Consumption Capital Asset Pricing Model (CCAPM): An Overview

Systematic Risk and Beta

Discuss about the Consumption Capital Asset Pricing Model.

The usage of portfolio management techniques for the investment analysis requires a reliable and accurate estimate of the underlying systematic risk that may be associated with any given security. A simplistic answer to this was provided by the CAPM model which came in vogue in the 1960’s and is based on Markowitz modern portfolio theory. The CAPM model relies on comparison of the systematic risk of an underlying security in comparison with the broad market which is captured by the beta and compensating the investors in terms of the risk assumed (Graham & Smart, 2012). The CAPM model tends to have two factors that make it particular lucrative. First, it seeks to provide time adjusted risk free returns to the investors and hence accounting for the time value of money. Secondly, it tends to provide a premium returns to investors who are willing to invest in investments that have higher risk. The basic equation for this model is depicted below (Kane & Marcus, 2013).

E(R) = R_f + β(R_M – R_f)

In the above equation, E(R) denotes the returns expected on a particular stock

R_f represents the risk free rate

β represents the systematic risk associated with an underlying security

R_m represents the expected returns on the market index

The above relation between the beta and expected returns is referred to as SML or Security Market Line and the graphical representation of the same is shown below (Damodaran, 2008).

The SML along with the Markowitz theory clearly indicates that the market portfolio derived is the most efficient portfolio. For a specific SML portfolio, the rate of return would be influenced by the value of the risk free rates and also the various risks which would be represented in terms of standard deviation of the returns.  This is captured below and is known as Capital Market Line (CML) (Petty et. al., 2015).

The CAPM is derived on the set of certain assumptions which are highlighted below (Brealey, Myers & Allen, 2008).

Investors tend to be averse to risk and rational in their outlook and choices. As a result, the investors would tend to prefer assets that offer the same return at lower risk. Further, while making investment decisions, the investors tend to act rationally.

The investors tend to invest in a diversified portfolio which effectively eradicates the diversifiable risk.

Critical analysis of CAPM Assumptions

It is possible for the market participants to borrow and lend unlimited supply of funds at the risk free interest rate.

The investors do not have the capacity to influence the market prices and thus essentially are price takers.

The various assets can be divided into smaller sub-parts and are highly liquid.

The various trades that the investors initiate do not have any transaction costs and no taxes are levied on the same.

The expectation of all investors is homogeneous and this derives the same level of behaviour from the market participants.

It is assumed that there is perfect information symmetry and all the relevant information is available for all investors.

The central issue with regards to establishing the validity of CAPM rests around the relevancy of risk being appropriately measures by the beta of the security. While there have been some studies which indicate that there is positive and statistically significant correlation between the bets of the stock and the expected returns. However, this was not as significant as represented in the CAPM model (Guerard, 2013). However, a host of academic studies have indicated that the beta is not an accurate measure of the undelying systematic risk associated with the firm. In some of these studies additional factors like the size and book value are found to be directly altering the returns. Further, there are issues with regards to the empirical testing as it is based only on past data and hence, introduces a bias (Brigham & Ehrhardt, 2013).

The major criticism of the CAPM model is on account of the unrealistic assumptions which do not capture the reality of the modern day markets.  A particular assumption of the model is that investors aim to maximise their portfolio returns only in the given period which is untrue as investors are driven by the long term portfolio management where decisions taken today have long term implciations (Northington, 2013). Further, the assumption about non-existence of transaction charges and taxes is clearly untrue for all financial markets. Another key assumption which is false is with regards to symmetry of information across investors which is false and tends to give rise to varied decision making. There are significant information costs in certain markets that are not very efficient. Besides, the behaviour of the investors is not rational as the behaviour aspects tend to influence investing decisions. Also, there are question marks with regards to investors having expectations of homogenous nature as these are driven by their respective risk profile and objectives. Yet, another assumption that does not hold ground is that investors could lend and borrow unlimited funds at the risk free rate. In wake of the above unrealistic assumptions associate with CAPM, it is imperative to explore the various alternative models to CAPM (Parrino & Kidwell, 2011).

Arbitrage Pricing Theory (APT)

One of the alternatives to the CAPM model is APT. As per this model, the return on a given security is a function of various factors that tend to take into consideration the specific macroeconomic variables such as GDP growth, inflation, unemployment etc.  However, since the constituent factors would be different for each security, hence customisation is required with regards to the factors to be considered (Damodaran, 2008). In this regard, APT allows for the requisite flexibility by ensuring that multiple factors can be included which is not possible under the CAPM regime. The intrinsic price of the given security is determine based on the underlying multifactor model and when this is compared with the existing market price, the opportunities for arbitrage trade or profit is identified (Kane & Marcus, 2013). Therefore, unlike the CAPM, this model allows for multiple parameters to be built in which are more reflective of the actual returns of the stock which essentially leads to better estimation of the intrinsic price (Deegan, 2011).

