Risk Analysis Techniques in Projects

This assignment delves into the realm of risk analysis techniques commonly employed in project management. It examines different approaches, including sensitivity analysis, scenario analysis, and the break-even method, highlighting their applications and limitations. The document emphasizes the importance of selecting appropriate techniques based on the specific characteristics of each project.

Running Head: Risk Analysis in Capital Budgeting
Capital Budgeting
Techniques

Risk Analysis in Capital Budgeting 1
Table of Contents
Introduction...........................................................................................................................................1
Sensitivity Analysis.................................................................................................................................2
Scenario Analysis...................................................................................................................................2
Break-even Analysis...............................................................................................................................3
Simulation Analysis................................................................................................................................4
Practical analysis of capital budgeting techniques................................................................................5
Sensitivity analysis.............................................................................................................................5
Scenario analysis................................................................................................................................6
Breakeven analysis............................................................................................................................7
Simulation analysis............................................................................................................................9
Conclusion.............................................................................................................................................9
References...........................................................................................................................................10

Risk Analysis in Capital Budgeting 2
Introduction
Capital Budgeting is the most important constitute of financial management as it involves
decisions making about the capital expenditures to be made under any project. As these
projects requires the deployment of huge funds for a long term, project managers must study
each and every element of project in details. Capital budgeting covers the critical analysis of
project and all the alternative project plans considering various factors such as risk and return
factor, the discounting rate, the technological and environmental factors, the initial
investment requirements etc. While selecting a project, the project manager has to analyse
and access the key variations that may occur in future while undertaking the project and
comprehensively examine the project’s behaviour in terms of profitability. For all the project
planning decisions there are various techniques and analyses available in today’s world which
are advanced enough to understand the changes in the output that may be occurred due to
input variations. These techniques are sensitivity analysis, simulation analysis, scenario
analysis, breakeven analysis etc. The detailed discussion on such capital budgeting technique
is given below:
Sensitivity Analysis
This technique is the most commonly used capital budgeting technique while making project
planning decisions. The sensitivity analysis helps the managers to analyse the change in the
project output with the changes in the key input variables (Saltelli, 2007). The basic purpose
of using this approach is to examine the sensitivity of any project in terms of Net Present
Value (Cao & Wan, 2017). There is no inclusive list of variable input parameters but there
can be factors like interest rates, useful life of asset, the fixed cost, variable cost per unit,
selling price or the number of units to be sold, residual value estimations etc. that may get
changed frequently over the life of project (Edmans, Jayaraman, Schneemeier, 2017). Before
investing the huge amount of funds in any project plan the firm must identify the significant
parameters that may undergo changes if the assumptions goes wrong. Once the key variable
factors are identified the project manager must determine the percentage change in the NPV
of the project if the input factors changes with a certain percentage.

Risk Analysis in Capital Budgeting 3
Sensitivity analysis is also known as ‘what-if’ analysis (Baker & English, 2011). This
analysis has its own advantages and at the same time it has some limits which makes it
unreasonable in certain situations. Following are some of the advantages and disadvantages
of sensitivity analysis:
Advantages:
 It enables the project managers to identify the key parameters which may impact the
future cash flows of the project.
 It helps in analysing the cause and effect of variations in the input parameters thereby
enabling the managers to take appropriate actions to control them and to plan the
future course of actions for the uncertainties.
 The risk involved in the capital budgeting decisions can be analysed to a certain
extent using this approach.
Disadvantages:
 This technique does not provide managers with the firm decision rather it provides the
relevant information that can be used in decision making.
 The assumptions that the variables are not dependent on each other is not reasonable
in maximum situations.
 The probability consideration of occurrence of variations is lacking in the sensitivity
analysis.
 The project managers while undertaking the sensitivity analysis bases his assumptions
for the budgeting and forecasting purpose on three approaches that are optimistic
pessimistic and expected.
Scenario Analysis
One of the most common way of analysing the risk involved in the investment to be made by
the firm is the scenario analysis (Kalyebara & Islam, 2014). Under this methodology the firm
calculates the NPV of a project considering several scenarios. The scenarios that are
considered under the scenario analysis are based on optimistic pessimistic and expected
mind-sets. The analysis initiates with the consideration of base case scenario. The project
NPVs are calculated using the base case scenario firstly and then the other possible scenarios
are selected. There is no limit of numbers of scenarios a firm must consider while evaluating

