There Exists Circularity between WACC and Value? Another Solution

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