# Theoretical Valuation Methodologies (FCFF, FCFE, CCF, and APV)

4 major theoretical valuation methodologies:

1. Discounting Free Cash Flow to the Firm (FCFF) at the Weighted Average Cost of Capital (WACC)
• Adjusts for the tax benefit of debt from the cash flow numerator (i.e. FCFF should be calculated as though the firm is all-equity financed) because it will be handled by a smaller WACC denominator (due to using the after-tax cost of debt).
• FCFF = EBIT*(1-t) + Depreciation – Capex – Change in NWC
• FCFF is the cash flow available to the owners when the debt is paid down after the purchase of the business.
• Assumes a constant amount of debt.
2. Discounting Free Cash Flow to Equity (FCFE) at the Cost of Equity
• FCFE = FCFF – Net debt repayments – Interest + Tax saved from interest (i.e. include the tax shield benefit back in)
• FCFD = Free Cash Flow to Debt = Interest + Net debt repayments
• FCFE = FCFF – FCFD + Interest tax shield
• Assumes constant debt/equity ratio.
3. Discounting Capital Cash Flow (CCF) at the Unlevered Cost of Capital
• CCF = FCFF + Tax saved from interest = FCFF + Interest*t = FCFE + FCFD
• CCF is the cash flow available to the debt and equity holders when the debt is left intact after the purchase of the business.
• Tax benefit is included in the numerator because it is not handled in the denominator.
• Assumes that the PVTS has the same risk as the FCFF.
• Level of debt can change from period to period. This will change the CCF in each period.
4. Discounting Free Cash Flow to the Firm (FCFF) at the Unlevered Cost of Capital, plus PVTS minus PVOC (a.k.a. Adjusted Present Value (APV))
• Value of Levered Firm = Value of Unlevered Firm + Present Value of Tax Shield (PVTS) – Present Value of Other Costs (PVOC) = Market Value of Equity + Market Value of Debt
• Value of Unlevered Firm = Discount FCFF at the Unlevered Cost of Capital
• PVTS = interest * tax rate / pre-tax cost of debt = (pre-tax cost of debt * debt * tax rate / pre-tax cost of debt) = debt * tax rate. This assumes a constant debt level where only interest is paid at each period.
• PVOC = Other costs not directly related to the project / business cash flows, e.g. issue costs for debt or equity. The costs are discounted at the risk-free rate.
• Using the cost of debt as the discount rate for PVTS assumes that the riskiness of the tax shield is the same as the riskiness of the debt.
• Level of debt can change from period to period. You can recursively compute (from the future periods back to today) the value of the levered firm at each period by discounting the period’s FCFF by the unlevered cost of capital, and sum that with the period’s tax savings discounted at the period’s pre-tax cost of debt.

Note:

1. Method 2 above gives you the value of equity. Methods 1, 3, and 4 compares with the enterprise value, so you still need to adjust (i.e. minus debt + excess cash) to get the value of equity.

Iterative Method of Valuation

There is an iterative method of valuation which is used when it is not certain what cost of equity should be used for the valuation. This iterative method can be used with any of the 4 valuation methods above.

• Step 1: Determine the market value of the debt of the company. This value does not change in the iterative process.
• Step 2: Set the current estimated value of the equity to some arbitrary value (e.g. book value).
• Step 3: Determine the unlevered equity beta for the industry.
• Step 4: Use the current estimated value for the equity and its implied debt-equity-ratio to lever up the beta from Step 3, then calculate the cost of equity.
• Step 5: Use the cost of equity in Step 4 to estimate a new equity value for the company.
• Step 6: If the new equity value in Step 5 = the estimated equity value in Step 4, then stop, equity value obtained. Else set the current estimated equity value = new equity value in Step 5, and go to Step 4 to iterate again.