Risk Analysis in Capital Budgeting 4
the project’s effectiveness in changing situations (Erdmann & Hilty, 2010). However, the
three basic scenarios that are majorly considered while assessing the risk involved in any
project plan (Ross, 2010). These are the worst case, best case and the normal case scenarios
as the worst and the best case scenarios will give the decision makers a tentative range in
which the NPV of the project will fluctuate subject to the variations. The main purpose of
conducting scenario analysis is to understand the combined impact on project’s NPV of
numerous factors that changes at the same time. Scenario analysis mainly involves following
essential components (Suryani, 2010). First one is the selection of the important factors based
on which scenarios will be established. Then to determine the number of scenario cases so as
to analyse each factor that was previously selected. After determination of scenarios the firm
will have to place necessary emphasis on each critical factor (Xuan & Yue, 2017). Finally,
the managers will have to allocate the probabilities to all the scenarios based on their
significance. Even scenario analysis has its pros and cons which are discussed below:
Pros:
 This analysis helps the managers to identify the possible situation a project may have
to face in future and the potential implications and advantages of each situation. As all
the possible outcomes under differing situations are analysed under this technique it
gets easy for the firm to take appropriate decisions.
Cons:
 Interpretation of the results provided by this analysis is difficult for the firm as it
involves probability distribution. Moreover, it is difficult to decide as to which
scenario must be given the preference.
 The parameters i.e. the uncertainty and impact of each scenario is extremely
subjective and hence complicated enough to be measured.
Scenario analysis is the extended application of sensitivity analysis. As sensitivity analysis
uses variation in single input variable to determine the projects sensitivity, it gives less clear
picture of risk analysis of a project. Whereas, scenario analysis takes into consideration more
than one input variables to understand the implications of changes on the projects
performance in profitability terms. Scenario analysis also considers the probability
distributions of the key input parameters which is ignored in the sensitivity analysis (Gotze,
Northcott & Schuster, 2016).

Risk Analysis in Capital Budgeting 5
Break-even Analysis
This analysis is used to decide how much output the company must sell to cover the overall
costs of conducting the business. Breakeven analysis is commonly known as the cost volume
profit analysis as it analyses the relationship between the most important elements of any
business i.e. the cost, profit and the sales elements. Breakeven technique calculates the level
of sales in both monetary terms as well as in units, a firm must achieve in order to cover the
total costs of business so that it does not suffer any loss (Gutierrez & Dalsted, n.d). Break-
even point is the point where firm neither incurs any loss nor earn any income. The main tool
to conduct breakeven analysis is the breakeven charts which indicates the overall relationship
between the total cost total fixed cost and total variable cost and the total revenues of the
business of the company. Breakeven analysis is conducted on certain assumptions which are
as follows:
 All the business costs can be divided into categories i.e. fixed cost and variable cost.
This analysis does not take into account the semi variable costs.
 Behaviour of costs and the revenues of the business functions in linear fashion.
 Methods of production, technological factors and efficiency of business remains
same.
 Breakeven analysis expects that there does not arise any change in the level of
inventory.
 Total fixed costs of a business are also assumed to be constant for all the levels of
output in this analysis.
 Selling price per unit also remains same.
Due to the above assumptions breakeven analysis is not relied upon by the decision makers in
every business. The assumptions puts limitations on the analysis as it totally ignores the
concept of semi variable costs (Tsorakidis et al., 2011). Also, it ignores factors like
technologies that keeps on changing in today’s era. Because of the unrealistic assumptions
this technique losses it practical implementation in business.
Despite of various loopholes in the methodology of breakeven analysis there are certain
reasons which compels the business managers to implement this approach in their businesses

Risk Analysis in Capital Budgeting 6
to determine the appropriate level of sales it must make to cover its total costs. It is
considered as a suitable approach in following circumstances:
 Before starting a new business, a firm may use break even analysis for the feasibility
test of the business plan.
 For the price fixation of the products mix manufactured by the company as it will
determine the desired level of revenue from sales.
 In the evaluation of alternatives options available with the company and the special
orders that it may take besides its regular market demands.
 To determine the minimum level activity of business without putting it jeopardy.
 Breakeven analysis is also ideal for measuring the profit and the losses at different
levels of output in the business.
Simulation Analysis
Simulation is the quantitative approach of dealing with the managerial business problems
using few models like mathematical or the physical models on which process of simulation is
run. This technique uses few experiments by adopting trial and error approach where a series
of trials are run on the simulation model to judge the projects behaviour in terms of output.
Simulation analysis does not offer an optimum solution to any business problem but it aims
to provide the possible set of out for the given inputs (Choe, 2016). In finance world
simulation often provides assistance in the determination of risk adjusted NPV of a project.
Also, it offers distribution and allocation of project’s NPV over certain factors like
discounting rates (Lima et al., 2017).
Monte-Carlo simulation is the most common type of simulation used in the business and is
mostly used by the project managers. The distinguishing feature of this analysis is that it
offers the managers with the NPVs with their probability distribution and not with the single
point estimation of NPVs. This technique initiates with the mathematical modelling of the
project or any managerial business process requiring solution (Tavare, 2013). This process of
project modelling involves identification of the key factors that may influence the project and
the interrelationships between them (Chiarella & Iori, 2002). After process modelling the
plotting of probability distribution of project NPVs based on the expected cash flows of
project is undertaken. Once the probability is distributed to all the key variables the standard

