The document discusses the critical role of risk analysis in capital budgeting and decision-making, emphasizing the uncertainty surrounding future cash flows and returns associated with capital expenditures. It outlines various methods for incorporating risk, such as probability distributions, sensitivity analysis, and decision trees, while explaining how different degrees of certainty, risk, and uncertainty affect decision-making. Additionally, it details how to calculate expected net present values (ENPVs) to evaluate investment projects and highlight the trade-offs between risk and profitability.

1. Dr. Mohamed Kutty Kakkakunnan
Associated Professor
P.G. Dept. of Commerce
NAM College Kallikkandy
Kannur – Kerala – India

2. Risk Analysis in Capital Budgeting
• Decision making the most important function
• Survival and growth of the firm depends upon the
decisions made by management
• Capital expenditure is a decision to invest funds in
assets with the anticipation of an expected series
of earnings in future
• Future is uncertain and thus, risky
OK. Now what is decision making?
Decision making refers to the process of selecting
the preferred course of action from a range of
possibilities

3.  Decision making is the process of selecting one course of
action out of possible courses of actions
 When select, a rational man will select?
 To select , it is assumed that, he
1. Has complete knowledge of all possible courses
2. Has complete knowledge on the consequences
selecting or rejecting alternatives
3. Can attach definite payoffs (returns) or utilities to each
possibilities
4. Can order the payoffs of each course of actions in
unique sequence from highest to the lowest payoffs

4. However, the assumptions do not hold
good due to :-
• Lack of knowledge about all the possibilities and
• Lack of knowledge about the consequences or
outcomes of each individual actions
Thus, decision making becomes a complex affair
and the decision maker takes his decisions under
risk and uncertainty
Further,
– Risk and profitability are related
– Higher risk creates loath among the investors
• Thus, proper balance must be struck between risk
and profitability

5. What is risk?
 Capital expenditure?
 Invests with the anticipation of future expected
earnings
 Estimates future cash inflows and earnings form
the project
 Uncertain future – future conditions may change-
cannot estimate with 100% accuracy
 Chances for variations in the actual
 Technically this variation is called ‘risk’
 Thus, risk is the variability in the actual returns in
relation to the estimated returns

6. What is risk?
 Is the variability that is likely to occur in the
future returns from the investment
 “the variability in the actual returns emanating
from a project over its working life, in relation to
the estimated returns as forecasted at the time of
initial capital budgeting decision”
Decision making situations
A decision maker has to face three situations while
taking the decision
1. Certainty
2. Risk
3. uncertainty

7. Under certainty, the decision maker knows all the
possible courses of actions and the effects of accepting
or rejecting each course of action
When the decision maker knows the effects, but does not
know the probability of occurring the events or
effects. Such situation is known as risky situation.
In such condition, on the basis of past experience,
decision maker may assign proximities for the events or
outcomes (objective probability)
When both the effects and probabilities are not known, it
is known as uncertainty
No past data or experience – rely on guess – (subjective
probability)

8. Thus the major difference between risk and
uncertainty is that risk can be quantified or risk is
concerned with quantification of the likelihood of
the future outcomes
No such quantification is possible in uncertainty
Risk can be measured by volatility (instability /
unpredictability) of returns, a certain outcome
has (stability), no variance and volatility
Risk means possibility of a future loss, which can
be foreseen
Business risk (resulting from investment
decisions) Financial risk (from financial decisions)

9. Risk Analysis in Project Selection
The evaluation criterion of projects are based on cash
flows (operational cash flows)
Capital investment refer to the current outlay of funds
with the anticipation of a series of future expected
cash inflows
Estimates future cash inflows or earnings
Chances for variation – known as risk
It is the volatility (instability) of returns, the dispersion or
spread of likely returns around the expected returns
Thus, while capital budgeting, the risk should be
considered

10. Techniques for Incorporating Risk in Capital Budgeting
1. Probability and Expected Values
2. Risk Adjusted Rate of Returns
3. Sensitivity Analysis
4. Simulation
5. Certainty Equivalent
6. Standard Deviation
7. Decision Tree And
8. Game Theory
9. Payback Period

