## 1. Internal Rate of Return and Capital Budgeting

1.How their decision making could be related to capital budgeting techniques such as, Internal Rate of Return relation to Capital Budgeting Techniques?

1. Explain and identify similarities and differences between Capital Asset Pricing Model and Capital Market Line?

**1.** Capital Budgeting is the process by which a Business makes decision on whether to take up a project or not. This involves analysis of the amount of money which is required to invest in the project and the revenue that the project will generate. A business uses various techniques and analysis tools to determine the effects of the various projects[1]. This may involve the calculation of the time taken for the undertaking to produce return to cover the initial contribution, or the amount of cash flow that will be produced from the undertaking totally in its entire span of period along with the amount of profit or loss generated from the same or the break even of the project can be calculated using the discount rate of the project[2]. All the techniques and methods involve making assumptions and making estimations about the future performance of the project. The results derived from the various techniques help the management in decision making. However, the assumptions and estimations so made can turn out to be inaccurate and there may be unexpected results from the project. Sensitivity Analysis and Scenario Analysis are two of the various techniques that provide additional insight for the corporate to make decision regarding investments in various projects.

Sensitivity analysis is a methodology which determines how distinct values of a separate variable effect a specific dependent variable under a given kit of assumptions. In different term, sensitivity analysis helps a business to estimate what will happen to the project if the estimates and assumptions turn out to be inaccurate and unreliable. It involves changing one assumption or estimates while the others remaining constant to see the impact on the project finances. Hence, this analysis helps the managers to prepare themselves for against the inaccurate assumptions and unexpected results from the project so that they can make a better analysis before decision making. Sensitivity Analysis is also referred to as “what-if analysis” or “simulation analysis” as it involves the prediction of outcomes under a certain range of variable input. This is done by creating a set of variable inputs and then studying the impact of change in input on the outcome of the project[3].

## 2. Sensitivity Analysis and Scenario Analysis in Capital Budgeting

This analysis ascertains how the alloacation of feasible Net Present Value or the Internal Rate of Return of a project under account is affected sequential to a change in one specific input variable. It begins with base-case scenario which is developed using expected values for each input. Sensitivity Analysis provide the solution for each and every situation that take place if there is any change in variables. For instance estimating the NPV of the project, if the selling price falls by 10%, or determining the Internal Rate of Return if the project life is 3 years instead of the expected life of 5 years. Sensitivity Analysis can additionally be applied to compute the break-even point of the project that is the revenue required to meet the cost in net present value terms[4].

As mentioned above, each variable is changed by a certain percentage in upward and/or downward direction from the estimated value and keeping the other inputs constant, new Net Present Value is computed. Then all the sets of Net Present Values are plotted on a graph to derive the sensitivity of the NPV to the change in each input. The steeper is the slope of the graph, the more sensitive the Net Present Value is to modify in an input[5].

The major advantages of Sensitivity Analysis is that it analysis critical issues that impacts the success and failure of the project. Also, Sensitivity Analysis is quite simple and can the results can be derived easily. But along with the advantages, Sensitivity Analysis also carries certain disadvantages. It expects that all elements are separate which is not feasible in reality. Also, it does not take into consideration the probability of changes in the variables.

Although Sensitivity Analysis is the most widely used technique of risk analysis, it contains certain limitations. Therefore, we require to lengthen sensitivity analysis to cope with the probability distributions of the variables. In addendum, it will be more feasible to differ more than one element while so that the blended consequence of changes can be seen. Scenario Analysis provides answer to these situations of expansions. Scenario Analysis brings in the probability of changes in the fundamental elements and also enable changes in excess of one element at a time[6].

Scenario Analysis is the process of estimating the Net Present Value of the project after a given period of time by assuming specific changes in the values of the key factors that take place in the project.

## 3. Capital Asset Pricing Model and Portfolio Management

Scenario Analysis starts with the base case or the most likely set of values for the input elements. Then the worst case scenario and best case situation is done. Differently we can say that scenario analysis talks about the badness of a particular project. Scenario Analysis seeks to establish the Best and Worst Scenarios so that the entire scope of results can be taken into account because in practical world, sometimes managers get carried away with the resullt of the most likely cases and do not consider critical factors.

Scenario analysis looks to be easy although it incorporates certain essential elements. The first element includes ascertaining the element over which the situations will be constructed. Second element is ascertaining the amount of situations to examine each element. Generally, three situations are built being the Best Case, Worst Case and the Average Case or the Most Likely Case. Third element is to put light on essential elements and construct few situations for all elements. Lastly, the assignment of probability to each and every scenario.

Now, lastly it is important to note that sensitivity analysis and scenario analysis are different. Sensitivity Analysis isolates each variable from one another and studies the impact of the possible outcomes on the same. Scenario Analysis on the other hand is based on a situation where all the variables are changed according to scenario to get a comprehensive picture if the situation[7].

