Slide 1

1Nature of RiskRisk exists because of the inability of the decision-maker to make perfect forecasts.In formal terms, the risk associated with an investment may be defined as the variability that is likely to occur in the future returns from the investment.Three broad categories of the events influencing the investment forecasts:General economic conditions Industry factors Company factors 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 risk2Risk-adjusted Discount Rate

Risk-adjusted discount rate method:NPV = NCFt / (1+k)t ,where k is a risk-adjusted rate. Risk-adjusted discount rate = Risk-free rate + Risk premium k = kf + kr Capital budgeting and RiskAn investment project will cost Rs.50,000 initially, expected to generate cash flows of Rs.25,000, Rs20,000, Rs.10,000 and Rs.10,000 in next four years. What is the project's NPV, if it is expected to generate certain cash flows with 10 per cent risk-free rate. Net present value using a 10 per cent risk-free discount rate, is:NPV = -Rs.50,000 + Rs25,000/(1+0.1)+ Rs.20,000/(1+0.1)2+ Rs.10,000/ (1+0.1)3 + Rs10,000/ (1+0.1)4 = +Rs.3,599 If the project is risky, then a higher rate should be used to allow for the perceived risk. Assuming this rate to be 15 per cent, the net present value of the project will be:NPV = -Rs.50,000 + Rs25,000/(1+0.15)+ Rs.20,000/(1+0.15)2+ Rs.20,000/ (1+0.15)3+ Rs.10,000/ (1+0.15)4 = - Rs845 For a firm using IRR method IRR for the project should be compared with risk-adjusted minimum required rate of return. If IRR is higher than adjusted rate, the project would be accepted, otherwise rejected.

Certainty EquivalentCertainty-equivalent approach involves computing NPV as:NPV = (t NCFt ) /(1+kf)twhere, NCFt = the forecasts of net cash flow without risk-adjustment = the risk-adjustment factor or the certainty-equivalent coefficientkf = risk-free rate assumed to be constant for all periods.

Certainty-equivalent coefficients can be determined as a relationship between certain cash flows and the risky cash flows. t = NCFt * /NCFt = Certain net cash flow/ Risky net cash flow If a risky cash flow of Rs.80,000 in period t and certain cash flow of Rs.60,000 is equally desirable, t = 60,000/80,000 =0.75A project costs Rs.6,000 with cash flows of Rs.4,000, Rs.3,000, Rs.2,000 and Rs.1,000 in years 1 through 4. Associated t factors are estimated to be: o = 1.00, l = 0.90, 2 = 0.70, 3 = 0.50 and 4 = 0.30, and the risk-free discount rate is 10 per cent. NPV=1.0(-6,000) + 0.9(4,000) / (1+0.10) + 0.7 (3,000) / (1+0.10)2 +0.5(2,000)/ (1+0.10)3+ 0.3(1,000)/ (1+0.10)4 = -Rs37Sensitivity AnalysisSensitivity analysis is analysing change in projects NPV (or IRR) for given change in one of the variables. It indicates how sensitive a projects NPV (or IRR) is to changes in particular variables. The more sensitive the NPV, the more critical is the variable.Process:Identification of all variables, which have influence on projects NPV (or IRR).Definition of underlying relationship between the variables. Analysis of impact of change in each of the variables on projects NPV. Modern Processing Company is considering installation of a plant costing Rs10000 to increase its processing capacity. Expected value of the underlying variables and projects after-tax cash flows over its expected life of 7 years are given below. Salvage value is assumed to be zero.Expected values of VariablesVariablesValueInvestment (Rs)Sales volume (unit)Unit selling price (Rs)Unit variable cost (Rs)Annual Fixed costs (Rs)Depreciation (WDV)Corporate tax rateDiscount rate10,0001,000156.754,00025%35%12%Net Cash Flows of the projectC0C1C2C3C4C5C6C7Investment Revenue variable cost Fixed costs Depreciation EBITTaxPATNCF

-10,000

-10,00015,0006,7504,0002,5001,7506131,1383,63815,0006,7504,0001,8752,3758311,5443,41915,0006,7504,0001,4062,8449951,8483,25515,0006,7504,0001,0553,1951,1182,0773,13215,0006,7504,0007913,4591,2112,2483,03915,0006,7504,0005933,6571,2802,3772,97015,0006,7504,0001780247086516053385Projects NPV at 12 percent discount rate and IRR are as follows: NPV = +4973 IRR = 27.05%Since NPV is positive (or IRR > discount rate), the project can be undertaken.Let us assume the pessimistic and the optimistic values for volume, price and cost.Forecasts Under Different AssumptionsVariablePessimisticExpectedOptimisticVolume (unit)Unit selling price (Rs)Unit variable cost (Rs)Annual fixed costs75012.757.4254,8001,000156.754,0001,25016.506.0753,200If we change each variable (others holding constant), the projects NPVs are recalculatedSensitivity Analysis Under Different Assumptions

The most critical variables are sales volume and unit selling price. If the volume declines by 25%, NPV becomes negative (-Rs1146).Similarly if the net selling price falls by 15%, NPV is minus Rs1,702

VariableNPV (Pessimistic) NPV (Expected)