Risk Analysis in Capital Budgeting 7
deviation is calculated to analyse the risk involved in the business. Simulation technique has
some advantages and some disadvantages with it which are discussed below:
Advantages:
 It insists the business managers to consider the uncertainties involved in the project
and the inter-dependencies of various factors impacting the project growth.
 Gives the opportunity to the decision makers to represent the complex business
problems through a mathematical model as these are complicated enough to be solved
with simple set of skills.
Disadvantages:
 Difficult project modelling process and probability distribution of external variables.
 Probability distribution of NPV is not accurate and hence it may be misleading the
decision makers.
 Risk free rate is used as discounting rate in calculation of NPV of a project in
simulation analysis and therefore it is difficult to interpret the results of this technique.
Practical analysis of capital budgeting techniques
Sensitivity analysis
Sales price 10 Discounting rate 10%
Units 10000 Useful life 5
VC 5 Initial investment -20000
Fixed cost 500
YEARS Cash Flows PVF@10% P.V. of Cash Flows
0 $ -20,000 1.000 $ - 20,000
1 $ 49,500.00 0.909 $ 45,000.00
2 $ 49,500.00 0.826 $ 40,909.09
3 $ 49,500.00 0.751 $ 37,190.08
NPV $ 1,03,099.17
Suppose the selling price changes from $10 to $8
Variables
Sales price 8 Discounting rate 10%
Units 10000 Useful life 5

Risk Analysis in Capital Budgeting 8
VC 5 Initial investment -20000
Fixed cost 500
YEARS Cash Flows PVF@10% P.V. of Cash Flows
0 $ -20,000 1.000 $ -20,000
1 $ 29,500.00 0.909 $ 26,818.18
2 $ 29,500.00 0.826 $ 24,380.17
3 $ 29,500.00 0.751 $ 22,163.79
NPV $ 53,362.13
Suppose the variable cost per unit from $5to $4
Variables
Sales price 10 Discounting rate 10%
Units 10000 Useful life 5
VC 4 Initial investment -20000
Fixed cost 500
YEARS Cash Flows PVF@10% P.V. of Cash Flows
0 $ -20,000 1.000 $ -20,000
1 $ 59,500.00 0.909 $ 54,090.91
2 $ 59,500.00 0.826 $ 49,173.55
3 $ 59,500.00 0.751 $ 44,703.23
NPV $ 1,27,967.69
From the above illustration it can be demonstrated that change in the selling price per unit has
resulted in the changed NPV. Therefore, NPV is sensitive to the selling price variable. As the
selling price per unit has decreased the NPV of the overall project has also decreased.
And when variable cost is decreased the NPV has increased which shows that NPV is also
sensitive to it.
Scenario analysis
Initial Investment
$(100000
)
Life of Project 4 years
Discounting Rate 10%
Annual
Cash
Flows $20000 $30000 $40000
Probability 0.1 0.6 0.3
Years Cash Cash Flows Cash Total DCF @ PV of

Risk Analysis in Capital Budgeting 9
Flows
(.10)
(.60) Flows
(.30)
Cash
Flows 10%
Cash
Flows
0 -10000 -60000 -30000 -100000 1 -100000
1 2000 18000 12000 32000 0.909 29088
2 2000 18000 12000 32000 0.826 26432
3 2000 18000 12000 32000 0.752 24064
4 2000 18000 12000 32000 0.683 21856
4 0 6000 6000 12000 0.683 8196
NPV 9636
The overall NPV of the project will be influenced by all the scenarios that is the worst case
best case and the average case
Breakeven analysis
Break-even Analysis:
Fixed
costs
Depreciation
$
50,000.00
Insurance
$
15,000.00
Rent
$
10,000.00
Utilities $ 8,000.00
Taxes $ 6,000.00
$ 89,000.00
Variable Costs
Direct Labour $ 8,000.00
Direct Material
$
10,000.00
Overhead
s
$
12,000.00
$ 30,000.00
TOTAL COSTS $1,19,000.00
Number of units 10000
Selling Price per unit $ 15.00

