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Traditional Valuation Methods and Ways of Applying Them

1.1. Introduction

It is imperative that the investments of a business generate a sufficient level of profitability to satisfy the demands held by the investors. If the obtained (or predicted) level of profitability is higher than the level of profitability that is expected given the risk, the value of the economic asset increases, impacting the value of shares in an upward fashion1. Otherwise, the investor will not be satisfied with the profitability of their investment in relation to the risk absorbed to sell their security. Enterprise and share value thus will fluctuate in a downwards fashion. And so, the direct consequence of the investment policy is a variation in economic value of equity, i.e. the market capitalization if the company is listed2. It thus follows that an investor's power lies, on the one hand, in their decision to allocate funds to the company (without financial backing, the company is no more) and, on the other hand, in the evaluation of the economic asset through securities that have already been issued3. Consequently, changes in the value of economic assets are reflected almost entirely on market capitalization. When the company faces significant difficulties, the role of creditors changes because from a financial perspective, they then own the company. When the equity value is almost zero, adjustments can only be made through the net debt, whose value becomes lower than the nominal value. Therefore, liabilities are the screen placed between the value of economic assets and the financial decisions taken by investors.

Just as the investment policy is able to create or destroy value, the financial policy through the financial structure can theoretically change the value of equity. It is not so much of question of increasing the free cash flow of economic assets as it is of reducing the weighted average cost of capital, synonymous with the financial cost of the company, i.e. the minimum rate of return that assets must generate. In this way, it seems pertinent to interrogate whether an optimal liability structure can be created. The said structure would enable the cost of capital to be minimized, thereby maximizing the enterprise value.

To guide their decisions to allocate their resources to companies, investors use traditional valuation methods. In this way, the economic valuation of shareholder equity can be obtained by relying on a stock market analysis by comparing the aggregate multiples of the balance sheet and/or the income statement, or by undertaking a transactional comparison of the processes being carried out in the sector that the company to be valued operates in. Furthermore, by producing a business plan, i.e. by providing free cash flows that are discounted at the cost of capital, the investors may estimate the value of the company based on its future plans. Finally, by adopting a proprietary approach, investors are able to concentrate on the real assets held at a given time by the company. These three approaches are in theory supposed to be combined in order to refine the valuation further. With this in mind, it becomes ever more important to investigate whether an optimal capital structure really exists. Indeed, when it comes to carrying out a valuation by discounting free cash flows, two possibilities arise in terms of maximizing the enterprise value. Either the investment policy is relevant in itself, as it generates significant cash flows which lie in the numerator of the formula, or it is possible to consider that an adequate financial policy is carried out on condition that it decreases the cost of capital, which is at the denominator of the formula. In both of these scenarios, the enterprise value is increased.

Auditing activities come in particular from this type of valuation exercise. Theories from organizations, which help to explain the levels of corporate debts, go beyond outlining how to adopt acquisition strategies. Indeed, the very nature of shareholding encourages one to implement different types of financial arrangement that influence both the evolution of the power of holders of capital and the choice of which financial structure to adopt in order to acquire the target company.

1.2. The cost of financial structure

The portfolio theory from Markovitz (1959) deals with determining the cost of equity. The investor's profitability demand depends on their degree of risk aversion. The portfolio to be chosen is graphically located at the intersection of the efficient frontier and one of the curves that characterizes the investor's iso-utility. Sharpe (1963) simplifies this theory by assuming that the expected return on an asset is linked to the return on a market index. Thus, the investor's demand for profitability depends solely on systematic risk. Efficient diversification of an asset portfolio eliminates the specific risk of the share.

An economic reading of a balance sheet consists of identifying, at a given moment, all the jobs involved in the company's operating cycle and the origin of its resources. Economic assets (or enterprise value) are the sum of fixed assets and working capital requirements, i.e. all of the network in progress that is aligned with the operating and investment cycle4. Economic assets are financed by equity and net debt. And so, the market value of the economic asset is divided between the market value of these two types of resources. This results in a balance sheet of the company that only includes market values. In this context, the question arises as to whether there is an optimal capital structure that maximizes enterprise value and thereby minimizes the cost of capital.

The traditional approach, wherein evaluation is carried out without taxation, ensures that there is an optimal liability structure resulting from a sound use of the leverage effect. By also considering a tax-free approach, equilibrium market theory asserts, on the contrary, that there is no optimal capital structure because investors are able to duplicate at their level the financial operations of companies without cost and without any additional risk. The arbitrations that they can mobilize in the event of initial situations where the financial structures would be different lead to a rebalancing of the market. That is to say, they help to ensure that the value of the financial liabilities of two companies that are equal in every aspect becomes equal again. In the presence of taxation, the value of an indebted company is equal to that of a company that is not indebted, to which we must add to the present value of the tax savings linked to the tax deductibility of interest charges. However, even in the presence of taxation, the theories presented by organizations teach us that the choice of whether or not to go into debt comes more from the agent conflicts between the different parties such as shareholders and creditors, or from signals sent to the market more than from intrinsic costs.

1.2.1. Financial asset valuation

The models for valuating financial assets or the capital assets pricing model (CAPM) is used to evaluate the equity of a company in a balanced market. This formula provides an estimate of the rate of return expected by the market for a financial asset according to its systematic risk.

Markowitz (1959) states that between two portfolios characterized by their supposedly random return, one would retain, at identical risk, the company with the highest expected return and, with the same expected return, the company with the lower risk. This principle means that a number of portfolios may be dismissed, as they are less efficient than others. The efficient frontier represents the curve that connects the set of efficient portfolios. The portfolios that sit below this curve are rejected.

Consequently, it is possible to determine the weight of two assets that appear in a portfolio in order to minimize the risk thereof:

or:

• - Rp: portfolio return;
• - xi: weight of asset i in the portfolio.

Variance is minimal when its derivative is zero. We then look for xA such that:

As a result:

Now considering Rp, the portfolio return made up of n assets characterized by their respective return R1..., Rn, we have:

In order to determine E(Rp) and V(Rp), we suppose that:

Assume first that the returns of each of the n assets fluctuate independently of each other. In this case, the variance of a sum is equal to the sum of its variances. And so:

If n approaches infinity, then goes to 0.

We then suppose that the performance of each of the n assets is correlated with each other. In this case:

where:

Let be the average covariance of portfolio P. By definition:

where N corresponds to the number of covariances.

In total, the number N of terms is equal to 0 + 1 + ... + (n - 1), so:

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