11. Probability and Expected Values
The concept of probability is fundamental to the use of risk
analysis techniques
What is probability?
Is a measure of someone’s opinion about the likelihood that an
event will occur
Varies from 0 to 1 (non-occurrence to occurrence)
A probability distribution consists of more than one estimates,
varying from certainty to uncertainty – from pessimism to
optimism
Thus, probability distribution shows the range of associated
probability and consist of a number of estimated
Generally, the number of estimates will be smaller and may
make, best guess, high guess and low guess or
Can be optimistic, most likely and pessimistic

12. Making a series of guesses (three in our example) is an
improvement over a single figure
The forecaster says the range of variation in cash inflows from
a minimum of Rs. 100000 to a maximum of Rs. 200000
Still there are chances for improvement by incorporating more
information
He can add his degree of confidence to the above guess, by
attaching probabilities of the likelihood of occurrence of the
above figures
Optimistic /
Best Guess
Rs. 200,000
High Guess
Rs. 150000
Pessimistic /
Low guess
Rs. 100,000
Best Guess
Rs. 200,000
Probability 0.2
High Guess
Rs. 150,000
Probability 0.6
Low guess
Rs. 100,000
Probability 0.2

13. With the help of probability one can say the chance
of cash earnings or inflows
Thus, there are chances for varying cash flow from
Rs. 20,000 to Rs. 90,000
The probability can be assigned on the basis of past
experience or past data (objective probability).
Lack of past data or experience compels one to rely
on guess (subjective probability)
Low guess 100,000 x 0.2 = 20000
High guess 150,000 x 0.6 = 90,000
Best guess 200,000 x 0.2 = 40000

14. Calculation of Expected Net Present Values (ENPV)
After assigning probabilities, the next step is to calculate
Expected Net Present Values
Expected Net Present Value is equal to the difference between
expected values of cash inflows minus expected value of cash
outflow
Or it is the sum of the present values of expected net cash flows
Expected values are calculated by multiplying the cash flows by
their respective probabilities
Since cash outflow takes place immediately (current / present) it
is certain and not related with future there is no need for
calculating expected values of cash outflows
Expected values of cash inflows need be calculated
Expected value of cash inflows = Cash Inflows X Probability
To calculate present value the product so obtained above will be
multiplied by the appropriate PV Factor at the prescribed
interest rate

15. Expected Net Cash Flow – Single Period
Two projects X and Y with initial investment of
Rs. 5000 and discount rate 10%
Possible
Events
PROJECT -X PROJECT - Y
Cash
Inflow
Probability Cash
Inflow
Probability
A 4000 0.1 12000 0.10
B 5000 0.2 10000 0.15
C 6000 0.4 8000 0.50
D 7000 0.2 6000 0.15
E 8000 0.1 4000 0.10

16. Calculation of Expected Values of Projects X & Y
Possible
events
1
PROJECT - X PROJECT - Y
Cash
inflow
2
Probabi
lity
3
Expecte
d values
4 (2x3)
Cash
inflow
5
Probab
ility
6
Expecte
d values
7 (5x6)
A 4000 0.1 400 2000 0.10 200
B 5000 0.2 1000 10000 0.15 1500
C 6000 0.4 2400 8000 0.50 4000
D 7000 0.2 1400 6000 0.15 900
E 8000 0.1 800 4000 0.10 400
EXPECTED CASH INFLOW 6000 8000
It shows that Project Y has higher Expected cash inflow than that
of X. thus, it is preferable

17. Now, we can calculate the expected net present
value of these projects
ENPV = EPVCIF – EPVCOF
Project X
EPVCIF @ 10% = 6000 X 0.909 = 5454
EPVCOF = 5000
ENPV = 5454 – 5000 = 454
Project Y
EPVCIF @ 10% = 8000 X 0.909 = 7272
EPVCOF = 5000
ENPV = 7272 – 5000 = 2272
Conclusion

18. Calculation of ENPV – Multi-period
Find the sum of Expected Present Values of Cash inflows of
different years and deduct the total from cash outlays
Project X; initial investment Rs. 5000; Discount rate 10 %
Year 1 Year 2 Year 3
Cash
inflow
Probability
Cash
inflow
Probability
Cash
inflow
Probability
1000 0.1 1000 0.2 1000 0.3
2000 0.2 2000 0.3 2000 0.4
3000 0.3 3000 0.4 3000 0.2
4000 0.4 4000 0.1 4000 0.1

