Techniques for Risk Analysis

• Statistical Techniques for Risk Analysis– Probability – Variance or Standard Deviation– Coefficient of Variation

• Conventional Techniques of Risk Analysis– Payback– Risk-adjusted discount rate– Certainty equivalent

Project Return & CAPM

• Derive Levered Beta from Equity Beta

• Average the samples for asset the beta• Cost of equity is • The project cost of capital is the weighted

average.

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PP Ltd. is considering an expansion project to strengthen its existing businesses. For this project, it proposes to employ debt-equity ratio of 2.5. Its pre-tax cost of debt will be 12% and its expected tax rate is 35%. The incremental cash flows from the project are given below:Year 0 1 2

Cash flows (Rs. in lakhs)

– 1600 10000 –10000

The equity-betas and debt-equity ratios of three companies engaged in the similar business are given below:

Company Equity-beta

D/E ratio

Jai Ltd. 1.40 2.25

Ayu Ltd. 1.25 1.80

Taru Ltd. 1.30 2.00

The risk-free rate is 6% and the expected return on market portfolio is 18%. Estimate the required rate of return on the expansion project. Also, appraise the project based on IRR.

Abandonment Analysis

Super Projects Ltd. has undertaken a project a few years ago. The project is still running and has a remaining useful life of 6 years. The company now feels that the project does not fit into its overall strategy and is considering whether it should be abandoned. The following information is available:Year Cash flow (Rs.Crore) Value if sold (Rs.Crore)1 175 5102 200 4753 235 4004 350 3005 400 2006 100 50The cost of capital of the company is 22%. Decide whether the project should be abandoned, and if yes, in which year.

Year 0 1 2 3 4 5 6 7

Abandonment Value

200

120 90 60 40 20 10 –

The opportunity cost of capital to the company is 12%. Cash inflow of the company increases by 25% every year in first four years, and then gradually it decreases by 50% every year. With this information the investment expert says that abandoning this project at the end of 4th year is a no-gain-no-loss proposition to the company. Conduct abandonment analysis and comment.

Chi Ltd. has bought one sugar mill near Hapur at a cost of Rs.200 crore. The investment horizon of the company is seven years. The management of the company gathered information regarding abandonment price of this mill in next seven years, as follows:

Mean & SD of Cash Flows

• Correlated cash flows

• Unrelated cash flows

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ANPV

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Coefficient of Variation • Relative Measure of Risk• It is defined as the standard deviation of the

probability distribution divided by its expected value:

Expected valueCofficient of variation = CV = Standard deviation

Coefficient of Variation• The coefficient of variation is a useful

measure of risk when we are comparing the projects which have– (i) same standard deviations but different expected

values, or – (ii) different standard deviations but same expected

values, or – (iii) different standard deviations and different

expected values.

Risk-Adjusted Discount Rate• Risk-adjusted discount rate, will allow

for both time preference and risk

preference and will be a sum of the

risk-free rate and the risk-premium

rate reflecting the investor’s attitude

towards risk.

• Under CAPM, the risk-premium is

the difference between the market

rate of return and the risk-free rate

multiplied by the beta of the project.

=0

NCFNPV = (1 )

nt

tt k

f rk = k + k

Evaluation of Risk-adjusted Discount Rate• The following are the advantages of risk-adjusted discount rate

method:–  It is simple and can be easily understood.–  It has a great deal of intuitive appeal for risk-averse businessman.–  It incorporates an attitude (risk-aversion) towards uncertainty.

• This approach, however, suffers from the following limitations:– There is no easy way of deriving a risk-adjusted discount rate. As discussed

earlier, CAPM provides for a basis of calculating the risk-adjusted discount rate. Its use has yet to pick up in practice.

– It does not make any risk adjustment in the numerator for the cash flows that are forecast over the future years.

– It is based on the assumption that investors are risk-averse. Though it is generally true, there exists a category of risk seekers who do not demand premium for assuming risks; they are willing to pay a premium to take risks.

Certainty—Equivalent

=0

NCFNPV = (1 )f

nt t

tt k

*NCF Certain net cash flow = NCF Risky net cash flow

tt

t

Risks of Certainty—Equivalent

– First, the forecaster, expecting the reduction that will be made in his forecasts, may inflate them in anticipation.

– Second, if forecasts have to pass through several layers of management, the effect may be to greatly exaggerate the original forecast or to make it ultra-conservative.

– Third, by focusing explicit attention only on the gloomy outcomes, chances are increased for passing by some good investments.

