Chapter 13RISK ANALYSIS IN CAPITAL BUDGETING Centre for Financial Management , Bangalore

OUTLINE

Sources and Perspectives of Risk Sensitivity Analysis Scenario Analysis Break-even Analysis Hillier Model Simulation Analysis Decision Tree Analysis Corporate Risk Analysis Managing Risk Project Selection under Risk Risk Analysis in Practice Centre for Financial Management , Bangalore

TECHNIQUES FOR RISK ANALYSISTechniques of riskanalysisAnalysis of stand-alone riskAnalysis of contextual riskSensitivityanalysisBreak-evenanalysisSimulationanalysisScenarioanalysisCorporate risk analysisMarket riskanalysisHilliermodelDecision treeanalysis Centre for Financial Management , Bangalore

SOURCES AND PERSPECTIVE OF RISKSources of Risk

Project-specific risk Competitive risk Industry-specific risk Market risk International risk

Perspectives on Risk

Standalone risk Firm risk Market risk Centre for Financial Management , Bangalore

SENSITIVITY ANALYSIS(000)YEAR 0YEAR 1 - 101. INVESTMENT(20,000)2. SALES18,0003. VARIABLE COSTS (66 2/3 % OF SALES)12,0004. FIXED COSTS 1,0005. DEPRECIATION 2,0006. PRE-TAX PROFIT 3,0007. TAXES 1,0008. PROFIT AFTER TAXES 2,0009. CASH FLOW FROM OPERATION 4,00010. NET CASH FLOW 4,000

NPV = -20,000,000 + 4,000,000 (5.650) = 2,600,000 ( discount rate = 12 % )RS. IN MILLIONRANGENPVKEY VARIABLEPESSIMISTIC EXPECTED OPTIMISTIC PESSIMISTIC EXPECTED OPTIMISTIC INVESTMENT (RS. IN MILLION) 24 20 18 -0.652.604.22 SALES (RS. IN MILLION) 15 18 21 -1.172.606.40 VARIABLE COSTS AS A 70 66.66 65 0.342.603.73 PERCENT OF SALES FIXED COSTS 1.3 1.0 0.8 1.472.603.33

PESSIMISTIC, NORMAL AND OPTIMISTIC SCENARIO

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Pessimistic ScenarioExpected ScenarioOptimistic Scenario1. Investment2420182. Sales1518213. Variable costs10.5 (70%)12 (66.7%)13.65 (65%)4. Fixed costs1.31.00.85. Depreciation2.42.01.86. Pre-tax profit0.83.0 4.757. Tax0.271.01.588. Profit after tax0.532.03.179. Annual cash flow from operations2.934.04.9710. Net present value (9) x PVIFA (12%, 10 yrs) (1)(7.45)2.6010.06

BREAK-EVEN ANALYSIS ACCOUNTING BREAK-EVEN ANALYSISFIXED COSTS + DEPRECIATION 1 + 2 == RS. 9 MILLIONCONTRIBUTION MARGIN RATIO 0.333

CASH FLOW FORECAST FOR NAVEENS FLOUR MILL PROJECT

(000)YEAR 0YEAR 1 - 101. INVESTMENT(20,000)2. SALES 18,0003. VARIABLE COSTS (66 2/3% OF SALES) 12,0004. FIXED COSTS 1,0005. DEPRECIATION 2,0006. PRE-TAX PROFIT 3,0007. TAXES 1,0008. PROFIT AFTER TAXES 2,0009. CASH FLOW FROM OPERATION 4,00010. NET CASH FLOW (20,000) 4,000

CASH BREAK-EVEN ANALYSIS

HILLIER MODELUncorrelated Cash Flows n CtNPV = I t = 1 (1 + i)t n t2 (NPV) = t = 1 (1 + i)2t Perfectly Correlated Cash Flows n Ct NPV = I t = 1 (1 + i) t n t (NPV) = t = 1 (1 + i)t Centre for Financial Management , Bangalore

