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

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

This paper presents the Capital Cash Flow (CCF) method for valuing risky cash flows. I show that the CCF method is equivalent to discounting Free Cash Flows (FCF) by the weighted average cost of capital. Because the interest tax shields are included in the cash flows, the CCF approach is easier to apply whenever debt is forecasted in levels instead of as a percent of total enterprise value. The CCF method retains its simplicity when the forecasted debt levels and the implicit debt-to-value ratios change throughout forecast period. The paper also compares the CCF method to the Adjusted Present Value (APV) method and provides consistent leverage adjustment formulas for both methods.

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Richard S. Ruback (*)

The most common technique for valuing risky cash flows is the Free Cash Flow (FCF) method. In that method, interest tax shields are excluded from the FCFs and the tax deductibility of interest is treated as a decrease in the cost of capital using the after-tax weighted average cost of capital (WACC). Because the WACC is affected by changes in capital structure, the FCF method poses several implementation problems in highly leveraged transactions, restructurings, project financings, and other instances in which capital structure changes over time. In these situations, the capital structure has to be estimated and those estimates have to be used to compute the appropriate WACC in each period. Under these circumstances, the FCF method can be used to correctly value the cash flows, but it is not straightforward.

This paper presents an alternative method for valuing risky cash flows. I call this method the Capital Cash Flow (CCF) method, because the cash flows include all of the cash available to capital providers, including the interest tax shields. In a capital structure with only ordinary debt and common equity, CCFs equal the flows available to equity--NI plus depreciation less capital expenditure and the increase in working capital--plus the interest paid to debtholders. The interest tax shields decrease taxable income, decrease taxes and, thereby, increase after-tax cash flows. In other words, CCFs equal FCFs plus the interest tax shields. Because the interest tax shields are included in the cash flows, the appropriate discount rate is before-tax and corresponds to the riskiness of the assets.

Although the FCF and CCF methods treat interest tax shields differently, the two methods are algebraically equivalent. In other words, the CCF method is a different way of valuing cash flows using the same assumptions and approach as the FCF method. The advantage of the CCF method is its simplicity. Whenever debt is forecasted in levels, instead of as a percent of total enterprise value, the CCF method is much easier to use, because the interest tax shields are easy to calculate and easy to include in the cash flows. The CCF method retains its simplicity when the forecasted debt levels and the implicit debt-to-value ratios change throughout the forecast period. Also, the expected asset return depends on the riskiness of the asset and, therefore, does not change when capital structure changes. As a result, the discount rate for the CCFs does not have to be re-estimated every period. In contrast, when using the FCF method, the after-tax WACC has to be re-estimated every period. Because the WACC depends on value -weights, the value of the firm has to be estimated simultaneously. The CCF method avoids this complexity so that it is especially useful in valuing highly levered firms whose debt is usually forecasted in levels and whose capital structure changes substantially over time.

The CCF method is closely related to my work on valuing riskless cash flows (Ruback, 1986) and to Stewart Myers' work on the Adjusted Present Value (APV) method (Myers, 1974). In my paper on riskless cash flows, I showed that the interest tax shields associated with riskless cash flows can either be equivalently treated as increasing cash flows by the interest tax shield, or as decreasing the discount rate to the after-tax riskless rate. The analysis in this paper presents similar results for risky cash flows; namely, risky cash flows can be equivalently valued by using the CCF method with the interest tax shields in the cash flows or by using the FCF method with the interest shields in the discount rate.

The APV method is generally calculated as the sum of FCFs discounted by the cost of assets plus interest tax shields discounted at the cost of debt. It results in a higher value than the CCF method, because it assigns a higher value to interest tax shields. The interest tax shields that are discounted by the cost of debt in the APV method are discounted by the cost of assets explicitly in the CCF method and implicitly in the FCF method. Stewart Myers suggests the term "Compressed APV" to describe the CCF method, because the APV method is equivalent to CCF when the interest tax shields are discounted at the cost of assets. However, most descriptions of APV suggest discounting the interest tax shields at the cost of debt (Taggart, 1991 and Luehrman, 1997).