risk analysis in capital budgeting. nature of risk risk exists because of the inability of the...
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Risk Analysis
in
Capital Budgeting
Nature of Risk
Risk exists because of the inability of the
decision-maker to make perfect forecasts.
the risk associated with an investment may
be defined as
– the variability that is likely to occur in the
future returns from the investment.
Nature of Risk
Three broad categories of the events
influencing the investment forecasts:
– General economic conditions
– Industry factors
– Company factors
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
Probability
Probability may be described as a measure
of someone’s opinion about the likelihood that
an event will occur.
A typical forecast is single figure for a period.
This is referred to as “best estimate” or “most
likely” forecast:
Probability
For these reasons, a forecaster should not
give just one estimate, but a range of
associated probability–a probability
distribution.
Assigning Probability The probability estimate, which is based on a
very large number of observations, is known
as an objective probability.
Such probability assignments that reflect the
state of belief of a person rather than the
objective evidence of a large number of trials
are called personal or subjective
probabilities.
Expected Net Present Value Once the probability
assignments have been made to the future cash flows the next step is to find out the expected net present value.
Expected net present value = Sum of present values of expected net cash flows.
= 0
ENPV = (1 )
n
tt
ENCF
k
ENCF = NCF × t jt jtP
Variance or Standard Deviation
Variance measures
the deviation about
expected cash flow of
each of the possible
cash flows.
Standard deviation is
the square root of
variance.
2 2
=1
(NCF) = (NCF – ENCF)n
j jj
P
Coefficient of Variation It is defined as the standard deviation of the
probability distribution divided by its expected
value:
Expected valueCofficient of variation = CV =
Standard deviation
Risk Analysis in Practice Companies in India account for risk while
evaluating their capital expenditure decisions. The following factors are considered
– price of raw material and other inputs
– price of product
– product demand
– government policies
– technological changes
– project life
– inflation
Risk Analysis in Practice The most commonly used methods of risk
analysis in practice are:– sensitivity analysis– conservative forecasts
Sensitivity analysis see the impact of the change in the behaviour of critical variables on the project profitability.
Conservative forecasts include using short payback or higher discount rate for discounting cash flows.
Payback
This method is more an attempt to allow for risk in capital budgeting decision rather than a method to measure profitability.
The merit of payback– Its simplicity. – Focusing attention on the near term future
and recovery of capital.– Favouring short term projects over what
may be riskier, longer term projects.
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.
= 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.
Evaluation of Risk-adjusted Discount Rate This approach suffers from the following
limitations:
– There is no easy way of deriving a risk-adjusted discount rate.
– 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.
Certainty—Equivalent Reduce the forecasts of
cash flows to some
conservative levels.
The certainty—
equivalent coefficient
can be determined as a
relationship between the
certain cash flows and
the risky cash flows.
= 0
NCFNPV =
(1 )f
nt t
tt k
*NCF Certain net cash flow =
NCF Risky net cash flowt
tt
Evaluation of Certainty—Equivalent This method suffers from many dangers
– forecasts have to pass through several
layers of management, the effect may
make it ultra-conservative.
– 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
the risk-adjusted discount rate adjusts for risk
by adjusting the discount rate.
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.
Sensitivity Analysis
The following three steps are involved in the use of sensitivity analysis:
– Identification of all those variables, which have an influence on the project’s NPV (or IRR).
– Definition of the underlying (mathematical) relationship between the variables.
– Analysis of the impact of the change in each of the variables on the project’s NPV.
Sensitivity Analysis
The decision maker, while performing
sensitivity analysis, computes the project’s
NPV (or IRR) for each forecast under three
assumptions:
– pessimistic,
– expected, and
– optimistic.
Decision Trees for 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.
Decision Trees for Sequential Investment Decisions
Steps in Decision Tree Approach
– Define investment
– Identify decision alternatives
– Draw a decision tree
• decision points
• chance events
– Analyse data
Usefulness of Decision Tree Approach The merits of the decision tree approach are:
– 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.
Usefulness of Decision Tree Approach
The demerits of the decision tree approach are:
– The decision tree diagrams can become more and more complicated to include more alternatives and more variables
– It is complicated even further if the analysis is extended to include interdependent alternatives and variables that are dependent upon one another.
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