1. Explanation of Concepts Associated with Capital Budgeting Techniques?
2. Similarities and Differences between Capital Asset Pricing Model and Capital Market Line?
1. Sensitivity Analysis
A sensitivity analysis is a technique used to determine how different values of an independent variable affect a particular dependent variable under a given set of assumptions. This technique is used within specific boundaries that depend on one or more input variables, such as the effect that changes in interest rates have on bond prices. The sensitivity analysis is based on the variables affecting valuation, which a financial model can depict using the variables' price and EPS (Ai, Croce and Li 2013). The sensitivity analysis isolates these variables and then records the range of possible outcomes. A scenario analysis, on the other hand, is based on a scenario. The NPV of the project is recalculated under these different assumptions. This method of recalculating the NPV or IRR, by changing each forecast is called sensitivity analysis.
Sensitivity analysis is a way of analyzing change in the project’s NPV (or IRR) for a given change in one of the variables. It indicates how sensitive a project’s NPV (or IRR) is to changes in particular variables. The more sensitive the NPV, the more critical is the variable. The following three steps are involved in the use of sensitivity analysis:
- Identification of all those variables, which have an influence on the project’s NPV (or IRR)
- Definition of the underlying (mathematical) relationship between the variables
A whole range of questions can be answered with the help of sensitivity analysis. It examines the sensitivity of the variables underlying the computation of the NPV or IRR, rather than attempting to quantify risk (Borgonovo and Plischke 2016). It can be applied to any variable, which is an input for the after-tax cash flows. Before proceeding to sensitivity analysis, it is necessary to have knowledge about some term. Sensitivity analysis needs to be realized in a systematic manner. To meet the above purposes, the following steps are recommended to be followed:
1.Identify key variables to which the project decision may be sensitive
2.Calculate the effect of likely changes in these variables on the base-case IRR or NPV, and calculate a sensitivity indicator and/or switching value
3.Consider possible combinations of variables that may change simultaneously in an adverse direction
4.Analyze the direction and scale of likely changes for the key variables identified, involving identification of the sources of change (Fujimori et al. 2014).
Scenario analysis can be thought of as performing multiple sensitivity analyses at the same time. Investors conducting this type of analysis will look at the variables that affect a company's bottom line and use them to plan accordingly. For example, investors considering purchasing a company will want to understand the cash flow of the business. This is more than just considering revenue and expenses (Gospodinov, Kan and Robotti, 2014). Expenses can manifest themselves in a number of ways including wages, pensions, benefits, costs associated with production, and so forth. By changing a combination of these factors, investors can get a feel for a number of different scenarios.
Scenario analysis is a method of predicting future values of portfolio investments based on potential events. This process is also used in company operations outside of the investment world. Most managers perform scenario analysis in their business decision-making process to determine the best course of action to take the organization to maximize profits (best-case scenario). They also use this technique to examine the worst possible solution (worst-case scenario) and anticipate potential losses and operational problems (Kuehn, Simutin and Wang 2016). Management also uses this process when launching a new product to avoid cannibalization of existing product sales. Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows. With the help of scenario analysis, NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account.
NPV analysis is sensitive to the reliability of future cash inflows that an investment or project will yield. This is used in capital budgeting to assess the profitability of an investment or project (Lee and Su 2014). Scenario analysis is an extension of sensitivity analysis with the difference being that the former evaluates the impact on the project cash flows (and ultimately NPV and IRR) of changing more than one uncertain variable at a time. A common approach with scenario analysis is to calculate the NPV and IRR using the conventional method and assumptions. This is referred to as the ‘base case’. Thereafter, a ‘best case’ and ‘worst case’ are indicated, at which the values of the flexed variables are calculated. From this, we can establish the values of the project cash flows, NPV and IRR for each scenario.
Capital budgeting is, by definition, forward looking. When dealing with expected resources and demands, uncertainty is a major factor. Sensitivity analysis is a statistical tool that determines how consequential deviations from the expected value occur (Mønster et al. 2014). Sensitivity Analysis deals with finding out the amount by which we can change the input data for the output of our linear programming model to remain comparatively unchanged. Sensitivity Analysis in Capital Budgeting seeks to identify the effect of changes in one variable, e.g. Life of the Project, Cost of Capital, Project size, etc on the Net Present Value or Internal Rate of Return by keeping all other variables constant. It is a study, which determines how changes or errors in the values of parameters affect the output of a model. Scenario Analysis is evaluation of Net Present Value or Internal Rate of Return of a Project under series of specific scenarios, based on macro economic factors, industry and firm specific factors (Rangvid, Santa-Clara and Schmeling, 2016).
2. Capital Asset Pricing Model
The capital asset pricing model (CAPM) is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for the pricing of risky securities, generating expected returns for assets given the risk of those assets and calculating costs of capital. The CAPM model says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken (Tian 2013). The security market line plots the results of the CAPM for all different risks (betas). The capital market line (CML) appears in the capital asset pricing model to depict the rates of return for efficient portfolios subject to the risk level (standard deviation) for a market portfolio and the risk-free rate of return. With its insight into the financial markets’ pricing of securities and the determination of expected returns, CAPM has clear applications in investment management. Its use in this field has advanced to a level of sophistication far beyond the scope of this introductory exposition.