19. Year 1 Year 2 Year 3
Cash
inflow
Proba
bility
Expect
ed
values
Cash
inflow
Proba
bility
Expect
ed
values
Cash
inflow
Proba
bility
Expect
ed
values
1000 0.1 100 1000 0.2 200 1000 0.3 300
2000 0.2 400 2000 0.3 600 2000 0.4 800
3000 0.3 900 3000 0.4 1200 3000 0.2 600
4000 0.4 1600 4000 0.1 400 4000 0.1 400
Expected cash
flows 3000 2400 2100
ENPV = EPVCIF – EPVCOF
EPVCIF @ 10% = 3000 X 0.909 + 2400 X 0.826 + 2100 X 0.751
= 6287
EPVCOF = 5000
ENPV = 6287 – 5000 = 1287

20. ENPV help us to incorporate risk in capital projects
decisions
To get better insight into the risk we calculate dispersion of
cash flows
Dispersion is the difference between possible cash flows
that can occur and their expected values
It indicates the degree of risk
Commonly used measures of dispersion are standard
deviation and variance
Standard deviation is the square root of the mean of
squared deviations
Deviation is the difference between an outcome and the
expected mean value of all outcomes

21. Variance measures the deviation about expected
cash flows of each of the possible cash flows
It is the square of standard deviation
The greater the standard deviation and variance the
greater the dispersion and thus, risk and
uncertainty also
Variance of NCF = (NCF1-ENCF)2 Probability 1 +
(NCF2-ENCF)2 Probability 2 + ….
(NCFn-ENCF)2 Probability n
Standard deviation = square root of variance

22. 1. Calculate the mean value of possible cash inflows
(CF) = Expected cash flow, as calculated in ENPV
2. Calculate the deviation between the mean value and
the possible cash flows (DCF)
3. Square the deviations (DCF)2
4. Multiply the squared deviations by the assigned
probabilities, to calculate the weighted squared
deviations (PDCF)2
5. Find the sum of the weighted squared deviations
(ΣPDCF)2
6. The resultant figure will be the Variance and
7. Find out the square root to get standard deviation.
Higher the value more will be the risk

23. When different projects having – (not homogenous)
a. Same standard deviation but different expected
values
b. Different standard deviations but same expected
values or
c. Different standard deviations and different
expected values, we use co-efficient of variation –
the relative measure of risk

24. Risk Adjusted Discount Rate
• Based on the assumption that risky project should get more
returns when compared to risky-free investments
• Risk premium for undertaking business risk over risk-free
investments
• Greater the risk, greater the premium
• Thus, while using discount rate for evaluation of capital
projects this risk premium is added with the usual discount rate
• Such a rate is known as risk adjusted rate of discount rate
• Such rate considers both time preference (time value and risk
preference
• Risk adjusted discount rate = risk free rate+ risk premium
• Acceptance rule:-
NPV (Positive) and IRR (IRR> Risk Adjusted Discount Rate)

25. If cost of capital and risk index is given the
following formula can be used for calculating
RADR
RADR = Rf + [Ri x (K0 – Rf)
Where Rf = risk free rate
Ri = risk index
K0 = cost of capital

26. • More or less similar to the risk adjusted
discount rate
• Here, the forecaster tries to forecast cash-
flows to some conservative level and adjusts
the “best estimate” with “intuitive correction
factor” known as “certainty-equivalent
coefficient” to be more safe
• This leads to estimate “certainty-equivalent
cash flow”
Different steps involved in this approach are:-

27. Step1
 Under this method, risk is incorporated by modifying the expected
cash flows by using a correction factor known as certainty
equivalent coefficient
 It expresses the relationship between certain (riskless) cash flows
and uncertain (risky) cash flows
 Its value lies in between 0-1 and is indicated by “ἀ”
 “ἀ0” represents cash outflow in the initial period; “ἀ1” cash flow
in the first year; “ἀ2” represents second year and so on.
 There is an inverse relationship between this value and the risk
(higher the value lower the risk and vice versa)

28.  Convert the expected cash flows into certainty
equivalent cash flows by using the CEC
Calculate the present value by using the
appropriate discount rate, which reflects the time
value of money (the same discount rate used for
evaluation capital projects)
Acceptance rule (both NPV and IRR can be used)
NPV (Positive)
IRR (IRR> risk-free discount rate)

