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Risk Analysis in Capital BudgetingDecisions
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Risk exists because of the inability of the decision maker
to make perfect forecasts.
It may arise due to:
Inaccurate cash flow forecasts
Inaccurate discounting rate or cost of capital calculation
Unfavourable economic conditionsRajasree, MBA, MS, CFA
Why do risks exist?
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Project Specific Risk: due to estimation error, quality of manpower,
unavailability of material etc
Competitive Risk: unanticipated actions by competitors
Industry Specific Risk: unexpected technological changes/
developments
Market Risk: due to inflation, interest rate, growth rate etc
International Risk: exchange rate or political risk
Rajasree, MBA, MS, CFA
Sources of Risk: in a project
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Nature of Risk
Risk exists because of the inability of the
decision-maker to make perfect forecasts.
An investment is not risky if we can specify a
unique sequence of cash flows for it.
However there are always uncertainties about
cash flows which render risk to the capital
investment proposals with regard to their
acceptance.
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Concept of Probability
The concept of probability is fundamental to
the use of risk analysis techniques.
The probability estimate based on a very large
number of observations is known as an
objective probability.
The probability estimates that are dependent
on the state of belief of a person are called
subjective probabilities.
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Statistical Techniques for Risk
Analysis
Expected Net Present Value (ENPV) = The
expected net present values can be found out
by multiplying the monetary values of the
possible events (cash flows) by their
probabilities.
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Standard Deviationthe absolute
measure of risk
Variance of NCF = (NCF1ENCF)2 * Prob1 +
(NCF2ENCF)2 * Prob2 + (NCFnENCF)
2 *
Probn
Standard Deviation = Root of variance.
Coefficient of variation : it is the relative
measure of risk.
CV = Standard Deviation / Expected Net Cash
Flow.
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Conventional Techniques of Risk
Analysis
Risk-adjusted discount rate
Certainty Equivalent Pay back period
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Risk-adjusted Discount rate
Risk-adjusted discount rate method uses a
higher discount rate for more risky cash flows
and lesser discount rate for less risky cash
flows.
Risk-adjusted discount rate = Risk-free rate +
Premium for the risk
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Certainty Equivalent
Certainty Equivalent approach computes theNPV of the project by converting the riskycash flows into equivalent risk-free cash flows
and discount them with riskfree rate. The certainty equivalent coefficient can be
calculated as : Certain net cash flow/Risky netcash flow.
The certainty equivalent coefficient is always avalue between 0 and 1.
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Pay back Period
The oldest and commonly used method ofrecognising risk associated with a capitalbudgeting proposal is pay back period.
Under this method shorter period is givenmore preference than the longer periods
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Sensitivity Analysis
Sensitivity Analysis is a way of analyzing change in
the projects NPV or IRR for a given change in one
of the variables.
The following three steps are involved:1. Identifying the variables which have an impact on
the firms NPV
2. Defining the relationship between those variables3. Analyzing the impact of each of those variables on
the firms NPV.
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Scenario Analysis
Scenario Analysis measures the change in
NPV of the project under different scenarios
changing several variables at a time because of
interrelationship of variables amongst
themselves
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Decision Tree Analysis
A decision tree is a powerful tool of analyzing
sequential decisions. It breaks up complex
decisions into smaller decisions and calculate
the NPV backwards to arrive at the most
pragmatic decision based on maximization of
NPV.