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The Utility of Real Options in the Valuation of Liabilities

1.1. Introduction

Traditional valuation methods can appear overly static when faced with the need to account for the notion of the overall company risk through the volatility of its assets, as well as the need to determine the economic value of the debt, which until now, has been ignored. Indeed, insofar as the final objective of each of these valuation methods is to obtain the economic value of equity, that of net debt cannot be separated from this consideration if we take it to its logical conclusion.

Moreover, each of these traditional methods can be critiqued. The subjectivity of hypotheses in the construction of a business plan at the heart of the DCF method, the disparities at the heart of a sample set of companies belonging to the same business sector leading to falsified sector-specific multiples, and even the failure to consider any potential growth at the heart of the patrimonial approach are all faults that bias the valuation and raise the question of the pertinence of these traditional methods, suggesting the possibility that a complementary and innovative method exists.

Insofar as the assets of a company can be considered a portfolio of real options, nothing negates the idea that it would be the same for liability. And indeed, the value of company equity and debts can also be studied in the field of options.

This approach allows us to separate the equity of a company into intrinsic value and time value. The intrinsic value is the difference between the present economic value of the asset and the nominal amount of debt. The time value is the expectation that the company value will become greater than the amount of net debt to be repaid. Otherwise, the time value is zero. In this case, real options are therefore useful in valuating equity economically by distinguishing the possible creation of value for shareholders after a merger-acquisition, but they turn out to be just as necessary for economically valuating the net debt. It then turns out that the risk of debt can have an entirely different impact on the value of a company, due to the emergence of a probability of bankruptcy and the rate of non-recovery in the models.

1.2. Real options: a mitigating alternative to the deficiency of traditional valuation methods

Traditional valuation methods are subject to fundamental methodological critiques in general and in the case of each one. In each method, the volatility of assets is not accounted for and the value of net debt is counted when it should be, as with equity, economic. Furthermore, the multiples method can give the impression of large gaps in the multiples of the standard, tied in particular to significant differences in terms of marginal rates, investment politics, accounting norms used, financial structures or tax rates between companies. Thus, the sector-specific multiples used to valuate a company can be biased. An intuitive and legitimate reflex, at the end of the day, leads to the removal of elements that seem inacceptable.

Nonetheless, this reflex is subjective. If, theoretically, the DCF method is infallible in the sense that its logic brings us to the conclusion that a company is worth what it will become, the necessary parameters for the creation of a model are based on strong hypotheses that can vary considerably from one analyst to another. Finally, the patrimonial method, which remains difficult for an external analyst to apply, finds its limit in the fact that, by focusing on the patrimonial present of a company, any forecasts are voluntarily excluded.

By insisting on economically valuating the structure of liabilities, real options allow us to adopt an alternative point of view. By adopting an optional logic, it becomes possible to consider that equity is the reflection of the purchase from a call and that debt is that of a sale from a put. Thus, the Black-Scholes model (1973) is legitimized.

1.2.1. The limits of traditional approaches

The comparables approach must allow us to define pertinent standards. This is a complicated task, however. In order for the sample to be reliable, it must indeed be representative of the business sector and account for a certain level of risk and development related to financial performance and a similar model. Moreover, significant deviations can be seen in the fact that the chosen standards might include international companies that apply different accounting norms. To limit large disparities, it is possible to apply regressive statistical tools. This reveals a linear relationship between a valuation multiple and the principal performance criteria that affects them. In the case of transactional comparables, we must recall that a control premium was applied by the buyer.

It is therefore necessary to subtract value in order to correct this effect. Traditionally, practitioners begin with a large standard that becomes smaller over time to maintain companies or "satisfying" transactions, with respect to the different points raised here. Otherwise, the major inconvenience of the patrimonial approach is that it does not consider the growth potential of a company. In the DCF approach1, the company value (or enterprise value, EV) is the discounted value of future free cash flows FCF, the discount rate being the weighted mean cost of capital or WACC K:

where E is the value of equity and D is the net debt. The WACC contained in the calculation of the company value is based on the equity value, which is found using the DCF method. It is the reason why practitioners include an iterative life cycle in their approach. By supposing an infinite rate of growth of FCF g starting at year 1 and a WACC equal to K:

By referring to the cost of capital adjusted by Modigliani and Miller (1963), we can eliminate the life cycle. Indeed, , where ? is the cost of capital for a debtless company with the same sector-specific rate risk. In other words, thanks to the CAPM, ? = r + ß*[E(RM) - r], where r is the rate without risk. Thus:

where Dt is the tax rate that results from fiscal deductibility of interest to the extent that we suppose an infinite net debt. Indeed, in the Modigliani-Miller theory, Dt comes from the simplification of , where iDt is the interest tax economy and i is the corresponding tax rate. In this case, D is obviously the remaining debt owed, found in the latest available financial statements. When practitioners deduct D from EV to obtain the value of equity, the following formula E is obtained:

The Modigliani-Miller theory shows that the strike price on risky debt has no impact on the WACC, and, as a result of this, it has no impact on the value of equity: the cost of debt does not appear in the two previous formulas, and a rise in the strike price of the debt corresponds to a rise in the risk that can be tolerated by the investors and banks. It is therefore logical that a drop in risk is tolerated by shareholders. For a simple example, Table 1.1 shows that the transfer of risk between shareholders and investors does not change the value of the WACC.

With an FCF equal to 100, a risk-free rate of 2%, a market risk premium of 7% and a debtless beta of 0.9, two hypotheses about the cost of debt before taxes arise: 3.40%, based on a debt beta of 0.20, and 5.50%, based on a debt beta of 0.50. The corresponding indebted betas, based on the Hamada formula, are, respectively, 1.18 and 1.06, and the deducted equity costs are 10.27% and 9.43%, respectively. Thus, the two WACC and adjusted capital costs are 7.06%. Finally, the company value is the same in both cases: 2,538.

Table 1.1. Transfer of risk between shareholders and investors without impacting the WACC using the DCF approach2

The calculation of the WACC is "subjective" given the numerous...