The CCAPM is a modification of the original CAPM as instead of taking the portfolio return as the benchmark, this model tends to be driven by the aggregate consumption level. The central idea is that as the exposure of the investor in case of risky assets increases, it also has adverse impact on the future consumption of the investor as the returns from riskier assets are highly uncertain. As a result, instead of using beta, the CCAPM model deploys consumption beta which in turn tends to reflect the underlying covariance between the market returns and the investor’s ability with regards to goods and services consumption (Graham & Smart, 2012). This model has limited utility in case of consumers as they are not active participants in the financial markets but seem to be widely in use in case of corporate where the participation is more active. This model was suggested as an incremental improvement to the CAPM but had some utility but has lost grounds since the introduction of multi factors models based on research by Fama and French (Brealey, Myers & Allen, 2008).

The DDM approach is used to estimate the intrinsic price of the stock based on the assumption that the present value is equivalent of the discounted value of the future dividend payments expected from the stock over its life. Based on the estimation of the intrinsic price, the investor can take positions in the stock. If the intrinsic value of the stock is lower than the current market price, then the stock is overvalued and hence should not be invested into (Brigs, 2013). However, if the current market value is lower than the intrinsic value, then the stock is undervalued and must be invested into (Bhimani et. al., 2008).  This model is similar to CAPM is simple to use but the estimation of inputs is a problem. For instance, the DDM requires the estimation of a constant growth rate of dividend which might be difficult to estimate. Further, the model cannot be used to price stocks that are growth stocks and hence may not pay any dividends. Besides, the return on equity for the application of this method should always be greater than the dividend growth rate. Hence, considering the dynamic nature of the inputs in the future, the utility of this model in real world valuation is limited (Brigham & Ehrhardt, 2013).

Consumption Capital Asset Pricing Model (CCAPM)

There are a host of issues associated with CAPM that limit its utility despite it being a convenient method to apply. Firstly, the beta is based on empirical data from the past which cannot be assume to be a fair representation of the risk in the future and thus the usage of CAPM for estimation of future prices seems unfair and inherently biased. Additionally, due to difference in the underlying expectations of investors, the SML for different investors would tend to vary unlike a simplistic single SML that the model assumes (Petty et.al., 2015).  Further, with regards to estimation of beta or appropriate discount rate for specific projects, obtaining a proxy may be difficult which actually makes the prediction of beta with reliability and precision an uphill task. Besides, the unrealistic assumptions of the CAPM model along with questions regarding utility of beta as a measure of risk as has been highlighted earlier (Parrino & Kidwell, 2011)

In wake of the evident shortcomings with the CAPM model, various alternatives have been presented. In this regards, CCAPM is only an incremental improvement over the CAPM model but fails to act as a multi factor model and hence is not an apt replacement for the CAPM model. Similarly, the other alternative in the form of DDM has issues with estimation of input variables with accuracy as it is based on estimated future dividends which would not be too accurate (Kane & Marcus, 2013). Hence, it has limited practical utility and also is applicable for only those companies that pay dividends.  Hence, the most viable alternative to the CAPM model seems to be the multi factor model such as APT which provides the requisite customisation for each security and ensures that the multiple factors may be introduced which enhance the fit of the model and improve the accuracy of the estimated price.  Further, with the developments in technology, it has become increasingly easier to account for multiple variables as predicted in the multi factor models such as Fama French Models taking multiple variables into consideration for accurate asset pricing (Damodaran, 2008).

Conclusion

Based on the arguments presented above, it is apparent that CAPM is a simplistic technique which seeks to provide a relation between the risk and return for a particular asset class as reflected by the SML. However, the model is based on a plethora of assumptions which do not hold good in the actual modern day financial markets which limit the utility of this model. Further, there are conceptual issues with the model particularly with regards to beta being able to capture all the risk associated with the stock. Additionally, there are issues with regards to bias since future predictions are based on historical data. Hence, there is a clear need to alternatives to augment the underlying concept. The most credible alternative that is available to the CAPM is the multi factor models such as APT and Fama French multi factor models which in the information age are not difficult to implement and act as significant augmentation to the single risk factor CAPM approach.

Based on the given information, some of the relevant conclusions are drawn below.

Dividend Discount Model (DDM)

The cost incurred on the feasibility study i.e. $ 25,000 is a sunk cost and would not be considered for the project evaluation since it cannot be avoided and has already been incurred (Petty et. al., 2015).

Lost of new machine = $ 350,000. As depreciation is according to prime method, hence a straight line method would be adopted over the five year effective life to reduce the carrying cost to zero.

Hence, annual depreciation expense for the new machine = 350000/5 = $ 70,000

The previous machine that is currently in place had life of 10 years and was purchased at a cost of $ 300,000.