SIMULATION ANALYSIS

PROCEDURE

1. CHOOSE VARIABLES WHOSE EXPECTED VALUES WILL BE REPLACED WITH DISTRIBUTIONS

2. SPECIFY THE PROBABILITY DISTRIBUTIONS OF THESE VARIABLES

3. DRAW VALUES AT RANDOM AND CALCULATE NPV

4. REPEAT 3 MANY TIMES AND PLOT DISTRIBUTION

5. EVALUATE THE RESULTS Centre for Financial Management , Bangalore

DECISION TREE ANALYSIS

STEPS DELINEATE THE DECISION TREE EVALUATE THE ALTERNATIVESC21 : HD ANNUAL CASH FLOW 0.630 MILLION

D21 : INV C2 EMV (C2) = RS.194.2 m150 mC11 : S D2 EMV (D2) = RS.44. 2 mC22 : LD ANNUAL CASH FLOWp : 0.7 0.420 MILLIOND11 : PILOT PROD C1 EMV (C1) = RS.30. 9 m D22 : STOP & TEST MKTG - RS.20 m C12 : F D1 EMV (D1) = RS.10. 9 m D3 D31 : STOP p : 0.3 D12 : DO NOTHING Centre for Financial Management , Bangalore

LIMITATIONS

SENSITIVITY ANALYSIS NO IDEA OF LIKELIHOOD ONE FACTOR IS VARIED AT A TIME

SCENARIO ANALYSIS SCENARIOS MAY NOT BE CLEARLY DELINEATEDSIMULATION ANALYSIS DEFINING THE DISTRIBUTIONS IS DIFFICULT TRADITIONAL SIMULATION ANALYSIS DOESNT PERMIT INTERACTIONS AMONG VARIABLE BUSINESS AS USUAL ASSUMPTIONS

DECISION TREE ANALYSIS STAGES MAY NOT BE CLEARLY DEFINED OUTCOMES MAY NOT BE CLASSIFIED INTO BROAD CLASSES PROBABILITIES & CASH FLOWS ARE DIFFICULT TO DEFINE Centre for Financial Management , Bangalore

CORPORATE RISK ANALYSIS

A projects corporate risk is its contribution to the overall risk of the firm

On a stand-alone basis a project may be very risky but if its returns are not highly correlated or, even better, negatively correlated with the returns on the other projects of the firm, its corporate risk tends to be low Centre for Financial Management , Bangalore

MANAGING RISK FIXED AND VARIABLE COST PRICING STRATEGY SEQUENTIAL INVESTMENT FINANCIAL LEVERAGE INSURANCE LONG-TERM ARRANGEMENTS STRATEGIC ALLIANCE DERIVATIVES Centre for Financial Management , Bangalore

PROJECT SELECTION UNDER RISK Judgmental Evaluation Payback Period Requirement Risk Adjusted Discount Rate Certainty Equivalent Method Centre for Financial Management , Bangalore

RISK ANALYSIS IN PRACTICE Conservative Estimation of Revenues Safety Margin in Cost Figures Flexible Investment Yardsticks Acceptable Overall Certainty Index Judgment on Three Point Estimates Centre for Financial Management , Bangalore

SUMMING UP A variety of techniques have been developed to handle risk in capital budgeting. Sensitivity analysis or what if analysis answers questions like what happens to NPV if sales decline by 5 percent? Scenario analysis is an extension of sensitivity analysis Break-even analysis establishes the minimum quantity at which loss is avoided. The break-even point may be defined in accounting terms or financial terms. Simulation analysis is a technique for developing the profitability profile of a criterion of merit by combining values of variables that have a bearing on the chosen criterion. Decision tree analysis is a useful tool for analysing sequential decisions in the face of risk. A projects corporate risk is its contribution to the overall risk of the firm. There are several ways of incorporating risk in the decision process : judgmental evaluation, payback period requirement, risk-adjusted discount rate method, and certainty equivalent method Centre for Financial Management , Bangalore

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