Capital Budgeting Techniques and Sensitivity Analysis

Sensitivity analysis can be understood as research of the uncertainty within the production of a mathematical model or system that can be allocated to several uncertainty sources within its inputs (Ai, Croce and Li 2013). Sensitivity analysis serves as techniques employed for determining the ways in which several values of certain variable impact on a a dependent variable within a specific cluster of assumptions. Sensitivity analysis is generated for analyzing the impact that the great range of variables has on the desired outcome. This analysis is relied on the variables effecting valuation that a financial model can indicate through employing the price and EPS variables (Borgonovo and Plischke 2016). For instance, Apple Inc employs sensitivity analysis along with the consideration of long-term cost of capital. Sensitivity analysis that is employed by Apple Inc serves as a technique of evaluating alterations in particular project’s NPV or the IRR for the given change within one of the variables. This signifies the extent to which a project is NPV or IRR is sensitive for a considered change in one among the variables (Fujimori et al. 2014). Apple Inc considers that the more the NPV of a project is sensible the more critical can be the variable. The following steps are deemed associated with the implementation of the sensitivity analysis that is mentioned under: Sensitivity analysis of the efficiency criteria for the purpose of investment project analysis serves as the calculating technique of researching and deciding the impact of changes in the individual values considered on the investment project analysis (Gospodinov, Kan and Robotti 2014). Apple Inc stated that strong implementation of the sensitivity analysis within the investment decision-making under certain uncertainty situations includes numerous major input parameters like the income, investment value, costs, discount rate in accordance with the impacts and effects of the alterations of these parameters (Kuehn, Simutin and Wang 2016). This is on the values of numerous basic criteria that can be considered as investment decision-making process namely the criteria of internal rate of return, net present value and the payback period. Sensitivity analysis serves as major criteria for the evaluation of investment projects serves as extremely complex process. With the help of the sensitivity analysis, the investors will be capable to obtain a great number of information regarding the impact of the input parameters on the criteria those are examined for conducting effective investment decision-making (Lee and Su 2014). Apple Inc stated that information can also be gathered regarding the impact of input parameters based on the criteria value that can further enhance investment decision making. Capital budgeting serves as a process though which investors determine which projects to select. Sensitivity analysis offers superior insight for the investors to take effective business decisions. Scenario analysis serves as the technique of evaluating likely future events through taking into account certain alternative possible outcomes. For this reason, for Apple Inc. scenario analysis can serve as a technique that can be the major form of projection, which does not attempt to indicate one accurate picture of the future (Mà ¸nster et al. 2014). Scenario analysis acts as a technique of anticipating the expected portfolio value that is in response to certain unfavorable event and might be employed to analyze theoretical worst-case circumstances.   Moreover, scenario analysis serves as a process in order to ascertain and evaluate the likely events that can take place in the upcoming years. This serves as a vital tool that is increasingly used in making projections over the upcoming years (Rangvid, Santa-Clara and Schmeling 2016). Scenario analysis is increasingly associated with capital budgeting techniques. An investment’s scenario analysis might include the followin g steps: Revealing the best-case output within most suitable value for all the inputs is an option of scenario analysis. For instance, Apple Inc considers that at the time of calculating net present value, the most suitable value for discount rate is used along with considering likely cash flow growth along with lower tax rate (Tian 2013). With implementation of effective capital budgeting techniques such as NPV and IRR, it can be stated that scenario analysis is a model output that is calculated for over an ample scenarios. Scenario analysis is widely employed in order to estimate proper investment value in several situations. Scenario analysis is greatly used in taking investment decisions through implementation of capital budgeting techniques like NPV and IRR (Zabarankin, Pavlikov and Uryasev 2014). For Apple Inc, scenario analysis was deemed most vital techniques for evaluating risks associated with the investment projects. The scenario analysis served as the techniques those are used by investors along with using the discount rates must be used for projects with several risks. Capital Asset Pricing Model (CAPM) is a model employed for theoretically determining suitable asset based rate on return in order to make decisions regarding adding assets within an efficiently diversified portfolio. Capital asset pricing model explains the prediction of the relationship that can be observed within the risk associated with asset along with its expected return (Ai, Croce and Li 2013). Taking into consideration that the Capital Market Line (CML), the market portfolio is deemed to encompass segmentation of all the risks assets. This is done through employing the market value of the assets in order to determine the weights (Borgonovo and Plischke 2016). The CML line is deemed to be arrived from CAPM that decides the anticipated return at numerous risk levels. In the