Capital Cash Flows: a simple approach to valuing risky cash flows

Financial Management (Financial Management Association), Summer, 2002 by Richard S. Ruback

The capital structure changes in each period, because the ratio of the value of the remaining cash flows, and the amount of debt outstanding does not remain constant throughout the life of the project. Repeating the process of valuing the enterprise, determining the debt and equity proportions, unlevering the asset beta, and estimating the equity cost of capital according to the CAPM, results in a WACC of 16.0% for the second year and 16.6% for the third year. These after-tax WACCs rise as the percentage of debt in the capital structure, and the corresponding amount of the interest tax shields, fall.

Total Enterprise Value (TEV) is calculated by discounting the FCFs by the after-tax WACCs. Since the after-tax WACCs change, the discount rate for each period is the compounded rate that uses the preceding after-tax WACCs. The resulting value of the FCFs is $136,996, exactly the same value as obtained in the CCF calculations in Panel B of Table I.

B. Proof of Equivalency

This section shows that the CCF method is equivalent to the FCF method. To keep the analysis simple, assume the asset being valued generates a constant pre-tax operating cash flow. This cash flow is before tax, but after cash adjustments such as depreciation, capital expenditures, and changes in working capital. The after-tax operating cash flow equals earnings before interest and after-tax plus the cash flow adjustments and equals FCF, which measures the cash flow of the firm if it were all equity financed.

The value, [V.sub.FCF], is calculated using the FCF method by discounting the FCFs by the after-tax WACC:

[V.sub.FCF] = FCF/WACC (9)

where V is the value of the project being valued. WACC, the after-tax WACC, is defined as:

WACC = D/V [K.sub.D](l - [tau]) E/V [K.sub.E] (10)

with D and E equal to the market value of debt and equity, respectively; [tau] is the tax rate; [K.sub.D](l - [tau]) is the after-tax expected cost of debt; and [K.sub.E] is the expected cost of equity.

The CCF is the expected cash flow to all capital providers with its projected financing policy, including any benefits of interest tax shields from its financial structure. Since FCF measures the cash flow assuming a hypothetical all equity capital structure, then CCF is equal to FCF plus interest tax shields:

CCF = FCF Interest Tax Shield = FCF [tau][K.sub.D]D (11)

where [K.sub.D]D is the interest tax shield calculated as the tax rate, [tau], times the interest rate on the debt, [K.sub.D], times the amount of debt outstanding, D.

Value is calculated using the CCF method, [V.sub.CCF], by discounting the CCFs by the expected return on assets. The expected asset return is measured using the Capital Asset Pricing Model (CAPM) and the asset beta ([[beta].sub.U]) of the project being valued:

[V.sub.CCF] = FCF [tau][K.sub.D]D/[R.sub.F] [[beta].sub.U][R.sub.P] (12)

where [R.sub.F] is the risk-free rate and [R.sub.P] is the risk premium.

The goal is to show that the value obtained using FCFs and WACC is the same as the value obtained using CCFs and [K.sub.A]. In other words, the goal is to show that equation (9) is identical to equation (12). By combining equations (9) and (10):