Investment made in the securities is profitable as well as thrilling for the investors. Investing in the securities is involves both risk and reward. So there should be good amount of scientific and analytical skills required for investments in the securities[8]. An investor must invest in diversified portfolio of a number of securities instead of one single security. Every investment is characterised by risk and return. Hence, portfolio management should be done in order to get the proper combination of securities in the changing market conditions to get the utmost out of the securities market. Portfolio theories form the basis of portfolio management. Portfolio Theories involves Capital Asset Pricing Model or the Capital Market Theory[9].

The central theme of Capital Asset Pricing Model or Capital Market Theory is that the investors are rationale and they invest in the market portfolio such that the unsystematic risk is eliminated and only the systematic risk captured by beta is relevant. Since the market portfolio is most diversified, internal risk i.e. the company specific risk called the unsystematic risk gets eliminated and the investors only need to bear the systematic risk. So the investors integrate the market portfolio with risk free lending or borrowing to achieve their desired level of return and risk[10].

As we know that the total risk is the sum total of systematic and unsystematic risk. Systematic risk is the market risk as a whole whereas the unsystematic risk is the risk related to a specific firm. As we increase the number of shares in an investment portfolio, the unsystematic risk gets diversified and the risk that remains is the systematic risk. So for an investor who invests in diversified portfolio the measure of risk will be the market risk i.e. Beta whereas for and investor who invests in a single stock the appropriate risk shall be the Standard Deviation of the single stock.

In the economy, the investors invest in diversified portfolio and hence the risk is the beta of the portfolio. And hence the return of the portfolio shall be given as below:

E(R) = R(f) – [ R(m) – R(f) ] x Beta

This is known as the Capital Asset Pricing Model.

According to the CAPM, the expected return on a risky asset depends on three components:

1) Risk free rate

2) Market risk premium

3) Beta

CAPM is the most celebrated model in finance and as per CAPM model, investor invest in market portfolio i.e. a portfolio comprising all risky assets. In such a portfolio there is no unsystematic risk. Investors face only systematic risk. Investor will either borrow or invest at R(f) to achieve their desired level of risk and return.

When a rational investor invest in risk free assets, then desired rate of return is R(f) but in CAPM world, Investor invest in Market portfolio then desired rate of return is Risk free rate + Something extra and that something extra is known as Risk premium. Investor wants some premium to take risk in investing market[11].

The combination of risk-free lending or borrowing [ R(f) ] and market portfolio [ R(m) ] taking the risk factors of the market portfolio leads to the following results of the return from the portfolio [ R(p) ] :

R(p) = R(f) + R(m) – R(f)

σm

This is known as the Capital Market Line.

Capital Market Line appears in the Capital Asset Pricing Model for showing the rates of return for efficient investment portfolios subjected to risk level of the market portfolio given by standard deviation and the risk free rate of return. Capital Market Line shows that the Market portfolio is the efficient frontier as it is the intersection of the market portfolio return and the risk free portfolio return[12].

Hence if we represent the Capital Market Line on a graph where the y axis represents the expected return and the x axis represents the risk, it is a tangent line drawn from the point of the risk free portfolio in an upward direction for the risky assets[13]. The investors keep their risky assets in the same ratios as their units in the market portfolio so the tangency point in the line represents the Market Portfolio. All investors have the same opportunities and the same tangency-portfolio. So the Capital Market line is derived from the efficient part of minimum variance frontier associated with the possibility of buying or selling risk-free assets. Capital Market Line represents the entire market as a whole[14].

The Capital Market Line and the Capital Asset Pricing Model can be confused easily as they are similar on the grounds that they have the same assumptions and graph, and also have the same implications. However there is some difference between the both on some of the grounds listed below:

- The purpose of Capital Market Line is to show the allocation between the Risk-free portfolio and the Market Portfolio whereas for Capital Asset Pricing Model it is the pricing of the securities[15].
- Capital Market Line has standard deviation as the relevant measure of risk whereas Capital Asset Pricing Model has beta as the relevant measure of risk[16].
- The slope of Capital Market Line is the Sharpe Ratio i.e. Reward to Variability Ratio whereas the slope of Capital Asset Pricing Model is the difference among the Risk-free Portfolio and Market Portfolio.

Conclusion:

In conclusion we can say that with the help of Sensitivity analysis, we ascertain how the allocation of feasible Net Present Value or the Internal Rate of Return of a project under consideration is affected consequent to a change in one specific input element and with the help of Scenario analysis, we estimate the Net Present Value of the project after a given period of time by expecting particular modification in the values of the key factors that take place in the project.

In conclusion we can say that Capital asset pricing model is one of the portfolio management theory where it is assumed that an investor invests in market portfolio rather than investing in one or two stock and capital market line shows the allocation among the Risk-free portfolio and the Market Portfolio.

