2.5 3.0 3.5 4.5

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%

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BASE SCENARIOCumulative Distribution of NPV (Equity Viewpoint)

Expected Value = 1,521Standard Deviation = 6,521

Probability of Negative Outcome = 43.0%Expected Loss = 1,902

Expected Loss Ratio = 0.357

0%

20%

40%

60%

80%

100%

(20,000) (15,000) (10,000) (5,000) 0 5,000 10,000 15,000 20,000 25,000 30,000

pro

bab

ilit

y

44

CONVERTING THE DOMESTIC LOAN INTO A U.S. DOLLAR LOANCumulative Distribution of NPV (Equity Viewpoint)

Expected Value = 1,462Standard Deviation = 4,561

Probability of Negative Outcome = 38.8%Expected Loss = 1,194


0%

20%

40%

60%

80%

100%

(15,000) (10,000) (5,000) 0 5,000 10,000 15,000 20,000

pro

bab

ilit

y

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 = 2,803Probability of Negative Outcome = 31.5%

Expected Loss = 547Expected Loss Ratio = 0.213

0%

20%

40%

60%

80%

100%

(8,000) (6,000) (4,000) (2,000) 0 2,000 4,000 6,000 8,000 10,000 12,000

pro

bab

ilit

y

46

COMBINING A U.S. DOLLAR LOAN WITH MILK CONTRACTCumulative Distribution of NPV (Equity Viewpoint)

Expected Value = 1,590Standard Deviation =1,861

Probability of Negative Outcome = 21.0%Expected Loss = 208


0%

20%

40%

60%

80%

100%

(4,000) (2,000) 0 2,000 4,000 6,000 8,000

prob

abili

ty

47

Risk Analysis Results

DETERMINISTIC NPV (in ‘000 Pesos): 1,461

Base Scenario(domestic loan)

ForeignLoan

Domestic Loanwith Contract

Foreign Loanwith Contract

Expected Value (‘000 Pesos) 1,521 1,462 1,471 1,590

Standard Deviation (‘000 Pesos) 6,521 4,561 2,803 1,861

Coefficient of Variation 4.286 3.120 1.905 1.171

Probab. of Negative Outcome 43.0% 38.8% 31.5% 21.0%

Expected Loss 1,902 1,194 547 208

Expected Loss Ratio 0.357 0.310 0.213 0.104

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

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?

Impact of Input Specification on Output of Monte Carlo Analysis

51

Relative Probability Distribution for Price of Oil Next Year

Probability (%)

10

10%5% 20% 35% 25%

15 20

5%

25 30 40 50 60

Price of Oil ($/barrel)

Probability Price of Oil $ x

100%

50%

5%15%

35%

70%

95%Cumulative Probability Distribution

Price of Oil ($/barrel)

10 15 20 25 30 40 50 60

52

Single - Valued or Deterministic Model

Based on BEST estimate or expected valuesModel:

NPV = -p0 + p1/(1+r)

p0 = $20r = 10%

p1 = expected value of oil next year= 5% * $12.50 = 0.625+ 10% * $17.50 = 1.75+ 20% * $22.50 = 4.5+ 35% * $27.50 = 9.625+ 25% * $35.00 = 8.75+ 5% * $50. 00 = 2.5

$27.75NPV = -20 + 27.75/1.1 = 5.23Result: Therefore, undertake the project

53

Monte Carlo Simulation of Model

Model:NPV = -20 + RV/1.1RV = risk variable

= price of oil next year defined by step distribution

SIMULATION:

Repeatedly (500 times, for example) pick price values from distribution at random. This is done by picking a random number between 0 and 100% and looking up the corresponding price value from the cumulative probability distribution. For each simulation, calculate value of NPV. After 500 simulation runs, 500 values of NPV are obtained for which expected NPV and other characteristics of NPV distribution can be found.