NPV (Optimistic)

Volume Unit selling priceUnit variable cost Annual fixed costs

-1,146-1,7022,9702,5994,9734,9734,9734,97310,0009,4226,9757,346SCENARIO ANALYSISScenario Analysis: Summary Report

Scenario summaryBase valuesPessimisticOptimisticExpectedVariable combinations: Sales volume (unit) Selling price / unit (Rs) Variable cost/unit (Rs) Fixed costResults:NPV (Rs)1,00015.006.754,000

4,97275012.757.434,800

-10,0381,25016.506.753,200

19,0261,25013.507.104,400

3,044Total Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL A State Probability Cash FlowDeep Recession.05 Rs -3,000Mild Recession.25 1,000Normal.40 5,000Minor Boom.25 9,000Major Boom.05 13,000Probability Distribution of Year 1 Cash Flows.40.05.25Probability-3,000 1,000 5,000 9,000 13,000Cash Flow (Rs)Proposal AExpected Value of Year 1 Cash Flows (Proposal A) CF1 P1 (CF1)(P1)Rs -3,000 .05 Rs -150 1,000 .25 250 5,000 .40 2,000 9,000 .25 2,250 13,000 .05 650

S=1.00 CF1 = Rs5,000Variance of Year 1 Cash Flows (Proposal A) (CF1)(P1) (CF1 - CF1)2(P1) Rs -150 ( -3,000 - 5,000)2 (.05) 250 ( 1,000 - 5,000)2 (.25) 2,000 ( 5,000 - 5,000)2 (.40) 2,250 ( 9,000 - 5,000)2 (.25) 650 (13,000 - 5,000)2 (.05) Rs5,000Variance of Year 1 Cash Flows (Proposal A) (CF1)(P1) (CF1 - CF1)2*(P1) Rs -150 3,200,000 250 4,000,000 2,000 0 2,250 4,000,000 650 3,200,000 Rs5,000 14,400,000Summary of Proposal AThe standard deviation = SQRT (14,400,000) = Rs3,795The expected cash flow = Rs5,000Coefficient of Variation (CV) = Rs3,795 / Rs5,000 = 0.759

CV is a measure of relative risk and is the ratio of standard deviation to the mean of the distribution.An Illustration of Total Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL B State Probability Cash FlowDeep Recession.05 Rs -1,000Mild Recession.25 2,000Normal.40 5,000Minor Boom.25 8,000Major Boom.05 11,000Probability Distribution of Year 1 Cash Flows.40.05.25Probability-3,000 1,000 5,000 9,000 13,000Cash Flow (Rs)Proposal BExpected Value of Year 1 Cash Flows (Proposal B) CF1 P1 (CF1)(P1)Rs -1,000 .05 Rs -50 2,000 .25 500 5,000 .40 2,000 8,000 .25 2,000 11,000 .05 550 S=1.00 CF1=Rs5,000Variance of Year 1 Cash Flows (Proposal B) (CF1)(P1) (CF1 - CF1)2(P1) Rs -50 ( -1,000 - 5,000)2 (.05) 500 ( 2,000 - 5,000)2 (.25) 2,000 ( 5,000 - 5,000)2 (.40) 2,000 ( 8,000 - 5,000)2 (.25) 550 (11,000 - 5,000)2 (.05) Rs5,000Variance of Year 1 Cash Flows (Proposal B) (CF1)(P1) (CF1 - CF1)2(P1) Rs -50 1,800,000 500 2,250,000 2,000 0 2,000 2,250,000 550 1,800,000 Rs5,000 8,100,000 Summary of Proposal BThe standard deviation of B < A (Rs2,846< Rs3,795), so B is less risky than A.The coefficient of variation of B < A (0.569-(Rs266.67)

What is the new project value?-Rs900(.20) Rs1,200 (.20) -Rs600(.60) Rs450Year 1123(.60) Rs1,200(.30) Rs 900(.10) Rs2,200(.35) Rs 900(.40) Rs 600(.25) Rs 300(.10) Rs 500(.50) -Rs 100(.40) -Rs 700Year 2Project Abandonment Rs 2,238.32 Rs 1,331.29 Rs 1,059.18 Rs 344.90 Rs 72.79-Rs 199.32 -Rs 1,280.95 -Rs900(.20) Rs1,200 (.20) -Rs400*(.60) Rs450Year 1123(.60) Rs1,200(.30) Rs 900(.10) Rs2,200(.35) Rs 900(.40) Rs 600(.25) Rs 300(1.0) Rs 0Year 2*-Rs600 + Rs200 abandonmentSummary of the Addition of the Abandonment OptionThe standard deviation*= SQRT (740,326) = Rs857.56 The expected NPV* = Rs 71.88 NPV* = Original NPV + Abandonment Option Thus, Rs71.88 = -Rs17.01 + Option Abandonment Option = Rs 88.89

* For True Project considering abandonment optionCORPORATE 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 low50RISK ANALYSIS IN PRACTICE Conservative Estimation of Revenues Safety Margin in Cost Figures Flexible Investment Yardsticks Acceptable Overall Certainty Index Judgment on Three Point Estimates51