Discuss the concept of risk in investment decisions. Understand some commonly used techniques, i.e., payback, certainty equivalent and risk-adjusted discount rate, of risk analysis in capital budgeting. Focus on the need and mechanics of sensitivity analysis and scenario analysis.  Highlight the utility and methodology simulation analysis. Explain the decision tree approach in sequential investment decisions. Focus on the relationship between utility theory and capital budgeting decisions.

1. Chapter - 12
Risk Analysis in Capital
Budgeting

2. 2Financial Management, Ninth
Chapter Objectives
 Discuss the concept of risk in investment decisions.
 Understand some commonly used techniques, i.e.,
payback, certainty equivalent and risk-adjusted
discount rate, of risk analysis in capital budgeting.
 Focus on the need and mechanics of sensitivity
analysis and scenario analysis.
 Highlight the utility and methodology simulation
analysis.
 Explain the decision tree approach in sequential
investment decisions.
 Focus on the relationship between utility theory and
capital budgeting decisions.

3. 3Financial Management, Ninth
Nature of Risk
 Risk exists because of the inability of the
decision-maker to make perfect forecasts.
 In formal terms, the risk associated with an
investment may be defined as the variability
that is likely to occur in the future returns from
the investment.
 Three broad categories of the events
influencing the investment forecasts:
 General economic conditions
 Industry factors
 Company factors

4. 4Financial Management, Ninth
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

5. 5Financial Management, Ninth
Probability
 A typical forecast is single figure for a period. This is
referred to as “best estimate” or “most likely” forecast:
 Firstly, we do not know the chances of this figure actually
occurring, i.e., the uncertainty surrounding this figure.
 Secondly, the meaning of best estimates or most likely is not
very clear. It is not known whether it is mean, median or
mode.
 For these reasons, a forecaster should not give just
one estimate, but a range of associated probability–a
probability distribution.
 Probability may be described as a measure of
someone’s opinion about the likelihood that an event
will occur.

6. 6Financial Management, Ninth
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.

7. 7Financial Management, Ninth
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
t
t
ENCF
k+
∑
ENCF = NCF ×t jt jtP

8. 8Financial Management, Ninth
Variance or Standard Deviation
 Simply stated,
variance measures
the deviation about
expected cash flow
of each of the
possible cash flows.
 Standard deviation
is the square root of
variance.
 Absolute Measure of
Risk.
2 2
=1
(NCF) = (NCF – ENCF)
n
j j
j
Pσ ∑

9. 9Financial Management, Ninth
Coefficient of Variation
 Relative Measure of Risk
 It is defined as the standard deviation of the
probability distribution divided by its expected
value:
Expected value
Cofficient of variation = CV =
Standard deviation

10. 10Financial Management, Ninth
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.

11. 11Financial Management, Ninth
Risk Analysis in Practice
 Most companies in India account for risk while evaluating their capital expenditure
decisions. The following factors are considered to influence the riskiness of
investment projects:
 price of raw material and other inputs
 price of product
 product demand
 government policies
 technological changes
 project life
 inflation
 Out of these factors, four factors thought to be contributing most to the project
riskiness are: selling price, product demand, technical changes and government
policies.
 The most commonly used methods of risk analysis in practice are:
 sensitivity analysis
 conservative forecasts
 Sensitivity analysis allows to 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.
 Except a very few companies most companies do not use the statistical and other
sophisticated techniques for analysing risk in investment decisions.

12. 12Financial Management, Ninth
Payback
 This method, as applied in practice, 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 thereby
emphasising the liquidity of the firm through recovery of
capital.
 Favouring short term projects over what may be riskier,
longer term projects.
 Even as a method for allowing risks of time nature, it
ignores the time value of cash flows.

13. 13Financial Management, Ninth
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
NCF
NPV =
(1 )
n
t
t
t k+
∑
f rk = k + k

14. 14Financial Management, Ninth
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.

15. 15Financial Management, Ninth
Certainty—Equivalent
 Reduce the forecasts of
cash flows to some
conservative levels.
 The certainty—equivalent
coefficient assumes a value
between 0 and 1, and varies
inversely with risk.
 Decision-maker subjectively
or objectively establishes the
coefficients.
 The certainty—equivalent
coefficient can be
determined as a relationship
between the certain cash
flows and the risky cash
flows.
=0
NCF
NPV =
(1 )f
n
t t
t
t k
α
+
∑
*
NCF Certain net cash flow
=
NCF Risky net cash flow
t
t
t
α =

16. 16Financial Management, Ninth
Evaluation of Certainty—Equivalent
 This method suffers from many dangers in a
large enterprise:
 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.

17. 17Financial Management, Ninth
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.

18. 18Financial Management, Ninth
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 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.
 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.

19. 19Financial Management, Ninth
DCF Break-even Analysis
 Sensitivity analysis is a variation of the break-even
analysis.
 What shall be the consequences if volume or price or
cost changes (Sensitivity analysis)? You can ask this
question differently: How much lower can the sales
volume become before the project becomes
unprofitable? What you are asking for is the break-
even point.
 DCF break-even point is different from the
accounting break-even point. The accounting break-
even point is estimated as fixed costs divided by the
contribution ratio. It does not account for the
opportunity cost of capital, and fixed costs include
both cash plus non-cash costs (such as
depreciation).

20. 20Financial Management, Ninth
Pros and Cons of Sensitivity Analysis
 Sensitivity analysis has the following advantages:
 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 has the following limitations:
 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.

21. 21Financial Management, Ninth
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.

22. 22Financial Management, Ninth
Simulation Analysis
 The Monte Carlo simulation or simply the
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.

23. 23Financial Management, Ninth
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.

24. 24Financial Management, Ninth
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.
 Steps in Decision Tree Approach
 Define investment
 Identify decision alternatives
 Draw a decision tree
 decision points
 chance events
 Analyse data

25. 25Financial Management, Ninth
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.
 The demerits of the decision tree approach are:
 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.

26. 26Financial Management, Ninth
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.

27. 27Financial Management, Ninth
 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).
 Tthe owner may reject the
project in spite of its positive
ENPV.
ENPV = 10 × 0.6 + (–10) × 0.4 = Rs 2 lakh

28. 28Financial Management, Ninth
Benefits and Limitations of Utility
Theory
 It suffers from a few advantages:
 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.
 It suffers from a few limitations:
 First, in practice, 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.