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Risk Analysis in Capital Budgeting

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CA Inter FM-ECO CA Mayank Kothari1 | P a g eChapter 8Risk Analysis in Capital BudgetingQ1. What are the different techniques of risk analysis in capital budgeting?Answer:The different techniques of risk analysis in capital budgeting has been mentionedbelow:Q2. What are the different types of decision making that we can takeconsidering the fact that investment projects are exposed to variousdegrees of risk?Answer:Considering the fact that investment projects are exposed to various degrees ofrisk, there can be three types of decision making, as mentioned below:1. Decision making under certainty : When cash flows are certain2. Decision making involving risk: When cash flows involve risk andprobability can be assigned.3. Decision making under uncertainty: When the cash flows are uncertainand probability cannot be assigned.Techniques of Risk Anaysis in Capital BudgetingStatistical Techniques1. Probability2. Variance ofstandard deviation3. Coefficient ofvariationConventionalTechniques1. Risk-adjusteddiscount rate2. CertaintyequivalentsOther Techniques1. Sensitivity-Analysis2. Scenario Analysis3. SImulation4. Decision treeRisk Analysis in Capital Budgeting2 | P a g eQ3. Briefly explain the terms “Risk” and “Uncertainty”. Also comment on theirrelationship. Can they be used interchangeably?Answer:The terms “Risk” and “Uncertainty” has been explained as below: Risk is the variability in terms of actual returns comparing with theestimated returns. Most common techniques of risk measurement are Standard Deviationand Coefficient of variations. There is a very thin difference between risk and uncertainty. In case of risk, probability distribution of cash flow is known. However, when no information is known to formulate probabilitydistribution of cash flows, the situation is referred as uncertainty. However these two terms are often used interchangeably.Q4. Mention and briefly explain the different sources of risk.Answer:Risk can arise from different sources, depending on the type of investment, thecircumstances and the industry in which the organization is operating.Some of the sources of risk are as follows:1. Project-specific risk: These risks are related to a particular project and they affect theproject’s cash flows; it includes completion of the project inscheduled time, error of estimation in resources and allocation,estimation of cash flows etc. For example, a nuclear power project of a power generationcompany has different risks than hydel projects.2. Company specific risk: Risk which arise due to company specific factors like downgradingof credit rating, changes in key managerial persons, cases forviolation of Intellectual Property Rights (IPR) and other laws andregulations, dispute with workers etc. All these factors affect the cash flows of an entity and access tofunds for capital investments.CA Inter FM-ECO CA Mayank Kothari3 | P a g e For example, two banks have different exposure to default risk.3. Industry-specific risk: These are the risks which affects the whole industry in which thecompany operates. The risks include regulatory restrictions on industry, changes intechnologies etc. For example, regulatory restriction imposed on leather andbreweries industries.4. Market risk: The risk which arise due to market related conditions like entry ofsubstitute, changes in demand conditions, availability and access toresources etc. For example, a thermal power project gets affected if the coal minesare unable to supply coal requirements of a thermal powercompany etc.5. Competition risk: These are risks related with competition in the market in which acompany operates. These risks are risk of entry of rival, product dynamism and changein taste and preference of consumers etc.6. Risk due to Economic conditions: These are the risks which are related with macro-economicconditions like changes in monetary policies by central banks,changes in fiscal policies like introduction of new taxes and cess,inflation, changes in GDP, changes in savings and net disposableincome etc.7. International risk: These are risk which is related with conditions which are caused byglobal economic conditions like restriction on free trade,restrictions on market access, recessions, bilateral agreements,political and geographical conditions etc. For example, restriction on outsourcing of jobs to overseas markets.Risk Analysis in Capital Budgeting4 | P a g eQ5. What are the reasons for considering risk in capital budgeting decisions?Answer:The reasons for considering risk in capital budgeting decisions are mentioned asbelow:1. There is an opportunity cost involved while investing in a project for thelevel of risk. Adjustment of risk is necessary to help make the decision asto whether the returns out of the project are proportionate with the risksborne and whether it is worth investing in the project over the otherinvestment options available.2. Risk adjustment is required to know the real value of the Cash Inflows.Q6. Briefly explain the term “probability” and “Expected Net Cash Flows” and“Expected Net present value”.Answer:Probability: Probability is a measure about the chances that an event will occur.When an event is certain to occur, probability will be 1 and when thereis no chance of happening, an event probability will be 0.Expected Net Cash Flows: Expected Cash flows are calculated as the sum of the likely Cash flows ofthe Project multiplied by the probability of cash flows. Expected Cashflows are calculated as below: It is given by:E (R)/ENCF = ∑ Rini=1× PiWhere,E(R)/ENCF = Expected Cash FlowsPi = Probability of Cash flowsRi = Cash FlowsExpected Net Present Value: Expected net present value = Sum of present values of expected netcash flowsCA Inter FM-ECO CA Mayank Kothari5 | P a g e It is given by,ENPV = ∑ (1ENCF + k)tnt=1 Where,ENPV = Expected net present value,ENCF = Expected net cash flows (including both inflows and outflows)

