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.