# Capital Asset Pricing Model And Net Present Value Analysis For Business Decision Making

## Introduction to Capital Asset Pricing Model

Question:

Describe the topical issues in financial management – CAPM and Capital Budgeting?

Capital asset pricing model has been widely used for estimation of the cost of capital for business organizations. Additionally, this model is helpful in evaluation of the performance of managed portfolios (Fama and French, 2004). Capital asset pricing model considers the market return, risk free rate of return and systematic risk in order to estimate the cost of capital (Dempsey, 2012).

In the above formula,

Rf = Risk free rate of return

β = Systematic Risk

Rm =  Market return

The assumptions of capital asset pricing model are listed below:

• All investors operating in the market will focus on maximizing their economic utilities when the asset quantity is constant.
• Investors are rational and will be risk-averse in nature (Pennacchi, 2008).
• The investors are largely diversified according to different type of investment.
• The investors are not price takers or have no influence on the prices.
• The investors can borrow as well as lend unlimited amount at the rate of risk free rate of interest.
• Trade activities take place without the cost of transaction and tax (Fama and French, 2004).
• Investors have equal access to the market information and they all have homogeneous expectation.
• It is assumed that all assets can be liquefied and divided (Bornholt, 2012).

Capital market line refers to the line which is used in the capital asset pricing model for illustrating the rate of return for the efficient portfolios on the basis of risk free return and the level of uncertainty or risk for that specific portfolio. Capital market line can be drawn as a tangent line from the intercept point of the efficient frontier at which point the expected rate of return is same as the risk free rate of return. Capital market line demonstrates a relationship between the return as well as risk of the efficient portfolio. The capital market line helps in combining the risk free asset and the market portfolio. It is used for representing the risk premium earned from taking additional risk. Capital market line is considered to be superior to the efficient frontier as it includes the risk free asset within the portfolio (Lee et al., 2013).

Figure: Capital market line

Source: Lee et al., 2013

Security market line helps in plotting the systematic risk versus the market return for a specific period of time. It has been observed that in security market line all the risky marketable securities are include. Basically, security market line helps in plotting the results obtained from the capital asset pricing model. The market risk or bet is represented along the horizontal axis and the vertical axis represents the expected market return. From this graph, market risk premium can be estimated from the slope of the security market line. According to the capital asset pricing model, the market portfolio is the efficient frontier and it can be achieved with the aid of security market line (Pennacchi, 2008).

Figure: Security market line

Source: Pennacchi, 2008

Capital market line considers the total risk while security market is line includes the systematic risk. The inefficient portfolios lie below the capital market line and both the efficient and inefficient portfolios lie on the security market line (Skiadas, 2009).

It has been argued that capital asset pricing model is an effective tool in estimation of the expected return of a portfolio or cost of capital for business organization.  The research scholars have argued that the major advantaged of CAPM is it considers systematic risk which reflects the reality and helps in providing a proper insight to the market condition which the investors must consider. It helps in deriving a relationship between the systematic or market uncertainty and the required rate of return which is very important for the investors. It is a better approach than WACC as it includes the systematic risk (Smart, Megginson and Gitman, 2004).

## Capital Market Line and Security Market Line

However, some limitations of the CAPM have been identified by the research scholars. It has been observed that the CAM model is reliant upon the risk free rate of interest which refers to the government bonds. The rate of return of the government bond frequently changes depending on the economic situation of the nation. Hence, it will affect the calculation of long term investment. Additionally, it has been correctly argued that estimation of the equity risk premium becomes difficult and it is unstable. Moreover, the value of beta also varies over time (Subrahmanyam, 2012).

Some alternative models have been proposed such as multi beta model (the multifactor model and arbitrage pricing model), market price based model and accounting information based model.

Conclusion

This paper has provided an insight to the concept of capital asset pricing model and its assumptions. It has been found that the model is very useful as it considers the systematic risk. However, some limitations of the model have been discussed in this paper. CAPM is dependent on the beta and risk free rate of return which frequently changes. It has been found that some alternative models are proposed which will address the shortfalls of the CAPM.

Gordon Hall is considering replacement of his existing machine which has a remaining life of 5 years. The new machine will be bought from Li Ho with useful life of 5 years. In order to evaluate the replacement decision capital budgeting tool Net Present Value (NPV) analysis is an important tool (Ross, Westerfield and Jordan, 2000). It will be used in this paper for making replacement decision (Berk and DeMarzo, 2007).

First of all, it is important to estimate the depreciation of the new as well as old machine. Depreciation has been calculated in straight line method in the following two tables:

 Particulars Amount Purchasing Cost \$         280,000.00 Useful Life (years) 5 Value at the end of life \$            50,000.00 Depreciation per year \$            46,000.00 Salvage Value \$            40,000.00

Calculation of the depreciation of Old Machine

 Particulars Amount Purchasing Cost \$              340,000.00 Useful Life (years) 10 Value at the end of life \$                               – Depreciation per year \$                34,000.00 Salvage Value \$                               –

The initial cost of replacement is important to calculate. The initial cost of replacement will include the purchasing cost of new machine, amount paid for conducting feasibility study of the machine and the amount lost by selling the old machine (Holland and Torregrosa, 2008). The loss on sale of the old machine can be calculated by deducting the selling price of the old machine from the depreciated value of the machine at the end of 5th year (Helbæk, Lindest and McLellan, 2010).