Risk Analysis in Capital Budgeting 10
Sales $ 1,50,000.00
Less: Variable Costs $ 30,000.00
Contribution $ 1,20,000.00
Contribution per unit
=120000/1000
0
$ 12.00
Contribution Margin = 120000/150000*100
0.80
Breakeven sales
in $ = Total Fixed Cost
Contribution Ratio
=$ 89,000.00
0.80
Breakeven Sales =$ 1,11,250.00
in units = Total Fixed Cost
Contribution/unit
Breakeven Units =7417 units
This indicates that the firm should at least sell 7417 in order to recover the total cost involved
in the business.
Simulation analysis
Demands Probability cumulative probability Range
10 0.1 0.1 00-09
15 0.25 0.35 10-24
25 0.2 0.55 25-54
40 0.35 0.9 55-89
50 0.1 1 90-99
random 48 78 9 51 77

Risk Analysis in Capital Budgeting 11
no:
Random No.
Demand
(Units)
48 25
78 40
9 10
51 25
77 40
Total Demand 140 units
Conclusion
It is therefore well established from the above study that the capital budgeting techniques
plays vital role in long term investment decision making which involves deployment of huge
funds in capital expenditures. Before undertaking a project the firm must critically analyse all
the risks involved with the project. The project managers must carefully examine the
probability of variations that may be occurred in future and the implications of such
variations on the overall profitability of company. After studying the possible techniques of
risk analysis in capital budgeting it is implied that there is no unique technique suitable for all
the circumstances rather the variety of techniques are appropriate in variety of cases. As each
analysis has its own benefits and limitations, the project manager has to keep in mind the
project’s characteristics and very nature whenever the risk is analysed using the above
explained approaches.

Risk Analysis in Capital Budgeting 12
References
Baker, H. and English, P., 2011. Capital Budgeting Valuation. Somerset: Wiley.
Cao, X.R. and Wan, X., 2017. Sensitivity analysis of nonlinear behavior with distorted
probability. Mathematical Finance, 27(1), pp.115-150.
Chiarella, C. and Iori, G., 2002. A simulation analysis of the microstructure of double auction
markets*. Quantitative finance, 2(5), pp.346-353.
Choe, G. H., 2016, Stochastic Analysis for Finance with Simulations, Springer International
Publishing, Switzerland.
De Lima, J.D., Trentin, M.G., Oliveira, G.A., Batistus, D.R. and Setti, D., 2017. Systematic
Analysis of Economic Viability with Stochastic Approach: A Proposal for Investment.
In Engineering Systems and Networks (pp. 317-325). Springer, Cham.
Edmans, A., Jayaraman, S. and Schneemeier, J., 2017. The source of information in prices
and investment-price sensitivity. Journal of Financial Economics.
Erdmann, L. and Hilty, L.M., 2010. Scenario analysis. Journal of Industrial Ecology, 14(5),
pp.826-843.
Gotze, U., Northcott, D. and Schuster, P., 2016. INVESTMENT APPRAISAL. Springer
International Publishing, Berlin.
Gutierrez. P. & Dalsted, N., n.d, Break-Even Method of Investment Analysis, Colorado State
University, available at < http://extension.colostate.edu/docs/pubs/farmmgt/03759.pdf >
(viewed on 15-09-2017).
Kalyebara, B. and Islam, S., 2014. Corporate Governance, capital markets, and capital
budgeting. Dordrecht: Physica-Verlag.

Risk Analysis in Capital Budgeting 13
Ross, S., Traylor, R., Bird, R., Westerfield, R. & Jordan, B., 2010. Essentials of corporate
finance, edn 2nd, McGraw-Hill Education.
Saltelli, A. 2007, Sensitivity analysis in practice. Chichester: John Wwiley and Sons.
Suryani, E., Chou, S.Y., Hartono, R. and Chen, C.H., 2010. Demand scenario analysis and
planned capacity expansion: A system dynamics framework. Simulation Modelling Practice
and Theory, 18(6), pp.732-751.
Tavare, N.S., 2013. Industrial crystallization: process simulation analysis and design.
Springer Science & Business Media.
Tsorakidis, N., Papadoulos, S., Zerres, M. and Zerres, C., 2011. Break-Even Analysis.
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