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Incorporating Risk and Uncertainty Factor in Capital Investment Projects.


Even though risk has many meanings, in financial sector it has a more definite and distinctive meaning. It actually refers to the situations referring to the decisions made based on certain calculations of many probabilities that certain outcome can actually materialise or when probabilities based on previous information and when we actually know statistical frequency which are known to us.

In order for any investment to be meaningful a representation of how much is the risk has to be represented. Only then the cash flows of an investment will differ from what is expected in terms of money and time. Risk can be called a certain degree of uncertainty.

Capital Investment Appraisal plays a huge role in the long-term successful performance of an organization. It influences strategic financial decisions dealing with past and future investments. The required rate of return has to be adjusted to provide for the additional risk involved or an adjustment should be in regard to the relevant cash flows.

Various techniques used to evaluate investment opportunities are Internal Rate of Return (IRR), Present Value Payback (PVP), Accounting Rate of Return (ARR), the Profitability Index (PI) and Net Present Value (NPV).

Handling risk can be considered as a complex task having major influence in fluctuating exchange rates, technology changes and unpredictability of the competition.

Risk handling methods can be classified as simple risk adjustment and risk analysis.

Risk analysis can be defined as a technique which identifies and assess the factors that may jeopardize the success of a project. It also helps to define preventive measures to reduce the probability of these factors from occurring and identify countermeasures to successfully deal with these constraints when they develop to avert possible negative effects on the competitiveness of the company.
These include sensitivity analysis, probability analysis, scenario analysis, decision-tree analysis, Monte Carlo simulation, option pricing and capital asset pricing model (CAPM) approaches, etc.

Simple risk adjustment methods have got assumptions that cannot be clearly understood and could lead decision makers to accept decisions against their original intentions even though they are simple to use.

Use of risk analysis provides a systematic and logical approach to investment decision making, helps communication within the organization, and allows managerial judgment to be presented in a meaningful way.

Risk analysis approach can provide useful insights into an investment project, can improves decision quality and can increases decision confidence.

Sensitivity Analysis

It is used in order to improve the accuracy and reliability of the cash flows. It requires the examination of the sensitivity of some variable to changes in another variable. The primary purpose of sensitivity analysis is not to quantify risk, but to establish how sensitive the NPV and the IRR are to changes in the values of key variables in the evaluation of investment projects. Its main objective is to identify the factors of uncertainty that has got impacts on a future projects return. It deals with a lot of is sampling-based analysis.

A good sensitivity analysis should conduct analyses over the full range of plausible values of key parameters and their interactions, to assess how impacts change in response to changes in key parameters.

Sensitivity Analysis methods should be able to:

(a) Deal with a model regardless of assumptions about a
Model’s linearity and additively;

(b) Consider interaction effects among model input Uncertainties.

(c) Cope with differences in the scale and shape of model inputs.

(d) Should cope with spatial and temporal model input.

(e) Evaluate the effect of an input while all other inputs are allowed to vary as well.

A sampling-based sensitivity is one in which the model which is executed again and again for combinations of values sampled from the distribution of various input factors.

How it’s done

The most common sensitivity analysis is based on sampling. It is based on the model which is executed repeatedly for combinations of values sampled from the distribution (assumed known) of the input factors. Sampling based methods can also be used to decompose the variance of the model output.

Sensitivity Analysis is performed jointly by executing the model repeatedly for combination of factor values sampled with some probability distribution. The following steps can be listed:
a) Specify the target function and select the input of interest
b) Assign a probability density function to the selected factors
c) Generate a matrix of inputs with that distribution(s) through an appropriate design
d) Evaluate the model and compute the distribution of the target function
e) Select a method for assessing the influence or relative importance of each input factor on the target function.


The main advantage is good compaction or aggregation of the information;
Sensitivity analysis helps in identifying critical assumptions or in comparing alternative model structures. It also guide future data collections as well as detects important data criteria and optimises the tolerance of the manufactured products in terms of uncertainty parameters and optimises resource allocation thereby resulting in model simplification.