capital asset pricing model, CML is only applicable only in case of an investor’s final portfolio and in the world of CAPM; the investors are likely to hold portfolios that rely on the CML. In CAPM, the capital market line is deemed higher than the efficient frontier as it focuses on the consideration of the risk-free asset within a portfolio (Fujimori et al. 2014). The capital asset pricing model signifies that market portfolio is majorly the efficient frontier. The assumptions of CAPM are deemed unrealistic and such reality simplification is vital for preparing useful models. Tolerance of the CAPM model’s assumptions that facilitates derivation of a well built, idealized through a model of manner within which the financial markets gauges risk and changes it within anticipated return. The capital asset pricing model indicates that the market portfolio serves as efficient frontier (Rangvid, Santa-Clara and Schmeling 2016). Within the CAPM, the securities are priced so that the anticipated risks counterbalance the decided returns. There are two aspects within the CAPM model, which requires generating Capital Market Line. The capital market line indicates the investment returns of an investor for a particular portfolio. The capital market line employs the CAPM formula in order to calculate the anticipated return of a portfolio or security (Rangvid, Santa-Clara and Schmeling 2016). CML serves as the graphical representation of the CAPM formula. It explains the relationship between the systematic risk and expected return related with a portfolio. The CAPM formula that consists of formula on capital market line is helpful in deciding whether a security can be considered for effective investment decision making. The association between the CAPM formula and capital market line are indicated in the formula below:   is deemed to denote the point associated with the market portfolio (M). All the portfolios selected by a rational investor are deemed to have a point   that relies on the capital market line (Mà ¸nster et al. 2014). Considering this formula, it can be said that the CAPM model can be employed in order to measure the systematic risk associated with a single share. Moreover, the transformation line, which remains tangential to the efficient set along with having intercepted within risk-free rate Rf, is the capital market line. This defines that a particular composition of the risky assets those investor wishes to hold. This is deemed as market portfolio (M). Moreover, CML serves as the transformation line, which is observed to be tangential with the efficient frontier (Mà ¸nster et al. 2014). Capital Market Line (CML) serves as a line that connects returns with no-risk investments along with overall market returns (Zabarankin, Pavlikov and Uryasev 2014). The difference between efficient frontier and capital market line is that capital market line involves less risk investments ad all the portfolios within it are efficient frontiers. Capita market line is employed in order to analyze the performance of portfolio. Certain points below any other point within the line will offer decreased returns along with similar risks and for such reasons these are not ideal. Capital market line is deemed a measure used to analyze performance of portfolio. Capital Market Line (CML) is a graph used within the capital asset pricing models in order to signify rates of return within the market portfolio (Borgonovo and Plischke 2016). Capital market line explains rates of return for the effective portfolios those are relied on the degree of risk along with risk free rate of return for a particu lar portfolio. Capital Market Line initiates from considering the assumption that all the company’s investors needs to possess market portfolio. Intensity of risk is deemed to be positively correlated to the anticipated return (Zabarankin, Pavlikov and Uryasev 2014). The Capital Market Line serves as the linear combinations of the risk-free asset and portfolio. Portfolios under the capital market line are deemed inferior that indicates new efficient set. Capital Market Line is observed to remain within the capital asset pricing model in order to indicate the rates of return for efficient portfolios likely to face the risk level for a market portfolio along with risk-free return rate (Borgonovo and Plischke 2016). The capital market line is generated through drawing a tangent line from the point of intercept on the efficient frontier to the situation where the expected return on a holding is similar to the risk-free return rate. The capital market line facilitates the investor in taking into account the risks of several additional assets within the remaining portfolio. The capital market line results from the association with the market portfolio along with the risk-free asset (Zabarankin, Pavlikov and Uryasev 2014). All the points in consideration to CML have increased risk-return profiles to certain portfolio within the efficient frontier with the exception of the market portfolio that serves as point within efficient frontier within which capita market line is a tangent. From the CML perception, such portfolio encompasses all the risky assets and has less holding on the risk free assets. As per CAPM, market portfolio signifies efficient frontier and this can be gathered as cluster of portfolios (Lee and Su 2014). The market portfolio in combination to the risk-free asset is able to produce an increased return than the efficient frontier. Therefore, it can be said that the combination of the market portfolio along with the risk-free asset leads to emergence of capital market line. The major techniques employed for project analysis are the NPV and IRR analysis. Sensitivity analysis considers the NPV and IRR of an investment project at the time more than one variable alterations (Lee and Su 2014). 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