= Period= Discount Rate

Q7. How will you classify Expected Net Present Value?Answer:Expected Net Present Value can be classified into following:a. Expected Net Present Value – Single Periodb. Expected Net Present Value – Multiple PeriodQ8. Briefly explain the meaning of the term “Variance”.Answer: Variance is a measurement of the degree of dispersion betweennumbers in a data set from its average. In simple words, variance is the measurement of difference between theaverage of the data set from every number of the data set. Variance is calculated as below :σ2 = ∑(NCFj – ENCF)2nj=1PjWhere,σ2= Variance in net cash flowP = ProbabilityENCF = Expected Net Cash Flow Thus, variance helps an organization to understand the level of risk itmight face on investing in a project.Risk Analysis in Capital Budgeting6 | P a g eQ9. Different values of variance have different meanings. Explain thosemeanings.Answer: A variance value of zero would indicate that the cash flows that wouldbe generated over the life of the project would be same. This might happen in a case where the company has entered into acontract of providing services in return of a specific sum. A large variance indicates that there will be a large variability betweenthe cash flows of the different years. This can happen in a case where the project being undertaken is veryinnovative and would require a certain time frame to market the productand enable to develop a customer base and generate revenues. A small variance would indicate that the cash flows would be somewhatstable throughout the life of the project. This is possible in case of products which already have an establishedmarket.Q10. Briefly explain the concept of standard deviation.Answer: Standard Deviation is a degree of variation of individual items of a set ofdata from its average. For Capital Budgeting decisions, Standard Deviation is used to calculatethe risk associated with the estimated cash flows from the project. Mathematically, the square root of variance is called Standard Deviation.Q11. Briefly explain the concept of coefficient of variation.Answer: The standard deviation helps in calculating the risk associated with theestimated cash inflows from an Investment. However in Capital Budgeting decisions, the management in severaltimes is faced with choosing between many investments avenues.CA Inter FM-ECO CA Mayank Kothari7 | P a g e Under such situations, it becomes difficult for the management tocompare the risk associated with different projects using StandardDeviation as each project has different estimated cash flow values. In such cases, the Coefficient of Variation becomes useful. The Coefficient of Variation calculates the risk borne for every percent ofexpected return. It is calculated as:Co – efficient of variation =Standard DeviationExpected Return or Expected Cash Flow When a selection has to be made between two projects, themanagement would select a project which has a lower Coefficient ofVariation.Q12. Briefly explain the concept of “risk-adjusted discount rate” as aconventional technique of risk analysis in capital budgeting.Answer: The use of risk adjusted discount rate is based on the concept thatinvestors demands higher returns from the risky projects. The required rate of return on any investment should includecompensation for delaying consumption equal to risk free rate ofreturn, plus compensation for any kind of risk taken on. In case, the risk associated with any investment project is higher thanrisk involved in a similar kind of project, discount rate is adjustedupward in order to compensate this additional risk borne. It is given by,NPV = ∑ (1NCF + kt)tnt=0– IWhere,NCFt = Net Cash Flow

