17 Sensitivity Analysis

Ms.Vinodini Kapoor

1. Learning Outcome:

After completing this module the students will be able to:

• Understand the basic concept of sensitivity analysis (SA).
• Understand the characteristics and benefits of sensitivity analysis.
• List the various steps involved in the SA process.
• Understand the importance of sensitivity analysis to support decision making.
• Analyze various industry applications of sensitivity analysis.

2. Introduction

After venturing into the food business about five years ago, you observe that in the past two years, sales have been quite dormant. A number of new eateries have opened nearby, leading to lower footfall in your restaurant. You hire a consultant to look into different aspects that can affect sales positively. He helps you draft a roadmap of activities for next twelve months. Best is to understand the situation using sensitivity analysis. You work out changes on the decoration, seating, lighting, menu and promotional offers. However, each change should be measured against its cost and the impact on sales. Eventually, changes in the menu and seating plan seem most viable in terms of costing. From a self service mode, if catering is introduced, it enhances customer experience and can possibly increase sales by 20%. To sum up, it is sensitivity analysis that measures each option with respect to increase in revenue without a substantial increase in the cost structure.

A sensitivity analysis is an estimation of what happens if variables are changed. The larger emphasis is on the overall impact by change in one variable. To change one particular aspect of your business, how will it affect the other attributes? To simplify, by changing one aspect of the restaurant format in the above example, how will it impact sales or optimize operations thereby leading to higher revenues?

This can also be understood from the statement in exhibit1. Keeping other variables constant, an increase in sales price decreases sales volume which is needed to attain a target income.

Exhibit 2: How Change in One variable affects business?Source: https://www.gljpc.com/sites/default/files/Risk%20%26%20Sensitivity%20Analysis%20-%20Economic%20Sensitivities_0.jpg

Sensitivity analysis helps managers make powerful analysis into everyday problems that affect business. It is important to note, that it does not give a solution to a problem. But, it provides the means to understand the problem better. Technically, “Sensitivity analysis is a method that states how the different values of an independent variable impact the dependent variable under certain constraints. This technique is used with boundaries or limiting factors that depend on certain variables, such as, the effect of change in interest rates on home loans or bond prices”.

As shown in exhibit 3, simulation model may encounter uncertainty and errors from various data sources. Some of these could include – errors present in data or mathematical models, errors due to parameter estimation or resolution levels.

3. Characteristics and benefits of Sensitivity Analysis

This concept analyses the possible uncertainty with regard to decision making. It considers each probable factor and calculates the required change to reverse the original decision. In other words, it takes into consideration, the ‘what – if’ question. Exhibit 4 highlights the same underlying concept which is the chief characteristic of sensitivity analysis. Sensitivity analysis would help determine the extent of this uncertainty.

3. Characteristics of Sensitivity Analysis

It is the influence that one parameter (the independent variable) has on the value of another (the dependent variable), both of which may be either continuous or discrete. Exhibit 5 represents a screen shot of parameter estimation functionality in the MATLAB –Mathwork software package while Exhibit 6 shows the optimization functionality.

• This statistical technique looks into how particular inputs and parameters change outputs. One input is changed at a time to understand the corresponding affect on output. It does not necessarily mean that inputs are interrelated.
• Sensitivity analysis is a limiting case of ‘what-if analysis’ that involves iterative changes to a single variable at a time. Usually in a business related scenario, managers repeat changes to a variable and observe the effects on others variables.

Exhibit 7 below highlights a scenario where impact each of the variables such as development time, development cost, product cost and performance are monitored in regard to total project cost.

• Managers use this technique to interpret the variables that need to be monitored while making decisions. (E.g. at what certain point, the rate of interest of a home loan renders the project unfeasible).

Benefits of sensitivity analysis

• Sensitivity analysis is a tool that is largely used by the managers at senior levels of the organization. The likely outcome is referred as a what-if analysis. It is used to test the effect of critical and non critical variables on the overall profitability of a company. It helps to focus the concentration of senior managers and strategic decision makers to ensure that business decisions are in line with the vision and mission statements of the firm.

• Capital budgeting is a very critical application of sensitivity analysis. It helps to get an idea of the relationship between different attributes such a sales, liquidity, profitability etc
• Sensitivity analysis also measures the extent of change in variables and approximation of the bottom line of the cash flow and profitability of a project.
• It helps to create a rough draft of the project before actually committing resources. This helps the decision makers in the long run to get a better estimate of how the project would turn out.
• It helps to organize the information in a more structured and organized manner. This facilitates better decision making as critical information influencing decisions is highlighted. This concept is understood better from Exhibit 8 where the need for sensitivity analysis is highlighted w.r.t availability of data.

• It is easy to feed values in a sensitivity analysis software package that can assess values and perform calculations faster. The graphic user interface one such case of a software package is shown in Exhibit 9. This shows how sensitivity analysis and uncertainty analysis should be performed in cohesion. While an uncertainty analysis determines the variability of results, sensitivity on the other hand determines the inputs to be varied for change in output as shown in Exhibit 10.
• Sensitivity analysis helps the management to lay higher emphasis to quality control and leaves an impact on determining the success or failure of a project.

4. Steps involved in Sensitivity Analysis

The first and foremost step in this method includes the identification of the dependent variable. This further helps to predict the independent variables that impact the dependent variable.

Further, the following steps are to be kept in mind.

• Determination of the target function and choosing best estimates to arrive at a decision.
• Analyzing the variables one by one to determine how much the original estimate can change.
• Allocating a distribution function and creating a matrix highlighting inputs.
• Assessing the model and calculating the target function distribution.
• Choosing a technique for evaluating the impact or comparative weight of every input element on the target function.

