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Sensitivity and Scenario Analysis in Capital Budgeting

Discuss about the Empirical and Theoretical Analysis.

Capital budgeting is a technique through which the business takes decision related to selection of the project to be carried out by it. It takes into consideration the investment made by the company in a particular project and the returns that will be generated from the project. Sensitivity analysis helps in providing additional information relating to the selection of the project. There are different methods used to examine the financial effect of a certain project. Sensitivity analysis is a technique used to evaluate the impact of independent variables on the dependent variable under a given set of assumptions. Besides this, it has some limitations as it takes into consideration one or more variables as an input to know their effect on the dependent variable for example changes in the interest rates have an effect on the prices of bonds (Ehrhardt and Brigham, 2008).

It is also regarded as a what-if analysis which facilitates in prediction of an outcome of a decision with certain number of variables. These variables help in gaining knowledge of the effect of changes in one variable on the outcome. Sensitivity analysis facilitates in providing the information related to the impact of range of variables on a given outcome. This analysis facilitates businesses to gain knowledge regarding the outcome that will be obtained related to the project at the time of the assumptions turned out to be unreliable. Besides this, it also make changes in the assumption in order to find its impact on the finances generated from the project. This help businesses to make strategies for the projects that does not generate expected profits (Peterson and Fabozzi, 2004).

Sensitivity analysis is carried out on a project before making investment in it in order to gain knowledge regarding its results under valid and reliable assumptions. It helps in assessing the risks by the way of variables that have a large influence on the net benefits of the project. Besides this, it also helps in measuring the influence of the variables on the net benefits of the project in numerical terms. It also facilitates in testing or verifying the effects of the variations in the variables on the IRR of the project. It is the tool used to quantify the risk parameters and its consequences for the purpose of establishing a valid risk level in a particular situation. Besides this, sensitivity analysis also helps in the assessment of the responsiveness of the NPV to changes in the variables used for the calculation of the NPV (Dayananda, 2002).

Scenario Analysis in Capital Budgeting

There are different independent variables on which the NPV of the project depends such as selling price, sales volume, initial outlay, discount rates and so on. Therefore, the sensitivity analysis provides information related to the impact on the NPV of the project by the changes made in one or more of these variables. Along with this, this analysis also helps in finding out the reasons behind the failure of the project. It also helps in finding out that to which variables, NPV is most sensitive. This information helps in controlling of those variables to which NPV is most sensitive in order to attain positive returns from the project after a certain period (Zhamoida and Matsiuk, 2011).

It is the process that helps in the estimation of the expected value of a portfolio after a given period of time by making assumptions related to the changes in the values of the securities present in the portfolio. It is mainly used to estimate the changes in the value of the portfolio in response to an unfavourable event. It also facilitates in making changes in the value of a portfolio on the basis of the occurrence of different situations that are referred to as scenarios. There are several methods through which scenario analysis can be done such as standard deviation of monthly security returns and estimating the expected value of the portfolio that provides returns (Baker and English, 2011).

Scenario analysis helps in accessing different outputs of the project. In addition to this, it also facilitates in determination of standard deviation, variance of NPV. In addition to this, it poses difficulty in estimating the probabilities of the occurrence of the events. Scenario analysis helps in the estimation of cash flows from risky assets by the way of estimation of the cash flows from most likely scenario and the use of probability average of the cash flows in different scenarios. There might be also a possibility that cash flows might be higher than the expected in some scenarios. Besides this, it might also be possible that the scenarios might be less than the expected cash flows in some scenarios. For the purpose of gaining insights regarding the effect of risk on different variables, scenario analysis is used as it helps in the determination and anticipation of the value of the asset and cash flows under various scenarios (Gitman, Juchau and Flanagan, 2015).

For the purpose of assessing the value of the firm, there is a need of estimating the revenue and profit at high levels and discount rates at low level. This scenario is considered best for the company as it results in increasing the bottom line of the organisation. In place of estimating the revenue growth and margins, there is a requirement of making a choice between taking those scenarios in consideration related to profit margin and revenue growth that provides feasible yields and outcome. There are four steps in which a scenario analysis is conducted (Lee and Lee, 2016).

Capital Asset Pricing Model and Capital Market Line

In the first step different factors are analysed and selected around which different scenarios are built. These factors may include a new plant, competitors for a consumer product firm, a new phone service and so on. It is required for the analysts to focus on two or three critical factors that help in the determination of the asset and framing scenarios around these factors. The second step is the determination of more number of scenarios for each factor in order to get realistic results. The next step is to estimate the cash flows for the asset under each scenario. The last step is to assigning probabilities to each scenario (Lasher, 2016).

Capital Asset Pricing Model (CAPM) is a model that helps in determination of the relationship between expected return for assets and systematic risk. CAPM model helps in the calculation of the return on investment and investment risk that are expected from a asset or stocks. There is an existence of two types of risks in an investment such as systematic risk and unsystematic risk. Systematic risk cannot be diversified and regarded as market risk such as recession and interest rates. In addition to this, unsystematic risk is a risk specific to individual stocks and can be diversified as there is an increase in the number of stocks in a portfolio. This type of risk is that part of the stock return which is not affected by the movements in the market environment (Levy, 2011). The formula of the CAPM model is expressed as follows.