= Risk adjusted discount rate

= Initial Investment

Risk Analysis in Capital Budgeting8 | P a g eQ13. What are the different concepts of “risk-adjusted discount rate”.Brieflyexplain such components.Answer: A risk adjusted discount rate is a sum of risk free rate and risk premium. The Risk Premium depends on the perception of risk by the investor ofa particular investment and risk aversion of the Investor.So, Risks adjusted discount rate = Risk free rate+ Risk premium Risk Free Rate:It is the rate of return on Investments that bear no risk. For e.g.,Government securities yield a return of 6 % and bear no risk. In suchcase, 6 % is the risk-free rate. Risk Premium:It is the rate of return over and above the risk-free rate, expected bythe Investors as a reward for bearing extra risk. For high risk project,the risk premium will be high and for low risk projects, the risk premiumwould be lower.Q14. Briefly explain the advantages and limitations of “risk-adjusted discountrate” as a conventional technique of risk analysis in capital budgeting.Answer:Advantages of Risk-adjusted discount rate:1. It is easy to understand.2. It incorporates risk premium in the discounting factor.Limitations of Risk-adjusted discount rate:1. Difficulty in finding risk premium and risk-adjusted discount rate.2. Assumption that investors are risk averse is always not true.CA Inter FM-ECO CA Mayank Kothari9 | P a g eQ15. Briefly explain the concept of “Certainty Equivalent (CE)” as a conventionaltechnique of risk analysis in capital budgeting.Answer: The definition of “Certainty Equivalent (CE)” as per CIMA terminologycan be stated as below:“An approach to dealing with risk in a capital budgeting context.” It involves expressing risky future cash flows in terms of the certaincash flow which would be considered, by the decision maker, as theirequivalent. Thus, in this approach a set of risk less cash flow is generated in placeof the original cash flows. As a result of this, the decision maker would be indifferent between therisky amount and the (lower) riskless amount, considering it to beequivalent.” The certainty equivalent is a guaranteed return that the managementwould accept rather than accepting a higher but uncertain return. This approach allows the decision maker to incorporate his or her utilityfunction into the analysis.Q16. Mention briefly the steps involved in “Certainty Equivalent (CE)”.Answer:Step 1: Remove risk by substituting equivalent certain cash flows from riskycash flows. This can be done by multiplying each risky cash flow bythe appropriate αt value (CE coefficient) For example, Suppose on tossing out a coin, if it comes head you will get `10,000 and if it comes out to be tail, you will win nothing. Thus, you have 50% chances of winning and expected value is `5,000.Risk Analysis in Capital Budgeting10 | P a g e In such case if you are indifferent at receiving ` 3,000 for a certainamount and not playing then ` 3,000 will be certainty equivalentand 0.3 (i.e. 3,000/10,000) will be certainty equivalent coefficient.Step 2: Discounted value of cash flow is obtained by applying risk less rate ofinterest. Since you have already accounted for risk in the numerator using CEcoefficient, using the cost of capital to discount cash flows willtantamount to double counting of risk.Step 3: After that normal capital budgeting method is applied except in caseof IRR method, where IRR is compared with risk free rate of interestrather than the firm’s required rate of return. Certainty Equivalent Coefficients transform expected values ofuncertain flows into their Certainty Equivalents. It is important to note that the value of Certainty EquivalentCoefficient lies between 0 & 1. Certainty Equivalent Coefficient 1indicates that the cash flow is certain or management is risk neutral. In industrial situation, cash flows are generally uncertain andmanagements are usually risk averse. Under this methodNPV = ∑ (α1t+NCF kf)t tnt=0– IWhere,NCFt = the forecasts of net cash flow without risk-adjustment

= the risk-adjustment factor or the certainty equivalentcoefficient= risk-free rate assumed to be constant for all periods


