__Part A__

The valuation of company assets depends a varies a great deal; attempts to find theoretical models that cover all of the aspects of a business valuation has proven difficult; as such, many of the major valuation theories have been proven to have both specific strengths and weaknesses. One of the core difficulties inherent to the great majority of theories available is the reliance on specific factors in their equations that remain subject to widespread debate as to how, precisely, they should be measured in order to attain the most accurate appraisal of a company’s given value. Many problems inherent to risk assessment and company valuation include: the weighting of future long-term assets versus short-term stock market value; the precise period from which historical data should be dated from; and how risk should be defined precisely. Of course, stock market appraisal is innately probabilistic, and the development of a coherent and foolproof theory for valuing company stock remains very unlikely. There are, however, many strengths and weaknesses inherent to the myriad of hypotheses and models available to us.

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One of the most ambiguous factors inherent to theories of valuation is the prediction of future growth, known as a forecast horizon. The economic growth model, which will be described later, suggests that forecasted profit over a pre-specified horizon does not affect the value of the company as such, but affects the manner in which that value is distributed over the period of the horizon. Thus, the specific horizon period utilized can impact upon the perceived growth of the company. Of course, the horizon period can indirectly impact upon the perceived value of the company in DCF and economic growth forecasting models, especially if value is tied to changes in economic assumptions regarding the general future growth of the company and its continuing value. Of course, measuring the exact forecast period is not an exact science, but must take into account a number of factors if it is to provide us with an accurate view of the relationship between explicit free cash flow and continuing value. Firstly, the horizon period should be long enough to predict that the company’s growth period will be over at the end of it. Secondly, the horizon period shouldn’t be overly long as this will inevitably impact upon the predictive capacity of the theory.

Of course, the length of the horizon period also impacts upon the Return on Invested Capital (ROIC), often because the horizon period is inappropriately equated to the competitive advantage of investment of a company. As such, ROIC is directly equated to levels of continuing value presupposed by the horizon period used in determining levels of continuing value as compared to the value of explicit cash flow. As Kollar et al. (2006) suggest, “the key value driver formula is based on *incremental* returns on capital, not companywide average returns. If you assume that incremental returns in the continuing-value period will just equal the cost of capital, you are not assuming that the return on total capital (old and new) will equal the cost of capital” (p. 283). Instead, original capital will continue to earn the same returns that were projected in the former period.

__Part B__

The attainment of the true value of a company based upon its position in the stock market is a difficult task, and many differing theories have been developed to come to terms with perceived valuation weaknesses in previous theories. This is especially prevalent today, as many recent problems, from the bubble bursting on the dot com revolution, to recent accounting scandals in large financial firms, have stressed the need for more rigorous methods of determining true value. One problem that management have had to encounter is the paradox of retaining short-term profits in a sustainable manner that can ensure long-term health of the company. The stock market obsession with factors such as the quarterly rate of return places emphasis on short-term profitability. One competing model, that takes into account assumed growth of the company, can be found in the many discounted cash flow (DCF) models that are being used more frequently as a result of the failings of simply using present rate of return to determine a company’s overall value.

DCF models differ from economic profit models because they forecast the potential of future growth of the company and incorporate that into the present-day value of the company. As such, DCF models incorporate estimates of future growth into the present model; however, further analysis of the two competing models for determining company value suggest that, in theory at least, the results should create the same overall value. The economic profit model uses the theory of Alfred Marshall (1890), in which he suggests that “What remains of the owner’s profits after deducting interest on his capital at the current rate may be called his earnings of undertaking or management” (p. 142). As such, any perceived value created by the company should take into account the opportunity cost of the capital as well as expenses. As such, in many respects the economic profit model is more rigorous in measuring the present-day value of the company, because DCF determines free cash flow through measuring investments in capital and fixed assets. Of course, because the level of investment can be delayed by management, it is possible to generate short-term value at the expense of long-term value. In theory however, both models should produce the same results.

Ultimately, DCF is useful for determining the price of an asset in the long run; as such, it provides one of the most useful tools for measuring the long-term profitability of an investment by factoring in future cash flow models. While the presence of short-term deviations in market value can be useful in certain contexts in determining value, many of the models practised are unreliable and unstable in practice. Fluctuations in short-term market value is difficult to measure with any degree of accuracy, whereas DCF models reflect the true value of a company more accurately as the model is based on the acquisition of long term profitability. Certainly, the role of strategic manager should be covered in the great majority of instances by the DCF model. As Koller et al. (2005) suggest, “What matters is the long-term behaviour of your company’s share price, not whether it is 5 or 10 percent undervalued this week. […] Managers who use the DCF approach to valuation, with their focus on increasing long-term free cash flow, ultimately will be rewarded with higher share prices” (p. 100). Therefore, the predictive capacity of DCF can be used as an effective model for creating future growth, although its predictive methods and mechanisms can occasionally be doctored to create larger levels of short-term growth at the expense of long-term growth, as a result of the correlative relationship between investment levels and free cash flow in any valuation process. In addition, DCF relies heavily on projected scenarios; as Mauboussin (2006) comments, “small changes in assumptions [in the DCF model] can lead to large changes in the value” (p. 7). This requires the need for rigorous assessment of a large quantity of possible growth scenarios.

