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

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

C. Numerical Example

Table I contains a numerical example that demonstrates the CCF method. The example assumes an initial investment of $100,000 to be depreciated equally over three years. Panel A details the assumptions. The asset beta is assumed to equal 1.0 in all three years. (3) The forecasted expected pre-tax operating profits are $50,000 in year one, $60,000 in year two, and $70,000 in year three. The risk-free rate is assumed to be 10%, the risk premium is assumed to be 8%, and the tax rate is assumed to be 33%. The debt is assumed to be risky, with a debt beta of 0.35 in the first year, 0.30 in the second year, and 0.25 in the third year. The project is financed with debt so that the initial debt is $100,000 at the beginning of year one, $50,000 at the beginning of year two, and $20,000 at the beginning of year three.

The CCF is calculated by following the NI path. The cash flow available is equal to NI plus noncash adjustments. CCF is calculated by adding the expected interest to the cash flow available.

The value of the CCFs is calculated using the expected asset return. The easiest way to calculate the asset return is to use the asset beta in the CAPM. Using a risk-free rate of 10%, an asset beta of 1.0, and a risk premium of 8% yields an expected asset return of 18%. The asset return does not depend on leverage because it is a pre-tax cost of capital. It remains constant even though the leverage changes through time. As Panel B of Table I shows, discounting the CCFs at the expected asset return results in a value of $136,996.

II. The Relation Between Capital Cash Flow and Free Cash Flow Valuation

The FCF and CCF methods are equivalent. I demonstrate this equivalency in subsection A by extending the numerical example of Table I and showing that the FCF valuation is the same as the CCF valuation. Subsection B presents a more general proof of the equivalence of the CCF and FCF methods. Because the two methods are equivalent, the choice between them is governed by the ease of use. Subsection C presents some suggestions on choosing between the methods.

A. Numerical Example

Panel C of Table I presents a FCF valuation of the same cash flows valued using CCFs in Panel B. The FCFs are calculated from EBIT, which is reduced by the hypothetical taxes on EBIT to determine EBIAT. Adding the non-cash adjustments to EBIAT results in FCFs.

The FCFs are valued using the after-tax WACC. The WACC has two components: the after-tax cost of debt and the levered cost of equity. The after-tax cost of debt depends on the assumed riskiness of the debt with the cost of debt calculated as its CAPM expected return using equation (2). The levered cost of equity is calculated by levering the asset beta to determine the levered equity beta. Because the fraction of debt is not the same each year, the WACC and its components need to be recomputed each year.

The formula for levering the asset or unlevered beta is:

[[beta].sub.E] = ([[beta].sub.U] - D/V [[beta].sub.D])/ E/V (8)

which requires information on the value of the firm to compute the percentage of debt and equity in the capital structure. (4) Generally, an iterative or dynamic programming approach is used to solve for a consistent estimate of enterprise value. (5) However, because the value is already computed in Panel B, that value can be used to compute the debt and equity proportions. Based on the implied equity-to-value ratio of 27.0% in the first year, the asset beta of 1.0, and the debt beta of 0.35, the implied equity beta is 2.76. Using the CAPM and the assumed market parameters, the expected cost of equity is 32.1% in the first year. Weighting the expected after-tax cost of debt and the expected cost of equity by their proportions in the capital structure results in a WACC of 14.9% for the first year.