The capital asset pricing model (CAPM) proves that the market portfolio is the efficient frontier. It is the intersection between returns from risk-free investments and returns from the total market (Zabarankin, Pavlikov and Uryasev, 2014). The capital market line (CML) represents this. The capital asset pricing model determines the fair price of investments. Once the fair value is determined, it is compared to the market price. A stock is a good buy if the estimated price is higher than the market price. However, if the price is lower than the market price, the stock is not a good buy. In the CAPM, the securities are priced, so the expected risks counterbalance the expected returns. There are two components needed to generate a CAPM and CML. The capital market line conveys the return of an investor for a portfolio. The capital market line assumes that all investors can own market portfolios. Capital market line and CAPM formula Let (σM, rM) denote the point corresponding to the market portfolio M. All portfolios chosen by a rational investor will have a point (σ, r) that lies on the so-called capital market line r = rf + rM − rf σM σ, (1)
The CML is considered superior to the efficient frontier1 since it takes into account the inclusion of a risk-free asset in the portfolio. The capital asset pricing model (CAPM) demonstrates that the market portfolio is essentially the efficient frontier. This is achieved visually through the security market line (SML) (Tian 2013).
Capital Market Line
The capital market line is created by sketching a tangent line from the intercept point on the efficient frontier to the place where the expected return on a holding equals the risk-free rate of return. However, the CML is better than the efficient frontier because it considers the infusion of a risk-free asset in the market portfolio. When analyzing a portfolio, the CML is preferred over such analysis as the efficient frontier, because the CML takes into account the risk-free assets that are included in the portfolio (Zabarankin, Pavlikov and Uryasev, 2014). The steeper the slope of the CML, the more the expected return must change for each unit of change in the standard deviation. CML analysis is one of the many ways investors allocate their investment portfolios to achieve the maximum amount of expected return for the minimum amount of risk. The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio. The CML is a line that is used to show the rates of return, which depends on risk-free rates of return and levels of risk for a specific portfolio.
CML is the efficient frontier after the risk free asset has been added to the minimum variance portfolios (the curvy line), of which the most important risky (i.e., all risk assets) is the Market portfolio (b/c it has the highest Sharpe ratio) (Ai, Croce and Li 2013). CML has total risk (volatility) on the X-axis. In the context of the capital market line (CML), the market portfolio consists of the combination of all risky assets and the risk-free asset, using market value of the assets to determine the weights. The CML line is derived by the CAPM, solving for expected return at various levels of risk. The CML results from the combination of the market portfolio and the risk-free asset (the point L). All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier, with the exception of the Market Portfolio, the point on the efficient frontier to which the CML is the tangent. From a CML perspective, the portfolio M is composed entirely of the risky asset, the market, and has no holding of the risk free asset, i.e., money is neither invested in, nor borrowed from the money market account (Ai, Croce and Li 2013).
The CML provides a risk return relationship and a measure of risk for efficient portfolios. The appropriate measure of risk for an efficient portfolio is the standard deviation of return of the portfolio. There is a linear relationship between the risk as measured by the standard deviation and the expected return for these efficient portfolios. With CML, CAPM can be used to identify underpriced and overpriced securities (Gospodinov, Kan and Robotti, 2014). If the expected return on a security calculated according to CAPM is lower than the actual or estimated return offered by that security, the security will be considered underpriced. On the contrary, a security will be considered to be overpriced when the expected return on the security according to CAPM formulation is higher than the actual return offered by the security.
Ai, H., Croce, M.M. and Li, K., 2013. Toward a quantitative general equilibrium asset pricing model with intangible capital. Review of Financial Studies, 26(2), pp.491-530.
Borgonovo, E. and Plischke, E., 2016. Sensitivity analysis: a review of recent advances. European Journal of Operational Research, 248(3), pp.869-887.
Fujimori, S., Kainuma, M., Masui, T., Hasegawa, T. and Dai, H., 2014. The effectiveness of energy service demand reduction: A scenario analysis of global climate change mitigation. Energy policy, 75, pp.379-391.
Gospodinov, N., Kan, R. and Robotti, C., 2014. Misspecification-robust inference in linear asset-pricing models with irrelevant risk factors. Review of Financial Studies, 27(7), pp.2139-2170.
Kuehn, L.A., Simutin, M. and Wang, J.J., 2016. A labor capital asset pricing model.
Lee, M.C. and Su, L.E., 2014. Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate. Universal Journal of Accounting and Finance, 2(4), pp.69-76.
Mønster, J.G., Samuelsson, J., Kjeldsen, P., Rella, C.W. and Scheutz, C., 2014. Quantifying methane emission from fugitive sources by combining tracer release and downwind measurements–a sensitivity analysis based on multiple field surveys. Waste Management, 34(8), pp.1416-1428.
Rangvid, J., Santa-Clara, P. and Schmeling, M., 2016. Capital market integration and consumption risk sharing over the long run. Journal of International Economics, 103, pp.27-43.
Tian, W., 2013. A review of sensitivity analysis methods in building energy analysis. Renewable and Sustainable Energy Reviews, 20, pp.411-419.
Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.