Abstract
The purpose of this paper is to present the use of fuzzy logic to improve the calculation of weighted average cost of capital (WACC). The fuzzy WACC approach not only allows the pre-tax cost of debt, the effective tax rate, the tax benefit, and cost of equity to be treated as fuzzy numbers, it also offers ranking means to find the optimal debt ratio. This paper contributes to the literature by offering alternative methods to calculate the WACC and the optimal debt ratio for firms under uncertainty. Compared with the traditional WACC, the fuzzy WACC model can overcome the problems pertinent to uncertainty, complexity and imprecision. This paper thus sheds light on capital structure decision making.
Highlights
Sharpe [1] and Lintner [2] brought the theory of the capital asset pricing model (CAPM), which offers a very intuitive and straightforward method to gauge the cost of equity
In order to rank the weighted average cost of capital (WACC) at each level of debt for seeking a precise optimal capital structure, this paper adopts the latest method for ranking generalized trapezoidal fuzzy numbers by Chen et al [21], which we will discuss in more details later in Subsection 2.4
Using fuzzy logic to analyze WACC and optimal capital structure, we find that WACC follows a U-shaped curve
Summary
Sharpe [1] and Lintner [2] brought the theory of the capital asset pricing model (CAPM), which offers a very intuitive and straightforward method to gauge the cost of equity. The fuzzy WACC approach allows the pre-tax cost of debt, the effective tax rate, the tax benefit, and the cost of equity to be expressed as fuzzy numbers, and offers ranking means to find the optimal debt ratio. These fuzzy numbers can better capture the uncertainty in the computation of the WACC. In order to rank the WACC at each level of debt for seeking a precise optimal capital structure, this paper adopts the latest method for ranking generalized trapezoidal fuzzy numbers by Chen et al [21], which we will discuss in more details later in Subsection 2.4. For a trapezoidal fuzzy number A (a1, a2 , a3 , a4;1) with the membership function, its membership function fA (x) is given by f A
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