Decision and Risk Analysis Financial Modelling & Risk Analysis Kiriakos Vlahos Spring 2000

Session overview Why do we need risk analysis? Project evaluation Risk analysis approaches Scenario analysis Sensitivity analysis Monte-Carlo simulation Summary

Risk management in business Corporate risk Capital budgeting and portfolio evaluation Project Evaluation

Why do we need risk analysis? Single point forecasts are dangerous! Derive bounds for the range of possible outcomes Sensitivity testing of the assumptions Better perception of risks and their interaction Anticipation and contingency planning Overall reduction of risk exposure through hedging Risk analysis helps you develop insights, knowledge and confidence for better decision making and risk management.

Risk analysis approaches Scenario analysis Sensitivity analysis Monte-Carlo simulation Decision Analysis Option theory

Skywalker Proposal to open and operate a video store. “You can expect to make at least £50,000 in the first year”

Project Evaluation Evaluating a business proposition Does it make sense overall? Market conditions Trust issues What is the outlook under a basic set of assumptions? (Base Case) What are the risks involved? Writing a business plan

Base case model Closing cash exceeds £50000 at the end of the year

Scenario analysis “Scenarios are discrete internally consistent views of how the world will look in the future, which can be selected to bound the possible range of outcomes that might occur.” Michael Porter in “Competitive Strategy” “Shell flavour” of scenarios Scenarios should present testing conditions for the business. The future will of course be different from all of these views/scenarios, but if the company is prepared to cope with any of them, it will be able to cope with the real world. Do not assign probabilities to scenarios!

Skywalker - Scenarios analysis

Sensitivity analysis Explore robustness of results to variations in model parameters Understand and challenge assumptions Methodology Identify variables to which results are particularly sensitive and those to which they are relatively insensitive Gain an indication into range over which results might vary, thus assessing the risks Tools What-if questions One-way sensitivity analysis Two-way sensitivity analysis Tornado diagrams Spider plots

What-if analysis What-if Tape Price turns out to be 35? Changing Tape Price to 35, and leaving all other planning values at their base value, we get a December Closing Cash of £30,926 If Tape Price is 25, December Closing Cash is £70,982

One-way sensitivity analsysis e.g. Sensitivity of closing cash to Rent per day

Two-way sensitivity analysis Two-variable data table can be applied to a single cell such as December Closing Cash cell:

3-D plot of two-way sensitivity analysis Skywalker: Sensitivity of closing cash to to Rental & Plays per month Tutorial on data tables in Datatables.xls

Tornado diagrams Helps us determine visually the main uncertainty drivers. Around base case. Only one variable changes at a time. All other stay at base case values. Does not take into account of interactions between uncertain variables. Tutorial on Tornado diagrams in Tornado.xls

Constructing spider plots

Skywalker: Spider plot

Price/Demand Relationship Price is a decision variable and demand should depend on price, e.g. Regression equation: PlaysperMonth = 13.13 - 3.80RentperDay One-way sensitivity analysis to Rent per day Which price maximises closing cash?

Monte-Carlo simulation Uncertain variables Base Case Model Uncertain Parameters Base Value Hours Flown 800 Charter Price/Hour 700 Ticket Price/Hour 90 Capacity of Sch. flights 60% Ratio of charter flights 40% Operating Cost/hour 445 Profit & Loss Income from Scheduled £259,200 Income from Chartered £224,000 Operating costs (£356,000) Fixed Costs (£60,000) Taxable profit £67,200 Tax (£22,176) Profit after tax £45,024 Simulate Output distribution

Merck’s Research Planning Model Scientific, Medical Monte-Carlo constraints Simulation R&D variables Technological constraints Manufacturing variables Economic relationships Probability distributions for cash-flow Marketing Projections ROI, NPV variables of variables Macro- economic assumptions

@RISK - How it works Single simulation trial INPUTS MODEL CALCULATIONS RESULT = Profit = $62 Sales * Price - Cost 211 $5 $993 Multiple simulation trials INPUTS MODEL CALCULATIONS RESULT Profit Trial 1: 211 * 5 - 993 = $62 Trial 1: 193 * 8 - 700 = $884 Trial 1: 219 * 6 - 999 = $315 ... Trial N: 233 * 6 - 975 = $423

Novaduct case

Novaduct - Uncertainty “Market share increase is equally likely to be any value between -0.2% and 0.8%” -0.2 0.8 “Market growth is most likely to be a 2% increase but could range from a 10% decrease to an 8% increase” 90 102 108

Using @RISK 1. Introduce uncertainty into base model eg =RiskUniform(min, max) =RiskTriang(min, most likely, max) =RiskNormal(mean, std.dev.) 2. Select output cells (Cells for which we want simulation results) 3. Select simulation settings Number of iterations, random number seed 4. Execute simulation 5. View results Graphs, summary statistics 6. Return to spreadsheet and possibly repeat previous steps

Novaduct using @RISK @Risk Toolbar =RiskUniform(-0.2%,0.8%) ASSUMPTIONS Discount Rate 15% Prod Cost 5 103.0% Price 7 106.0% Market Share MS Incr 0.3% MktGrowth 102.0% =RiskUniform(-0.2%,0.8%) =RiskTriang(0.9,1.02,1.08) @Risk Toolbar Simulation settings Specify output cells Simulate Open & Save Simulation Results View input & output cells View @RISK Window

Simulation settings

@RISK Window

Simulation results NPV IRR Mean 914 Mean 25% Max 3174 Max 45% Min -1360 Min -14% P(NPV<0) = 0.17 P(IRR<15%) = 0.15 P(NPV<1,000) = 0.52 P(IRR<35%) = 0.85

Cashflow Summary Graph Central line connects mean values First band is 1 std.dev. Second band is interval between 5% and 95% percentiles

Summary Single point forecasts are dangerous! Challenge assumptions Scenario Planning Sensitivity analysis Data tables Tornado diagrams Monte-Carlo simulation Preparation for Workshop Datatables.xls and Tornado.xls @RISK tutorial Exercises