Risk-adjusted Discount Rate Vs. Certainty–Equivalent

• The certainty—equivalent approach recognises risk in capital budgeting analysis by adjusting estimated cash flows and employs risk-free rate to discount the adjusted cash flows. On the other hand, the risk-adjusted discount rate adjusts for risk by adjusting the discount rate. It has been suggested that the certainty—equivalent approach is theoretically a superior technique.

• The risk-adjusted discount rate approach will yield the same result as the certainty—equivalent approach if the risk-free rate is constant and the risk-adjusted discount rate is the same for all future periods.

Sensitivity Analysis

• Sensitivity analysis is a way of analysing change

in the project’s NPV (or IRR) for a given change

in one of the variables.

• The decision maker, while performing sensitivity

analysis, computes the project’s NPV (or IRR) for

each forecast under three assumptions:

(a) pessimistic, (b) expected, and (c) optimistic.

Sensitivity Analysis?

• It compels the decision-maker to identify the variables, which affect the cash flow forecasts. This helps him in understanding the investment project in totality.

• It indicates the critical variables for which additional information may be obtained. The decision-maker can consider actions, which may help in strengthening the ‘weak spots’ in the project.

• It helps to expose inappropriate forecasts, and thus guides the decision-maker to concentrate on relevant variables.

• It does not provide clear-cut results. The terms ‘optimistic’ and ‘pessimistic’ could mean different things to different persons in an organisation. Thus, the range of values suggested may be inconsistent.

• It fails to focus on the interrelationship between variables. For example, sale volume may be related to price and cost. A price cut may lead to high sales and low operating cost.

Scenario Analysis• One way to examine the risk of investment

is to analyse the impact of alternative combinations of variables, called scenarios, on the project’s NPV (or IRR).

• The decision-maker can develop some plausible scenarios for this purpose. For instance, we can consider three scenarios: pessimistic, optimistic and expected.

Simulation Analysis

• The Monte Carlo simulation simulation analysis considers the interactions among variables and probabilities of the change in variables. It computes the probability distribution of NPV. The simulation analysis involves the following steps:– First, you should identify variables that influence cash inflows

and outflows.– Second, specify the formulae that relate variables. – Third, indicate the probability distribution for each variable.– Fourth, develop a computer programme that randomly selects

one value from the probability distribution of each variable and uses these values to calculate the project’s NPV.

Shortcomings• The model becomes quite complex to use. • It does not indicate whether or not the

project should be accepted. • Simulation analysis, like sensitivity or

scenario analysis, considers the risk of any project in isolation of other projects.

Decision Trees -Sequential Investment Decisions

Investment expenditures are not an isolated period commitments, but as links in a chain of present and future commitments. An analytical technique to handle the sequential decisions is to employ decision trees.

Usefulness of Decision Tree Approach• It clearly brings out the implicit assumptions and

calculations for all to see, question and revise.• It allows a decision maker to visualise assumptions and

alternatives in graphic form, which is usually much easier to understand than the more abstract, analytical form.

• The decision tree diagrams can become more and more complicated as the decision maker decides to include more alternatives and more variables and to look farther and farther in time.

• It is complicated even further if the analysis is extended to include interdependent alternatives and variables that are dependent upon one another.

Utility Theory and Capital Budgeting

• Utility theory aims at incorporation of decision-maker’s risk preference explicitly into the decision procedure.

• As regards the attitude of individual investors towards risk, they can be classified in three categories:– Risk-averse – Risk-neutral – Risk-seeking

• Individuals are generally risk averters and demonstrate a decreasing marginal utility for money function.

• Let us assume that the owner of a firm is considering an investment project, which has 60 per cent of probability of yielding a net present value of Rs 10 lakh and 40 per cent probability of a loss of net present value of Rs 10 lakh.

• Project has a positive expected NPV of Rs 2 lakh. However, the owner may be risk averse, and he may consider the gain in utility arising from the positive outcome (positive PV of Rs 10 lakh) less than the loss in utility as a result of the negative outcome (negative PV of Rs 10 lakh).

• The owner may reject the project in spite of its positive ENPV.

ENPV = 10 × 0.6 + (–10) × 0.4 = Rs 2 lakh

Benefits and Limitations of Utility Theory

– First, the risk preferences of the decision-maker are directly incorporated in the capital budgeting analysis.

– Second, it facilitates the process of delegating the authority for decision.

– Difficulties are encountered in specifying a utility function.

– Second, even if the owner’s or a dominant shareholder’s utility function be used as a guide, the derived utility function at a point of time is valid only for that one point of time.

– Third, it is quite difficult to specify the utility function if the decision is taken by a group of persons.