The main disadvantages that sometimes arise are that the variables are often interdependent, which makes examining them each individually unrealistic, e.g.: changing one factor such as sales volume, will most likely affect other factors such as the selling price. And quite Often the assumptions upon which the analysis is based are made by using past experience/data which may not work out efficiently in the future. Assigning a maximum and minimum (or optimistic and pessimistic) value is open to subjective interpretation. For instance an individual’s ‘optimistic’ forecast may be more conservative than that of another person performing a different part of the analysis. This sort of subjectivity can adversely affect the accuracy and overall objectivity of the analysis.

Scenario analysis

Scenario analysis is termed as a process of analyzing possible future events by considering alternative possible outcomes (scenarios). It is designed to allow improved decision-making by allowing more complete consideration of outcomes and their implications. It can be called as the process of estimating the expected value of a portfolio over a period of time, assuming specific changes in the values of the portfolio’s securities or key factors that would affect security values, such as changes in the interest rate.

How it’s done

It is commonly done by determining what the standard deviation of daily or monthly security returns are and then calculating what value would be expected for the portfolio if each security generated returns two or three standard deviations above and below the average return.
By this way, we can have reasonable certainty that the value of a portfolio is unlikely to fall below (or rise above) a specific value during a given time period.


Scenario analysis can take us from focusing on what is certain to happen to explore the range of what could happen. By defining scenarios, people have the opportunity to think about possibilities rather than what they expect to happen. This can stimulate creative ideas and solutions to the issues that arise from alternative futures.


Oversimplification – Scenarios can tend to oversimplify an issue as the analysis must balance detail with available time and resources.
Participant interaction and influence on content – The process of defining and assessing scenarios can raise sensitive issues for many participants, especially when they are from diverse backgrounds and organizations.

Computer simulation

Computer simulation allows the evaluation of the impact of changes in several variables simultaneously. Computer simulations can provide a lifetime of experience in a matter of seconds. Simulation has been one of prime methods used as a decision support tool in industry. Simulation is a very highly cost-effective method of testing new processes without having to carry out actual experiments. This can save enormous amounts of money, which would otherwise be spent on pilot programs, yet can produce better results much faster. One of the most popular Simulation models is the Monte Carlo simulation model.

Monte Carlo simulation is a versatile method for analyzing the behaviour of some activity, plan or process that involves uncertainty. Most business activities, plans and processes are too complex for an analytical solution so they rely on repeated random sampling to compute their results. Simulation should be used when it is expensive and/or dangerous to run the real systems.

How it’s done

The basic steps involved are:
• Define the process / problem
• Collection of Data on various events occurring in the process.
• Build Computer models
• Repeating independent events occurring in the process, the way they would occur in real processes. The computer model uses the observed probability distribution function of each event to do so.
• It gives the user the flexibility to control events and parameters of the process the way he desires.
• Run the simulation models through several recursions with a combination of real life variability generated by the computer, and controllable factors set by the user.
• Observe the results and their variation and document them.
• Make inferences and decisions based on the results of simulation.


• Gain better understanding of working of a system
• Identify problems prior to implementation
• Test the potential effects of changes
• Identify areas for resource deployment
• Design efficient and cost-effective systems
• Can maintain better control over experimental conditions than real system
• Can evaluate system on slower or faster time scale than real system


• Difficulty in estimating error.
• May be very expensive and time consuming to build simulation
• Easy to misuse simulation by “stretching” it beyond the limits of credibility
• Problem especially apparent when using commercial simulation packages due to ease of use and lack of familiarity with underlying assumptions and restrictions
• Slick graphics, animation, tables, etc. may tempt user to assign unwarranted credibility to output
• Monte Carlo simulation usually requires several runs at given input values
• Contrast: analytical solution provides exact values