29. • For evaluation of projects cash flows are estimated
• The forecasted cash flow depends upon several factors,
like volume of sales, selling price, variable costs, fixed
costs etc., which are subject to change
• Thus, NPV and IRR calculated on the basis of estimates
depends upon several factors and it is very difficult to
estimate or arrive at an accurate and unbiased forecast
of these variables
• Accuracy and reliability of NPV and IRR is questioned
and depends upon correct estimate of these variables
and reliability
• To ensure reliability and accuracy, impact of these
variables are ascertained –This method consider

30. Steps involved in Sensitivity Analysis
1. Identify the variables which influence NPV/IRR
2. Define the underlying relationship with the
help of mathematical equations
3. Analyze the impact of changes in each of these
variables
In sensitivity analyze, the decision maker makes
three assumptions – pessimistic, expected and
optimistic
On the basis of these assumptions, he can conduct
“what …. if” analysis. WHAT will be the NPV/IRR
IF the selling price is reduced by 10%?”

31. Then values of these variables are changed (at least three
times, considering pessimistic, expected and optimistic) and
NPV / IRR are recalculated under these assumptions.
This method of recalculating NPV / IRR by changing each of the
forecast variable is called SENSITIVITY ANALYSIS
It is a behavioral approach that uses a number of possible
values for a given variable to assess the impact on a firms
return
It is a way of analyzing change in the project’s NPV /IRR for a
given change in one of the variables
It indicates how sensitive a project’s NPV/IRR is to changes in
particular variables
The more sensitive the NPV/IRR, the more critical is the
variable

32. Decision Tree
A decision taken today may have several implications on
future. May affect future, decisions, investment and
outcomes.
Then it is necessary to foresee the future effects or
implications of present decisions and the decision becomes
a complex one
Thus, decision cannot be considered an isolated or individual
activity, ending with a particular consequence. May lead to
several consequences, several decisions and implications.
Depends upon the chance of occurring an event, its
consequences, which again lead to problems - decisions
and so on-
Thus, decision involves a series of sequential decisions to be
taken in the order of necessity

33. Decision tree continues
Decision tree is an analytical technique to handle such
sequential decisions
• Also known as Decision Flow Networks and Decision
Diagrams
• Is a powerful means of depicting and facilitating important
problems, especially that involves sequential decisions and
variable outcomes over time
• A decision tree is a pictorial representation in tree form
which indicates the magnitude an probability and inter-
relationship of all possible outcomes
• It is a graphic display of the relationship between a present
decision and future events, future decisions and their
consequences

34. • The sequence of events over time is depicted in a format similar to
the branches of a tree
• In capital budgeting, a decision tree shows the sequential cash
flows and NPV of the proposed project under different
circumstances
Steps in decision tree approach
• Decision tree deals with sequential decisions i.e present decision –
its consequences requiring future decisions and their future
consequences
• The consequences of present decision are influenced by chance
events and that of future consequences is also the effect of chance
events
• However, at the time of taking the decision chance event is
unknown but probability can be assigned and a probability
distribution can be constructed.
• When the decisions and outcomes are depicted by a graph we will
get the decision tree

35. Steps continues
The steps involved in the construction of decision tree
are:-
1. Define the investment proposal (purchasing machine,
entering new market, production of a new product
etc)
2. Identify the decision alternatives
3. Draw a decision tree indicating the decision points,
chance events and other data. The relevant data
regarding the probability distribution, cash flow,
expected present value etc should be shown on the
branches. Show the decision points by squares and
chance events by circles
4. Analyze the data and select the best alternative

36. Thus, the first step is to draw a diagram which shows the
structure of the problem.
Decision trees are constructed left to right. The branches
represent the possible alternatives which could be
made and various possible outcomes which might arise
Example
A company has a proposal to conduct a research project
for developing a product. If it conducts, there are
chances for success or failure in developing the
product. If it succeeds, the company may decide to
launch the product immediately or postpone the
launching for one year. There is a competitor to the
company in the market. Whatever be the decision, the
competitor may enter the market or stay away from
the market . Draw a decision tree (structure only)
assuming that all the possibilities have equal chance

37. D1
D2
CONDUCT 0.5
SUCCESS 0.5
FAILURE 0.5
IMM
EDIA
TE
0.5
POST
PONE
0.5
NOT TO CONDUCT 0.5
ENTER 0.5
STAY OUT 0.5
ENTER 0.5
STAY OUT 0.5
ENTER 0.5
STAYOUT 0.5
ENTER 0.5
STAY OUT 0.5