Hence, annual depreciation expense for the old machine = 300000/10 = $ 30,000

Thus, the annual incremental increase in depreciation deduction due to purchase of new machine would be only 70000 – 30000 = $ 40,000

• It is imperative to note that the finance costs are inbuilt in the cost of capital and thus are not included in the incremental cash flow calculation and have been ignored for computation purposes (Damodaran, 2008).
• The salvage value of the machine at the end of the five years is estimated to be $ 40,000.
• Also, the proceeds from the sale of existing machine today is estimated to be $ 80,000

The estimated incremental cash flows from the purchase of the new machine over the project life is represented below (Brealey, Myers & Allen, 2008).

Year	0	1	2	3	4	5
Savings in cooling cost		90000	90000	90000	90000	90000
(-) Loss of sales		10000	10000	10000	10000	10000
(-) Increase in account receivable	15000
(-) one off cleaning supplies	12000
(+) Recovery of the increase in WC and cleaning supplies						27000
(+) Sale of old machine	80000
(-) cost of new machine	350000
(+) Salvage value of new machine						40000
(-) Incremental Depreciation Costs		40000	40000	40000	40000	40000
Total cash inflow/(outflow) ($)	-297000	40000	40000	40000	40000	107000
Tax paid @ 30%	0	12000	12000	12000	12000	32100
Post tax cash inflow/(outflow ($)	-297000	28000	28000	28000	28000	74900
(+) Depreciation since it is non-cash	0	40000	40000	40000	40000	40000
Net incremental inflow/(outflow)($)	-297,000	68,000	68,000	68,000	68,000	114,900

The cost of capital for the project is given as 10% and the NPV is computed below using the given discount factor as shown.

Year	0	1	2	3	4	5
Savings in cooling cost		90000	90000	90000	90000	90000
(-) Loss of sales		10000	10000	10000	10000	10000
(-) Increase in account receivable	15000
(-) one off cleaning supplies	12000
(+) Recovery of the increase in WC and cleaning supplies						27000
(+) Sale of old machine	80000
(-) cost of new machine	350000
(+) Salvage value of new machine						40000
(-) Incremental Depreciation Costs		40000	40000	40000	40000	40000
Total cash inflow/(outflow) ($)	-297000	40000	40000	40000	40000	107000
Tax paid @ 30%	0	12000	12000	12000	12000	32100
Post tax cash inflow/(outflow ($)	-297000	28000	28000	28000	28000	74900
(+) Depreciation since it is non cash	0	40000	40000	40000	40000	40000
Net incremental inflow/(outflow)($)	-297000	68000	68000	68000	68000	114900
PV factor @ 10% discount rate	1	0.909091	0.826446	0.751315	0.683013	0.620921
PV of cash flows ($)	-297000	61818.18	56198.35	51089.41	46444.91	71343.86
NPV ($)	-10,105.29

It is apparent from the above that there the NPV for the proposed changeover would be -$ 10,105.3.  The negative value of the NPV suggests that there would be a net loss in the present value from the proposed changeover (Parrino & Kidwell, 2011).

Since the NPV of the proposed changeover to the new machine is negative, hence Harry must not go ahead with the changeover to the new machine and continue with the existing machine as switching is not value accretive for the interests of the shareholders (Brigham & Ehrhardt, 2013).

Reference

Bhimani, A, Horngren, CT, Datar, SM  & Foster, G 2008, Management and Cost Accounting 4^th eds., Prentice Hall/Financial Times, Harlow

Brealey, R, Myers, S & Allen, F 2008, Principles of Corporate Finance, 9^th eds., McGraw Hill Publications, New YorkBrigham, EF & Ehrhardt, MC 2013. Financial Management: Theory & Practice, 14^th eds., South-Western College Publications, New York

Brigs, A 2013, Financial reporting & analysis, 4^th eds., South-Western, Mason, Ohio

Damodaran, A 2008, Corporate Finance, 2^nd edn, Wiley Publications, London

Deegan, CM 2011, Financial accounting theory, 3^rd eds., McGraw-Hill, North Ryde, N.S.W

Graham, J & Smart, S 2012,   Introduction to corporate finance, 5^th eds.,  South-Western Cengage Learning, Sydney

Guerard, J 2013, Introduction to financial forecasting in investment analysis, 6^th eds., Springer. New York

Kane, B.Z. & Marcus, A.J. 2013. Essentials of Investment, 9^th edn, McGraw-Hill International, Singapore

Northington, S 2011,  Finance, 6^th eds., Ferguson, New York

Parrino, R & Kidwell, D 2011, Fundamentals of Corporate Finance, 3rd eds., Wiley Publications, London

Petty, JW, Titman, S, Keown, AJ, Martin, P, Martin JD & Burrow, M 2015, Financial Management: Principles and Applications, 6^th eds., Pearson Australia, Sydney.