__Part C__

CAPM uses three variables for determining the expected return of a stock, which can furthermore be used to determine the expected value of a company. Unfortunately, despite CAPM providing us with a “tour-de-force” (Fama & French 2004, p. 28) of theoretical analysis that can provide us with a useful series of principles by which central principles of asset pricing can be taught, its empirical record is poor enough, according to Fama & French (2004), to “invalidate the way it is used in applications” (p. 1). The problems with CAPM are built upon a number of difficult foundational principles that, in practice, prove to be unrealistic. Firstly, the Sharpe – Lintner CAPM model (see Sharpe 1964, Lintner 1965) assumes the presence of unrestricted riskfree borrowing in their equations. Of course, this is an unrealistic assumption that severely affects predicting the empirical data. Modifications by Black (1972) attempt to remedy this by creating effective asset valuations based on risk modelling; but Black’s analysis merely suggests that unrestricted short selling, rather than unrestricted riskfree lending, is a central assumption, and proves equally false in practice. The use of CAPM is therefore encumbered by a number of weaknesses, and relies on a number of assumptions that, in practice, prove difficult to measure. These include difficulties in ascertaining precisely which risk-free rate should be used in particular circumstances, as well as difficulties in measuring the market risk premium and beta.

A number of alternative models of determining company value based on risk assessment exist, all of which rely on a fundamentally different definition of risk itself. While CAPM defines a stock’s risk as its sensitivity to the stock market on the whole, other systems use more rarefied versions of risk assessment: the Fama-French three factor model, for example, defines risk in terms of sensitivity to three portfolios: the stock market, a portfolio based on book-to-market ratios and a portfolio based on firm size. Whether the Fama-French three factor model is a better system than the CAPM system remains to be seen; while it is widely held that the Fama-French model offers us a more comprehensive assessment of risk to value than CAPM, which does not rely on the assessment of other portfolios, many critics also state that the Fama-French model is subject to the same interpretative problems as the CAPM system – namely, the Fama-French model, like CAPM, does not state how much data should be used; this is especially important considering that the system is based on historical evidence. As Koller et al. (2005) suggest, “Since 1926, small companies have outperformed large companies, but since 1982, they have not” (323). The lack of a rigorous method for determining how far back the data related to regressed returns should go creates many inconsistencies in risk assessment and valuation, such as the one highlighted above.

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Arbitrage Pricing Theory (APT) offers us a model similar to the Fama-French model but more generalised in its practice. Of course, while it suffers from the same fundamental implementation-related weaknesses as other models, although it differs insofar as it factors into its central equation the actual return of a security, which is fully specified. While theoretically this model is successful, again it reveals many weaknesses in determining the overall value of a company based on the assessment of portfolio risk: implementation and application of the theory has seldom been presented because of the more generalised nature of the variables and the factors in the central equation; in practice, there has been little agreement on what these factors should be, how many there should be, and how these factors should be weighted and measured. As such, CAPM retains its validity despite its essential weaknesses as, some economists argue, it represents the “least worst” model for defining risk. As Koller et al. (2005) suggest, “It takes a better theory to kill an existing theory, and we have yet to see the better theory. Therefore, we continue to use the CAPM while keeping a watchful eye on new research in the area” (324).

__Bibliography__

Brealey, R. A. & Myers, S. C. (2003), *Principles Of Corporate Finance*, 7^{th} ed., London: McGraw-Hill.

Koller, T., Goedhart, M., Wessels, D. et al. (2005), *Valuation: Measuring and Managing the Value of Companies*, London: John Wiley and Sons.

Lintner, J. (1965), “The Valuation of Risk Assets and The Selection of Risky Investments in Stock Portfolios and Capital Budgets.” *Review of Economics and Statistics*. 47:1, pp. 13-37.

Marshall, A. (1890), *Principles of Economics*, Vol. 1, New York: MacMillan & Co.

Mouboussin, M. J. (2006), “Common Errors in DCF Models”, Legg Mason Capital Management.

Sharpe, W. F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”. *Journal of Financial Economics*, 10:3, pp. 237-68.