CA Inter FM-ECO CA Mayank Kothari11 | P a g eQ17. Mention the advantages and disadvantages of Certainty EquivalentMethod.Answer:Advantages of Certainty Equivalent Method:1. The certainty equivalent method is simple and easy to understand andapply.2. It can easily be calculated for different risk levels applicable to differentcash flows. For example, if in a particular year, a higher risk is associatedwith the Cash Flow, it can be easily adjusted and the NPV can berecalculated accordingly.Disadvantages of Certainty Equivalent Method:1. There is no Statistical or Mathematical model available to estimatecertainty Equivalent. Risk being subjective, it varies on the perceptionof the risk by the management because of bias and individual opinionsinvolved.2. There is no objective or mathematical method to estimate certaintyequivalents. Certainty Equivalent is subjective and varies as per eachindividual’s estimate.3. Certainty equivalents are decided by the management based on theirperception of risk. However the risk perception of the shareholderswho are the money lenders for the project is ignored. Hence it is notused often in corporate decision making.Q18. Write a short note on:“Risk-adjusted discount rate Vs. Certainty-Equivalent”Answer: Certainty Equivalent Method is superior to Risk Adjusted Discount RateMethod as it does not assume that risk increases with time at constantrate. Each year’s Certainty Equivalent Coefficient is based on level of riskimpacting its cash flow. Despite its soundness, it is not preferable like Risk Adjusted DiscountRate Method.Risk Analysis in Capital Budgeting12 | P a g e It is difficult to specify a series of Certainty Equivalent Coefficients butsimple to adjust discount rates.Q19. Briefly explain the concept of “Sensitivity Analysis” as one of thetechniques of risk analysis in capital budgeting.Answer: Definition of sensitivity analysis: As per CIMA terminology,”A modeling and risk assessment procedure in which changes are madeto significant variables in order to determine the effect of thesechanges on the planned outcome. Particular attention is thereafterpaid to variables identifies as being of special significance”. Sensitivity analysis, in simple terms, is a modeling technique which isused in Capital Budgeting decisions which is used to study the impactof changes in the variables on the outcome of the project. In a Project, several variables like weighted average cost of capital,consumer demand, price of the product, cost price per unit etc. operatesimultaneously. The changes in these variables impact the outcome of the project. However, it is very difficult to assess change in which variable impactsthe project outcome in a significant way. In Sensitivity Analysis, the project outcome is studied after taking intochange in only one variable. The more sensitive is the NPV, the more critical is that variable.Q20. Mention the steps involved in Sensitivity Analysis.Answer:The steps involved in conducting sensitivity analysis are explained as below:1. Finding variables, which have an influence on the NPV (or IRR) of theproject2. Establishing mathematical relationship between the variables.3. Analysis the effect of the change in each of the variables on the NPV (orIRR) of the project.CA Inter FM-ECO CA Mayank Kothari13 | P a g eQ21. Mention the advantages and disadvantages of Sensitivity Analysis.Answer:Advantages of Sensitivity Analysis:1. Critical Issues:This analysis identifies critical factors that impinge on a project’ssuccess or failure.2. Simplicity:This analysis is quite simple.Disadvantages of Sensitivity Analysis:1. Assumption of Independence:This analysis assumes that all variables are independent i.e. they arenot related to each other, which is unlikely in real life.2. Ignore probability:This analysis does not look to the probability of changes in thevariables.3. Not so reliable:This analysis provides information on the basis of which decisions canbe made but does not point directly to the correct decision.Q22. Briefly explain the concept of “Scenario Analysis” as one of the techniquesof risk analysis in capital budgeting.Answer: Although sensitivity analysis is probably the most widely used riskanalysis technique, it does have limitations. Therefore, we need to extend sensitivity analysis to deal with theprobability distributions of the inputs. In addition, it would be useful to vary more than one variable at a timeso we could see the combined effects of changes in the variables. Scenario analysis provides answer to these situations of extensions. This analysis brings in the probabilities of changes in key variables andalso allows us to change more than one variable at a time. This analysis begins with base case or most likely set of values for theinput variables.Risk Analysis in Capital Budgeting14 | P a g e Then, go for worst case scenario (low unit sales, low sale price, highvariable cost and so on) and best case scenario. So, in a nutshell Scenario analysis examines the risk of investment, soas to analyze the impact of alternative combinations of variables, onthe project’s NPV (or IRR).Q23. Write a short note on the following:“Scenario Analysis vs. Sensitivity Analysis”Answer: Sensitivity analysis and Scenario analysis both help to understand theimpact of the change in input variable on the outcome of the project. However, there are certain basic differences between the two. Sensitivity analysis calculates the impact of the change of a single inputvariable on the outcome of the project viz., NPV or IRR. The sensitivity analysis thus enables to identify that single criticalvariable that can impact the outcome in a huge way and the range ofoutcomes of the project given the change in the input variable. Scenario analysis, on the other hand, is based on a scenario. The scenario may be recession or a boom wherein depending on thescenario, all input variables change. Scenario Analysis calculates the outcome of the project considering thisscenario where the variables have changed simultaneously. Similarly, the outcome of the project would also be considered for thenormal and recessionary situation. The variability in the outcome under the three different scenarioswould help the management to assess the risk a project carries. Higher deviation in the outcome can be assessed as higher risk andlower to medium deviation can be assessed accordingly. Scenario analysis is far more complex than sensitivity analysis becausein scenario analysis all inputs are changed simultaneously consideringthe situation in hand while in sensitivity analysis only one input ischanged and others are kept constant.CA Inter FM-ECO CA Mayank Kothari15 | P a g eQ24. Briefly explain “Monte Carlo Simulation” as one of the techniques of riskanalysis in capital budgeting.Answer: Monte Carlo simulation ties together sensitivities and probabilitydistributions. This analysis starts with carrying out a simulation exercise to model theinvestment project. It involves identifying the key factors affecting the project and theirinter relationships. This analysis specifies a range for a probability distribution of potentialoutcomes for each of model’s assumptions. Monte Carlo simulation is a computerized mathematical technique thatallows decision makers to calculate risk and uncertainty in decisionmaking. Monte Carlo simulation generates a range of possible outcomes andtheir probabilities associated with those outcomes. It also shows the probabilities of extreme possibilities like theprobability of best case and the worst case along with the probabilitiesof a range of outcomes. The technique is widely used in fields as finance, project management,Portfolio Management, Stock Return Analysis etc. Under SimulationNPV can be calculated asNPV = ∑ (1NCF + ktt)tnt=0– IWhere,
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