Using the WACC methodology to improve the assessment of projects in the french farming industry. Empirical evidences from farm's results of Isère

2.2 The WACC Theory

2.2.1 The Importance of the WACC Theory.

The WACC is not considered easy to compute, but is one of the fundamental elements in modern finance (Quiry & Le Fur, 2012; Brealey, Myers, & Allen, 2008). The NPV calculation and the determination of the value of the stock are based on the results of the WACC, which underlines its importance (Quiry & Le Fur, 2012, p. 699). The underlying theory of the WACC is the CAPM. This model objective is to measures capital assets value depending on the risk and the expected return of the company. According to Brealey, Myers & Allen (2008), the after-tax WACC represents more the reality of the company and can be described as follow:

E

WACC = K(D) . (1 -- Tc) _r, + K(E)

K(D): cost of debt, at market value.

Tc: corporate tax rate.

D/V: total debt divided by total firm value. K(E): cost of equity.

E/V: total equity divided by firm value.

The cost of equity in the WACC theory has to be calculated using the CAPM, which can be described as follow:

E (Re) = Rf + f3. [E (Rm) -- Rf]

E(Re): expected return on equity. It corresponds to K(E) in the WACC formula [3: beta. It represents the risk.

E(Rm): expected return of the market in which the company operates. See part 2.1.2 page 20 on risk premium for the literature review dealing with risk premium. However, the risk premium is defined as the premium obtained compare to a risk-free asset.

Rf: risk free rate of return. The risk-free rate of return can be estimated by the long-term government bond yield (Brealey, Myers, & Allen, 2008; Quiry & Le Fur, 2012).

2.2.2 The Betas for Micro-Capitalizations

In this research, financial techniques are used to estimate the risk for listed companies to apply it for non-listed small companies. The bias introduced is consequent, as the beta has a negative relationship with the size of firms (Binder, 1992; Al-Rjoub, Varela, & Hassan, 2005; Shomir, Pat, & Jeong-gil, 2011). Therefore, small farms should have a higher Beta compared to listed companies operating in agriculture, as smaller firms present little or no diversification (Drew & Veeraraghavan, 2003). Table 6 presents the results found in the literature comparing large capitalizations and micro-capitalizations, which can be considered as the right comparison between the listed companies operating in agriculture which have activities in many countries and the small farms of Isère.

Authors	Time frame	Number of groups	micro-cap Beta premium
Al-Rjoub, Varela & Hassan (2005)	1970-2000	1^st decile vs 10^th d		0.51
Al-Rjoub, Varela & Hassan (2005)	1982-2000	1^st decile vs 10^th d		0.36
Al-Rjoub, Varela & Hassan (2005)	1990-2000	1^st decile vs 10^th d		0.24
Shomir, Pat & Jeong-gil (2011)	1980-2003	1^st quartile vs 4^th q		0.21
Bhardwaj & Brooks (1993)	1926-1988	1^st group vs 5^th g		0.72
Chan & Chen (1988)	1949-1983	1^st group vs 20^th g		0.69
Dongcheol (1993)	1926-1990	1^st decile vs 10^th d		0.58
Jegadeesh (1992)	1954-1989	1^st group vs 20^th g	0.32	- 0.62
Mean				0.47

Table 6: Market capitalization effect on the beta for micro-capitalization

As presented in Table 6, the effect of size is quite important on the beta. It is important to notice that the standard deviation also increases with the beta (Drew & Veeraraghavan, 2003; Dongcheol, 1993; Chan & Chen, 1988). From the results found in the literature, for micro-capitalizations compare to large capitalizations, the beta increases on average by 0.47, which is really significant regarding the impact of the beta on the WACC formula.