References

Barberis, N., Greenwood, R., Jin, L., & Shleifer, A. (2013). X-CAPM: An extrapolative capital asset pricing model (No. w19189). National Bureau of Economic Research.

Lee, Ming-Chang, and Li-Er Su. "Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate." Universal Journal of Accounting and Finance 2.4 (2014): 69-76.

Berry?Stölzle, Thomas R., Robert E. Hoyt, and Sabine Wende. "Capital market development, competition, property rights, and the value of insurer product?line diversification: A cross?country analysis." Journal of Risk and Insurance 80.2 (2013): 423-459.

Chow, Joseph YJ. "Activity?Based Travel Scenario Analysis with Routing Problem Reoptimization." Computer?Aided Civil and Infrastructure Engineering 29.2 (2014): 91-106.

economictimes.indiatimes.com › Definitions › Economy

finance.mapsofworld.com › Capital Market

handbook.cochrane.org/chapter_9/9_7_sensitivity_analyses.htm

Pianosi, Francesca, et al. "Sensitivity analysis of environmental models: A systematic review with practical workflow." Environmental Modelling & Software 79 (2016): 214-232.

Pianosi, Francesca, Fanny Sarrazin, and Thorsten Wagener. "A matlab toolbox for global sensitivity analysis." Environmental Modelling & Software 70 (2015): 80-85.

Saunders, Anthony, and Marcia Millon Cornett. Financial institutions management. McGraw-Hill Education,, 2014.

Seppelt, Ralf, Sven Lautenbach, and Martin Volk. "Identifying trade-offs between ecosystem services, land use, and biodiversity: a plea for combining scenario analysis and optimization on different spatial scales." Current Opinion in Environmental Sustainability 5.5 (2013): 458-463.

Tian, Wei. "A review of sensitivity analysis methods in building energy analysis." Renewable and Sustainable Energy Reviews 20 (2013): 411-419.

www.financeformulas.net/Capital-Asset-Pricing-Model.html

www.stern.nyu.edu/~adamodar/pdfiles/valrisk/ch6.pdf

xplaind.com/167040/sensitivity-analysis

Zabarankin, Michael, Konstantin Pavlikov, and Stan Uryasev. "Capital asset pricing model (CAPM) with drawdown measure." European Journal of Operational Research 234.2 (2014): 508-517.

Tian, Wei. "A review of sensitivity analysis methods in building energy analysis." Renewable and Sustainable Energy Reviews 20 (2013): 411-419.

xplaind.com/167040/sensitivity-analysis

Pianosi, Francesca, Fanny Sarrazin, and Thorsten Wagener. "A matlab toolbox for global sensitivity analysis." Environmental Modelling & Software 70 (2015): 80-85.

[4] handbook.cochrane.org/chapter_9/9_7_sensitivity_analyses.htm

Pianosi, Francesca, et al. "Sensitivity analysis of environmental models: A systematic review with practical workflow." Environmental Modelling & Software 79 (2016): 214-232.

Chow, Joseph YJ. "Activity?Based Travel Scenario Analysis with Routing Problem Reoptimization." Computer?Aided Civil and Infrastructure Engineering 29.2 (2014): 91-106.

Seppelt, Ralf, Sven Lautenbach, and Martin Volk. "Identifying trade-offs between ecosystem services, land use, and biodiversity: a plea for combining scenario analysis and optimization on different spatial scales." Current Opinion in Environmental Sustainability 5.5 (2013): 458-463.

Saunders, Anthony, and Marcia Millon Cornett. Financial institutions management. McGraw-Hill Education,, 2014.

Zabarankin, Michael, Konstantin Pavlikov, and Stan Uryasev. "Capital asset pricing model (CAPM) with drawdown measure." European Journal of Operational Research 234.2 (2014): 508-517.

Barberis, N., Greenwood, R., Jin, L., & Shleifer, A. (2013). X-CAPM: An extrapolative capital asset pricing model (No. w19189). National Bureau of Economic Research.

economictimes.indiatimes.com › Definitions › Economy

Lee, Ming-Chang, and Li-Er Su. "Capital Market Line Based on Efficient Frontier of Portfolio with Borrowing and Lending Rate." Universal Journal of Accounting and Finance 2.4 (2014): 69-76.

Berry?Stölzle, Thomas R., Robert E. Hoyt, and Sabine Wende. "Capital market development, competition, property rights, and the value of insurer product?line diversification: A cross?country analysis." Journal of Risk and Insurance 80.2 (2013): 423-459.

www.stern.nyu.edu/~adamodar/pdfiles/valrisk/ch6.pdf

www.financeformulas.net/Capital-Asset-Pricing-Model.html

finance.mapsofworld.com › Capital Market

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