Analytical Solution to the Circularity Problem in the Discounted Cash Flow Valuation Framework

In this paper we propose an analytical solution to the circularity problem between value and cost of capital. Our solution is derived starting from a central principle of finance that relates value today to value, cash flow, and the discount rate for next period. We derive a general formulation for the equity value, E, for the cost of unlevered equity, firm value and the weighted average cost of capital, WACC, without circularity. We furthermore compare the results obtained using these formulas with the results using the Adjusted Present Value approach (no circularity) and the iterative solution of circularity based upon the iteration feature of a spreadsheet. We conclude that all methods produce the same answer