Sensitivity Analysis is systematic study and a technique to determine the change in values for a change in variables in model and to changes in structure of model. We can easily measure that how sensitive a values is to changes in particular variables. Sensitivity analysis determines the changes in solution, when an objective function change, constraint is added to the problem, and the available resources changes.
Sensitivity analysis indicates how the projects is sensitive behave when there is a changes in variable. Sensitivity analysis is the important technique for project evaluation and project building. Sensitivity analysis examines the uncertainties which are often associated with variables. There are many variables in projects are difficult to measure or even some times it is impossible to measure it accurately in real world, in this scenarios sensitivity analysis indicates the what level of accuracy is necessary for a variable to make it valid and useful. Sensitivity analysis experiments the various behaviour of variables in extreme situations. With the help of sensitivity analysis, we can know the sensitivity of variables, such as if sensitivity analysis reveal that project is insensitive, than it is better to keep budgeted rather than actual in real world, and we can also know that which variable values are reasonable to use in project also. If the sensitivity analysis indicates that project is sensitive, it is rather good to keep actual value. When the value of sensitivity is more, the variable is more critical. With the help of sensitivity analysis, analyst can understand the dynamics of system also. By finding the how the changes will influences to variables can gives a leverage point in project and also gives the value which is significantly influence the changes in variables.
Sensitivity analysis is the answer to all of the questions such as what if fixed cost increase or decrease? What if variable cost increase or decrease? What if the production increase or decrease? What if the actual and budgeted life of projects increases or decreases? What if the selling price per unit is increase or decrease? Sensitivity analysis indicates the sensitivity of changes in variables.
Definition of Sensitivity Analysis
"A methodology for conducting a [sensitivity] analysis ... is a well-established requirement of any scientific discipline. A sensitivity and stability analysis should be an integral part of any solution methodology. The status of a solution cannot be understood without such information. This has been well recognised since the inception of scientific inquiry and has been explicitly addressed from the beginning of mathematics". (Fiacco, 1983, p3)
Uses of Sensitivity Analysis
There is a wide uses of sensitivity analysis. It is mainly divided in four parts such as impactful decision makes and recommendations, communicable, understanding the projects and project development.
Impactful decision making and recommendations
Analyst can take impactful decision and give recommendations by examines the strength of optimal solution, identifying values under extreme situations when there is a change is optimal strategy, calculating variables, examines the various solutions and by comparing the decision strategies such as simple and risky.
Communication
It is necessary that recommendations and decisions should be understandable, and it is possible with the help of sensitivity analysis. Analyst can also convey the commitment of any strategy which is lack.
Understanding the model
Analyst can estimate and understand the co relation between input and output variables and also develop various hypotheses for understanding of the model.
Project development
Analyst can know that whether model is accurate or not. Errors in the model are also searchable through sensitivity analysis. Analyst can also simplify and calibrate the model. Analyst can cope with data with the help of sensitivity analysis.
Approaches to Sensitivity Analysis
There many approaches to observing and changing the model.
What to vary
Analyst can choose all or any to vary such as maximisation of resources, minimisation of risk, and variable's contribution to objectives, constraints, activities and technical factors. This approach can vary to numerical constraints and in other scenarios, there is uncertainty that the results can occur or not in definite condition. E.g. What if government legislates to ban china's products for environmental reason? This kind of question arises when there is a change in structure. And after that revised outcomes can compare with original and also use to examine the wider effects of changes in sensitivity analysis.
What to observe
Analyst has to take care of the various values such as objective function and their difference of optimal strategy, variables, dual price and their rankings.
Experimental design
The combinations of vary in constraints and set levels refers as experimental design. Analyst has to decide to changes in constraints should be made at the same time and as per standard or base values. The relationship between variable is important issues and it need to be known by analyst.
Example:
Here I share my experience about sensitivity analysis to give further explanation of it from where I am working. I am working as purchase officer in Vale machinery limited. It is operate their business in construction machineries. I came to know that material evaluation is necessary before buying it. The evaluation regarding price, supply, demand and discount etc. is very important for business decision making. Here I am trying to show the effects of product when there it can buy at minimal discount rate in my below mention example. I found that sensitivity analysis is worth important for decision making in organization where it dealing with multinational organizations. There are a various changes in terms of exchange rate rapidly and which affects the organization also. The effects of changes in discount rate, exchange rate and all other variables need to know.
The net cash flow of carvings is £10000 and cladding stones is £ 20000 in the year 2000 and it is £ 40000 and £30000 in the year 2001 respectively. The initial investment is £ 20000.
Advise that which product is more risky when the discount rate is changes from 12% to 15% and do sensitivity analysis.
Solution:
First of all we have to calculate Net Present Value of Carvings and Cladding Stones,
Calculation of Net Present Value of Carvings:-
Year
Net Cash Flow
Discount Factor @ 12%
Present Value
Discount Factor @ 15%
Present Value
2000
£ 10000
0.893
£ 8930
0.870
£ 8700
2001
£ 40000
0.797
£ 31880
0.756
£ 30240
£ 40810
£ 38940
Net Present Value = Present Value - Initial Investment
NPV @12% = £ 40810 - £ 20000
= £ 20810
NPV @12% = £ 38940 - £ 20000
= £ 18940
Calculation of Net Present Value of cladding stones:-
Year
Net Cash Flow
Discount Factor @ 12%
Present Value
Discount Factor @ 15%
Present Value
2000
£ 20000
0.893
£ 17860
0.870
£ 17400
2001
£ 30000
0.797
£ 23910
0.756
£ 22680
£ 41770
£ 40080
Net Present Value = Present Value - Initial Investment
NPV @12% = £ 41770 - £ 20000
= £ 21770
NPV @12% = £ 40080 - £ 20000
= £ 20080
The below table shown the changes in percentage of Net Present Value:
Product
NPV @ 12%
NPV @ 15%
Percentage change in Net Present Value
A
£ 20810
£ 18940
18.70
B
£ 21770
£ 20080
16.90
As per above calculation, when there is change in discount rate from 12% to 15 %, the pet present value of both products such as carvings and cladding stones are declined. The degree of carvings and cladding stones is measured by sensitivity analysis. And hence the changes in percentage of carvings are more than cladding stones, the carvings is more risky product than cladding stones. And therefore one can say that if there is a change in discount rate, the carvings is more risky product for Vale machinery limited.
When there a changes in discount rate, interest rate, exchange rate, demand and supply, tax rate, labour cost and material cost etc., the sensitivity analysis is the valuable technique to identified how the net present value changes. There are various tools such as internal rate of return, cash flow and loan to measure under sensitivity analysis and it is helpful for decision making also. We can assume the changes in variables like price, revenue and costs etc. with the help of sensitivity analysis. E.g. we can assume the pet present value, when the cash flow is increase by 12% to 18%. The risk is always measured by its variation and when there is more variation in changes, it is always risky.
Sensitivity analysis is essential part to evaluate the effects when there are changes in variables. With the help of the sensitivity analysis we can find out the changes in sales, taxes, labour and how they affect the net present value. Sensitivity analysis define that how to change statement to the given model. Sensitivity analysis is impactful tool to determine what can be happen if own assumptions are not up to the level. Sensitivity analysis makes possible to get the desire outcome, and find out the loo false in our assumption and help to achieve the goal. It also minimise the risk of the investment.