As per the CAPM model, beta is considered as the best measure of the risk of a stock. Capital Market Line is the tangent line which starts from the risk free asset to feasible region for risky rates (Levy, 2011). The equation of capital market line is as follows:

E(Rp) = xE(Ry)+(1-x)Rf

Where: (1-x) = the portfolio percentage which is invested in the risk free asset

x= the portfolio percentage which is invested in risky assets

Rf= the risk free interest rate

E(Ry)= the expected return of the risky asset portfolio

There are certain assumptions made under CAPM model. It is assumed that investors diversify their portfolios. In addition to this, a single holding period is assumed by the CAPM for the purpose of making comparisons of the returns on different securities. It is also assumed that the investors borrow and lend the securities at risk free rate of return. The other assumption is that the securities are valued correctly so that the returns can be plotted on security market line. There is certain assumption such as there is absence of taxes and transaction costs (Sharifzadeh, 2010).

Besides this, the information is freely available to investors. Besides this, there is an existence of risk averse investors. In addition to this, CML does not provide information related to the relationship between risks associated with individual securities and returns obtained from them. CML considers only those portfolios in which the risks are not diversified. There is no use of risky investments in CML. Besides this, the relationship between risk and return on individual securities are calculated by security market line. In the capital market line, efficient portfolios are considered. In the above graph all the securities lie on the CML. The risk free assets are denoted by E (Rp), and risky portfolio is denoted by M. C denotes risk avoiders and L denotes risk takers (Kürschner, 2008).     
Similarities between CML and CAPM

Security market line shows the equilibrium relationship between the co variance of the securities with the market portfolio and expected return on securities. It is also referred to as CAPM. Besides this, there is an existence of a positive correlation between the CML and CAPM which states that the higher the risk the investor takes will receive high returns on their portfolio. Both the tools are considered as the best tool by the investors as it facilitates them to select the portfolio. These tools are considered viable for the purpose of management and analysis of the portfolios and investment (Pahl, 2009).

The relationship between E(r) and σ for the efficient portfolios along with the efficient frontier is represented by CML. In addition to this, it also provides information between equilibrium relationship between those securities that does not possess unsystematic risk. On the other hand CAPM takes into consideration all the securities and portfolio irrespective of their efficiency but CML only takes one efficient portfolio. CAPM measures risks by the beta coefficient whereas, CML measure risks by the way of standard deviation (Giovanis, 2010).

In addition to this, under CAPM, investors only takes into consideration risk and return and ignore transaction costs and taxes. In contrast to this, investors make a choice of the portfolio on the basis of riskless securities and market portfolio in CML. CAPM model provides risk return trade-off which means that the investors who make investment in risky assets gain high profits in return whereas in CML the investor estimates the return on its investment on the basis of its risk bearing capacity in a portfolio (Trunda, 2011). Besides this, the cost of equity, risk premium, returns and hurdle rates can be determined by the way of CAPM with regard to both efficient and inefficient portfolio, but in the case of CML, the cost, return, and hurdle rates are determined in efficient portfolios only (Elton, et al. 2009).

It can be concluded that nowadays, companies focus on making corporate decision making by the use of different capital budgeting techniques in order to select the best project which provides higher returns. For this purpose, managers take into consideration the sensitivity and scenario analysis. These tools help in considering different circumstances and their probable impact on the portfolio or the outcome of the project. This helps in taking appropriate decisions related to making investment in the project or not. For the purpose of taking decisions top level management involves middle level managers in order to take appropriate decisions as the risks can be quantified and its impact on the project and portfolio is determined. Besides this, CML and CAPM model is being used to make a decision by the investor to make a decision of making investments in a portfolio or not


Baker, H.K. and English, P. 2011. Capital Budgeting Valuation: Financial Analysis for Today's Investment Projects. John Wiley & Sons.

Bierman, H. and Smidt, S. 2014. Advanced Capital Budgeting: Refinements in the Economic Analysis of Investment Projects. Routledge.

Dayananda, D. 2002. Capital Budgeting: Financial Appraisal of Investment Projects. Cambridge University Press.

Ehrhardt, M. and Brigham, E. 2008. Corporate Finance: A Focused Approach. Cengage Learning.

Elton, E.J. et al. 2009. Modern Portfolio Theory and Investment Analysis. John Wiley & Sons.

Giovanis, E. 2010. Application of Capital Asset Pricing (CAPM) and Arbitrage Pricing Theory (APT) Models in Athens Exchange Stock Market. GRIN Verlag.

Gitman, L.J., Juchau, R. and Flanagan, J. 2015. Principles of Managerial Finance. Pearson Higher Education AU.

Kürschner, M. 2008. Limitations of the Capital Asset Pricing Model (CAPM). GRIN Verlag.

Lasher, W.R. 2016. Practical Financial Management. Cengage Learning.

Lee, J.C. and Lee, C.F. 2016. Financial Analysis, Planning & Forecasting: Theory and Application. World Scientific Publishing Co Inc.

Levy, H. 2011. The Capital Asset Pricing Model in the 21st Century: Analytical, Empirical, and Behavioral Perspectives. Cambridge University Press.

Pahl, N. 2009. Principles of the Capital Asset Pricing Model and the Importance in Firm Valuation. GRIN Verlag.

Peterson, P.P. and Fabozzi, F.J. 2004. Capital Budgeting: Theory and Practice. John Wiley & Sons.

Sharifzadeh, M. 2010. An Empirical and Theoretical Analysis of Capital Asset Pricing Model. Universal-Publishers.

Trunda, M. 2011. Capital Asset Pricing Model. GRIN Verlag.

Zhamoida, O.A. and Matsiuk, M.S. 2011. Sensitivity Analysis in Capital Budgeting. Economic Herald of the Donbas 4(26), pp. 132-136.

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