5. Importance of Sensitivity Analysis to support decision making

Decision support system works on the principle of analytical modeling. The different ways in which a DSS supports information systems are listed in Exhibit 11. Users explore alternatives without pre-specified information. There are several basic types of analytical modeling activities as shown in Fig1.

A decision maker may require some idea of how sensitive an alternative choice might be to the changes in one or more of those values. The analyst has to find the range of feasibility around which choice of the alternative remains the same. Successful decision making requires a sequence of steps, the first being to carefully define the problem.

Sensitivity analysis analyzes the problem intricately and answers a number of “what if” questions.In what-if analysis, a decision maker:

• Shall introduce a change in variables and study the relationship among them.
• Observes the effect on other variables.

A model based decision support system helps:

• To test the optimum function and highlight the critical values, the break even and threshold values.
• The threshold values explain whether change in a given variable will change the optimal decision.
• Identify sensitive variables and optimal solutions.
• To support decision making with respect to the present situation.
• Comparison of values between situations involving different levels of decision making.

The analysis helps to make assessments in a project in case the estimates turn out to be unreliable. This helps business analysts to analyze the results better before any further investment is made. This implies the identification of critical values of a project. E.g., project feasibility study, risk assessment.

6. Industry applications of sensitivity analysis

Measurement of sensitivity – The following steps are followed to conduct a sensitivity analysis.

Fundamentally, we keep the output at the base value of the input for which we intend to measure the sensitivity. Meanwhile, rest of the inputs in the model is kept constant.

• In an actual scenario, with the net present value at W1 we intend to measure the sensitivity at the discount rate. For this, the other inputs like cash flow, growth and tax rate, depreciation are constant.
• The value of output at a new value of the input (say W2) is obtained while keeping other inputs constant.
• The percentage change in input and the output is calculated. Sensitivity is then obtained by dividing the percentage change in output by the percentage change in input.

The next step is to test the sensitivity for another input while keeping the rest of inputs constant. This process is carried till we get the critical values for each input. Higher the sensitivity figure, more sensitive is the output to any change in the input and vice versa.

Exhibit 13 highlights a number of risk analysis techniques. Sensitivity analysis is one such method of estimating quantitative risk.

• Businesses decisions involve risk in lieu of a higher return or profit. The goal of the management is profit maximization and cost minimization. They strive to minimize the level of risk involved. Sensitivity analysis helps them in risk assessment.
• This concept helps managers to analyze what values lead to higher profits. The repercussion of undertaking any last minute change in project plan can be assessed. It helps in a cause effect analysis of any system.
• It helps to remove redundancy of data in a data acquisition system by filtering unsolicited data. This system converts analog data into its digital equivalent which is represented in binary form using combination of 0 & 1.
• A sensitivity model helps in price determination as shown in Exhibit 14, estimation of required expenditure on advertising, volume of production. Software packages make it easier to input values and obtain results. The inbuilt functionality of MS Excel, Lotus 1-2-3 and MATLAB are such packages that offer these functionalities.
• Sensitivity analysis finds numerous applications in areas of finance such as capital budgeting. It can help determine the discount rate, growth rate, internal rate of return etc.
• This technique is of business utility since it highlights the dependency of output value on every input variable. It reveals the extent to which variables can be altered to achieve the desired outcome.

• A technique which is reverse of sensitivity model is known as backward sensitivity analysis. This is also termed as goal-seek. This method sets a target value to be achieved. Other variables are changed time and again till the final outcome is achieved.
• For example, to increase the level of production by say 40 percent, the software assigns the target value to the production level. Eventually, the required changes are made to other factors, such as the amount of material, men, machinery to obtain the target production level.

6.1 Advantages and disadvantages of Sensitivity Analysis

There are various advantages to the concept of sensitivity. Few of them can be understood below:

• It makes the identification of variables easy for the decision maker.
• It helps to identify the weak areas of a project. It helps to align business processes in line with the corporate goals and mission of the organization.
• It helps to remove redundancy and focus on attributes that need attention by highlighting the relevant variables.
• The availability of software packages makes computation accurate and easier.

At the same time, there are several disadvantages listed below:

• At certain times, the results may not be very clear which makes the analysis more complex.
• It may be unable to highlight the interrelationships between certain variable that may affect the final result. In other words, the assumption that changes to variables can be made independently may not be correct in each case.
• Simulation models can enable us to change more than one variable at a time. But the probability of such a change cannot be highlighted, although it can state the extent to which these variables can be changed.
• Also, there is lack of probabilistic measure of the exposure to risk. Although one among the several outcomes may be achieved, the analysis cannot ascertain the likelihood.

7. Summary

Sensitivity analysis is an analysis method that is used to identify how much variations in the input values for a given variable will impact the results for a mathematical model. Sensitivity analysis is useful in various fields such as business analysis, finance, market analysis, engineering, physics and chemistry. In a business context, sensitivity analysis can be used to improve decisions made based on certain calculations or modeling. At the organizational level, companies use a number of computing software packages to carry out sensitivity analysis. A company uses this technique to identify the appropriate data and sees underlying assumptions regarding investment and return on investment (ROI), or to optimize allocation of assets and resources. Sensitivity analysis is commonly used for risk estimation. It helps to calculate the degree of change in variables and assumptions that reflect the criteria to determine the cash flow and profitability. The idea of carrying out risk assessment before the start of a project is to give managers a broad view of what critical aspects should be looked at. However, it is important to note that sensitivity analysis does not give a complete solution to any problem. It enables a better analysis and interpretation which helps to take business decisions better. It forms an integral part of the decision support systems in context of management information systems.

Web Resources

1. www.cimaglobal.com
2. http://www.computerbusinessresearch.com/Home/decision-making/goal-seeking-analysis
3. http://xplaind.com/167040/sensitivity-analysis