There exists circularity between WACC and value? Another solution.
| Autor | V |
ABSTRACT
Although we know there exists a simple approach to solve the circularity between value and the discount rate, known as the Adjusted Present Value proposed by Myers, 1974, it seems that practitioners still rely on the traditional Weighted Average Cost of Capital, WACC approach of weighting the cost of debt, Kd and the cost of equity, Ke and discounting the Free Cash Flow, FCF. We show how to solve circularity when calculating value with the free cash flow, FCF and the WACC. As a result of the solution we arrive at a known solution when we assume the discount rate of the tax savings as Ke, the cost of unlevered equity: the capital cash flow, CCF discounted at Ku. When assuming Kd as the discount rate for the tax savings, we find an expression for calculating value that does not implies circularity. We do this for a single period and for N periods.
KEY WORDS
Firm valuation, cost of capital, cash flows, free cash flow, capital cash flow, WACC, circularity
JEL CLASSIFICATION
M21, M40, M46, M41, G12, G31, J33
INTRODUCTION
Although we know there exists a simple approach to solve the circularity between value and the discount rate, known as the Adjusted Present Value proposed by Myers, 1974, it seems that practitioners still rely on the traditional Weighted Average Cost of Capital, WACC approach of weighting the cost of debt, Kd and the cost of equity, Ke and discounting the Free Cash Flow, FCF. We show how to solve circularity when calculating value with the free cash flow, FCF and the WACC. As a result of the solution we arrive at a known solution when we assume the discount rate of the tax savings as Ke, the cost of unlevered equity: the capital cash flow, CCF discounted at Ku. When assuming Kd as the discount rate for the tax savings, we find an expression for calculating value that does not implies circularity. We do this for a single period and for N periods.
The typical solution for solving the circularity between value and WACC is to activate the option for iteration in a modern spreadsheet (Vélez-Pareja and Tham, 2000,
Tham and Vélez-Pareja, 2004, and Vélez-Pareja and Tham, 2005). However, this approach seems to be not easy to apply. We have examined the analytical solution of this problem and found what is known well before: when discounting with the proper discount rate the CCF will give identical answer to the calculation of value with the FCF discounted at the weighted average cost of capital, WACC.
THE PRACTICAL SOLUTION OF CIRCULARITY
The solution of circularity is very simple. This problem can be easily solved: in the Excel spreadsheet select Tools, then select Options, and there, select the tab Calculate and tick the option Iterations. Done this, the formulas for WACC and Ke, (the cost of the levered equity), that imply circularity, can be constructed. (See, Vélez-Pareja and Tham, 2000 and 2005, Tham and Vélez-Pareja, 2004). The analytical solution is simple as well.
AN ANALYTICAL SOLUTION FOR CIRCULARITY
Modigliani and Miller (1958 and 1963), in illuminating and seminal works defined the relationship between cash flows and values. These are the free cash flow, FCF, the cash flow to debt, CFD, the cash flow to equity, CFE, the tax savings, TS and the capital cash flow1 and their corresponding values. These relationships are:
FCF + TS = CFD + CFE = CCF (1a)
[V.sup.L] = [V.sup.Un] + [V.sup.TS] = D + E (1B)
Where [V.sup.L] is...
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