 Particulars Amount Cost of new machine \$         280,000.00 Present Depreciated Value of the Old Machine \$              170,000.00 Selling Price of old machine \$                86,000.00 Loss on Sale \$                84,000.00 Feasibility Study \$                20,000.00 Total Cost of Purchasing New Machine or Initial Cost \$              384,000.00

The cash flow will be changed due to installation of the new machine The following two tables will consider the elements which will influence the cash flow in the next five years (Ross, Westerfield and Jaffe, 2005).

 Particulars Amount (+) Reduction in cooling Cost \$                70,000.00 (-) Reduction in Sale \$                10,000.00 Cash Flow \$                60,000.00

(Moles, 2011)

 (+) Requirement of cleaning supply \$                  9,000.00 (+) Increase in accounts receivable \$                14,000.00 (+) Sale of New Machine \$                40,000.00

Total present value of the cash flow after replacement of the old machine with the new one has been calculated in the following table:

 Year Cash flow Depreciation PBT Tax (@30%) PAT CFAT PVF (@9%) PV 1 \$            60,000.00 \$        46,000.00 \$          14,000.00 \$     4,200.00 \$        9,800.00 \$   55,800.00 0.917431193 \$        51,192.66 2 \$            60,000.00 \$        46,000.00 \$          14,000.00 \$     4,200.00 \$        9,800.00 \$   55,800.00 0.841679993 \$        46,965.74 3 \$            60,000.00 \$        46,000.00 \$          14,000.00 \$     4,200.00 \$        9,800.00 \$   55,800.00 0.77218348 \$        43,087.84 4 \$            60,000.00 \$        46,000.00 \$          14,000.00 \$     4,200.00 \$        9,800.00 \$   55,800.00 0.708425211 \$        39,530.13 5 \$            83,000.00 \$        46,000.00 \$          37,000.00 \$   11,100.00 \$     25,900.00 \$   71,900.00 0.649931386 \$        46,730.07 5 \$            40,000.00 \$                       – \$          40,000.00 \$   12,000.00 \$     28,000.00 \$   28,000.00 0.596267327 \$        16,695.49 Total Present Value \$     2,44,201.92

Net present value can be calculated by subtracting the present value of cash flow over the five years from the initial cost of replacement on 0th year.

 Particulars Value Total Present Value of Cash Flow \$        2,44,201.92 Total Initial Cost of Replacement \$        3,84,000.00 Net Present Value of Replacement \$      (1,39,798.08)

From the above table it is estimated that the net present value of replacement is estimated to be negative. It implies that if Gordon Hall replaces its existing machine with the new one from Li Ho, it will encounter loss of \$ 166,637.37 over the next five years. Hence, it can be stated that Henry must not purchase the new machine (Peterson Drake and Fabozzi, 2002).

References

Berk, J. and DeMarzo, P. (2007). Corporate finance. Boston: Pearson Addison Wesley.

Bornholt, G. (2012). The Failure of the Capital Asset Pricing Model (CAPM): An Update and Discussion. Abacus, 49, pp.36-43.

Dempsey, M. (2012). The Capital Asset Pricing Model (CAPM): The History of a Failed Revolutionary Idea in Finance?. Abacus, 49, pp.7-23.

Fama, E. and French, K. (2004). The Capital Asset Pricing Model: Theory and Evidence.Journal of Economic Perspectives, 18(3), pp.25–46.

Helbæk, M., Lindest, S. and McLellan, B. (2010). Corporate finance. New York: McGraw-Hill.

Holland, J. and Torregrosa, D. (2008). Capital budgeting. [Washington, D.C.]: Congress of the U.S., Congressional Budget Office.

Lee, C., Finnerty, J., Lee, J., Lee, A. and Wort, D. (2013). Security analysis, portfolio management, and financial derivatives. Singapore: World Scientific.

Moles, P. (2011). Corporate finance. Hoboken, N.J.: Wiley.

Pennacchi, G. (2008). Theory of asset pricing. Boston: Pearson/Addison-Wesley.

Peterson Drake, P. and Fabozzi, F. (2002). Capital budgeting. New York, NY: Wiley.

Ross, S., Westerfield, R. and Jaffe, J. (2005). Corporate finance. Boston: McGraw-Hill/Irwin.

Ross, S., Westerfield, R. and Jordan, B. (2000). Fundamentals of corporate finance. Boston: Irwin/McGraw-Hill.

Skiadas, C. (2009). Asset pricing theory. Princeton: Princeton University Press.

Smart, S., Megginson, W. and Gitman, L. (2004). Corporate finance. Mason, Ohio: Thomson/South-Western.

Subrahmanyam, A. (2012). Comments and Perspectives on ‘The Capital Asset Pricing Model’.Abacus, 49, pp.79-81.

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