54

Oil Speculation Project: Base Case

Assumptions: -P0 = $20-r = 0.10

• Step Rectangular Distribution• Range for Next year’s Oil Price $10 to $60• 500 Model Runs

Summary of Results:Model: NPV = -20 + RV/1.1Simulation results from 500 runsExpected NPV = 5.29Standard deviation of NPV = 9.24Probability NPV 0 = 27%Range: -9.69 to 34.18

Single-Valued Best EstimateNPV = -20 + 27.75/1.1 = 5.23

Result: Acceptance or rejection of project depends on risk attitudes/policies

55

Assumptions: -P0 = $20

-r = 0.10

• Step Rectangular Distribution• Range for Next Year’s Oil Price $10 to $60•500 Model Runs

-15 -10 -5 0 5 10 15 20 25 30 35

Expected Value (NPV) = 5.29 Standard Deviation = 9.24

Cumulative NPV DistributionOil Speculation Project: Base Case

100% Probability of result falling below corresponding value

Pro

babi

lity

80%

60%

40%

20%

0%

56

Eliminate Prospect of Prices Being in $30 to $60 Range

Let next year’s oil price range be as follows:

$10 to $15 15% Expected Value

$15 to $20 20%

$20 to $25 35% P1 = $21.5

$25 to $30 30%

Cumulative NPV DistributionBase case with Narrower Oil Price Range

-12 -10 -8 -6 -4 -2 0 2 4 6 8

Expected Value (NPV) = -0.38 Standard Deviation = 5.13

100%Probability of result falling below corresponding value

Pro

babi

lity

80%

60%

40%

20%

0%

57


-r = 0.10

•Uniform Distribution• Range for Next Year’s Oil Price $10 to $60•500 Model Runs

-15 -10 -5 0 5 10 15 20 25 30 35


Cumulative NPV DistributionBase Case with Uniform Distribution


Pro

babi

lity

80%

60%

40%

20%

0%

58


-r = 0.10

•Normal Distribution• Range for Next Year’s Oil Price $10 to $60•500 Model Runs

-10 -5 0 5 10 15 20 25 30 35


Cumulative NPV DistributionBase Case with Normal Distribution


Pro

babi

lity

80%

60%

40%

20%

0%

59


-r = 0.10

•Normal Distribution

• Range for Next Year’s Oil Price $10 to $45.50 (Mean P1 = 27.75, which is the same as base case

•500 Model Runs

-15 -10 -5 0 5 10 15 20 25


Cumulative NPV DistributionNormal Distribution with Range ($10, $45.50)


Pro

babi

lity

80%

60%

40%

20%

0%

60

Summary of Results for Oil Speculation Project

A. Base Case

B. Base Case with Narrower Oil Price Range ($10 to $30)

C. Base Case with Uniform Distribution

D. Base Case with Normal Distribution

E. Base Case with Normal Distribution and Range ($10 to $45.50)

Net Present Value Distribution

Expected Value

$5.29

-0.38

11.38

12.68

5.71

Standard Deviation

$9.24

5.13

13.08

6.31

5.02

61

r,p1 = 0.7

P1 has a normal distribution with a range of $10 to $60Let r = required rate of return with a range of 0.09 to 0.14

Add Positive Correlation between Discount Rate and the Future Price of Oil

•Shift Mean of Discount Rate

-5 0 5 10 15 20 25

Cumulative NPV Distribution Correlated Oil Prices & Req. Rate of Return


Pro

babi

lity

80%

60%

40%

20%

0%

Expected NPV

With Correlation Between the Price of Oil and the

Req. Rate of Return = 0.7

Without Correlation

Standard Deviation

10.14

5.78

12.68

6.31

62

Testing Rules (contracts) to Determine if they Reflect Historical Correlations

For Example: Let r = 0.1 + 0.001 (P1 - 20 )

Cumulative NPV DistributionOil Price and Rate of Return Formula

Thus, P1 r$10 0.0920 0.1030 0.11. .60 0.14

P1 has a normal distribution with a range of $10 to $60

-10 -5 0 5 10 15 20 25 30


100%

Prob

abil

ity

80%

60%

40%

20%

0%

63

Oil Speculation Project with Relationship between Oil and Required Rate of Return

Results with 500 Model Runs

Expected Value

Standard Deviation

Cost of AcceptingA “Bad” Project

Cost of Rejecting A “Good ProjectProbability NPV 0

Minimum Value

Maximum Value

Correlated r and P1

(r, p1 = 0.7)

$10.14

5.78

0.03

10.18

4.0%

$-2.36

23.66

r and P1 Formula$11.63

6.23

0.13

11.76

5.0%

$-6.83

25.86

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

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Transcript of 0 Lecture Ten FINA 522: Project Finance and Risk Management Updated: 7 May 2007.