Using Cost-Benefit Analysis to Identify the Optimal Capital Structure

The measurement of the costs and benefits of debt represents a significant advance in capital structure research. In an upcoming paper, Van Binsbergen, Graham, and Yang take these measurements further, using them to identify an optimal level of debt for individual firms.25 The foundation of this new model is that capital structure is optimized when the marginal benefit of debt is equal to the marginal cost of debt. By modeling the characteristics and behavior of firms that seem to operate under optimal capital structures, the authors built a general model to estimate both the benefits (tax shield and reduction in agency costs) and costs (financial distress costs) of debt that can work for any firm. In addition to consideration of the marginal tax rate, the model accounts for tax-loss carry-forwards and carry-backs. The model incorporates several variables in modeling the costs of debt, including collateral (physical assets plus inventory divided by total books assets), book-to-market equity ratio, intangible asset ratio, and cash flows to book asset ratio. The model also considers whether a firm pays dividends. Outcomes from the model are consistent with empirical studies and commonsense inferences. For example, the model predicts that firms with a low collateral ratio will have higher costs of debt than those with a high collateral ratio. Figure 8.1 depicts the cost and benefit curves for Six Flags and Performance Food Group. Relative to the optimal capital structures determined by the model, Six Flags was overlevered and Performance Food Group was underlevered. The shaded areas depict the net benefit (cost) of debt. For Six Flags, it indicates a net cost of debt since the firm's actual debt level is greater than the optimal level; the costs of debt exceed the benefits of debt. In contrast, Performance Food Group uses too little debt. The shaded area depicts the amount by which the benefit of debt exceeds its costs. Note that at the optimal level, the marginal benefit of debt equals the marginal cost of debt, and debt levels beyond this point will have a net cost. The model can also measure how the cost of debt and firm value are affected by operating with a suboptimal capital structure.26

The Cost of Capital

Capital structure policies are put in place in an effort to maximize shareholder returns. Managers do this by maximizing cash flows and minimizing the cost of capital. The calculation of the cost of capital is important in part because it represents an important parameter in a firm's capital budgeting decisions. According to the Census Bureau, capital expenditures on property and equipment in 2010 were over $1 trillion for U.S. nonfarm businesses. Without question, the cost of capital estimate was a key determinant in these spending decisions. Miscalculating the cost of capital can lead a firm to reject a potentially valuable project if the cost of capital is overestimated, or accept a project that fails to meet investors' required return if the cost of capital is underestimated. Here we look at the considerations in estimating the cost of capital. The components of the cost of capital include the required returns on equity and debt, and

Figure 8.1. Benefit of Debt for Six Flags and Performance Food Group

Benefit of Debt for Six Flags and Performance Food Group

the relative weighting of equity and debt in the capital structure. Although there are different types of equity and debt (e.g., preferred equity and convertible debt), we focus on common shares and straight debt. Offbalance sheet items are also a source of capital, thus we discuss their impact.

The Cost of Equity

According to a study by Bruner, Eades, Harris, and Higgins, CAPM is the dominant measure of cost of equity.27 They reported that 80 percent of corporations and advisors and 100 percent of textbooks use CAPM as the primary measure of the cost of equity. A more recent survey by Graham and Harvey found that 75 percent of corporations use some form of the CAPM to measure the cost of equity.28 Some corporations and advisors may also use multifactor models that consider not only market risk but also sensitivity to other factors such as firm size and book-to-market value.

The return on a risky asset must provide compensation for the time value of money and a risk premium based on the asset's level of risk. The CAPM recognizes two sources of risk: systematic risk and unsystematic risk. Systematic (market) risk affects all assets in the market and reflects sensitivity to variables including GDP, inflation, interest rates, and other macroeconomic factors. Unsystematic risks are specific to a firm and reflect variables that can include lay-offs, strikes, supply shortages, upper-management changes, and other firm-level factors. There are two underlying assumptions of the model: market prices are efficient (i.e., they are fair and reflect all available information), and all investors hold a well-diversified portfolio (i.e., they are free of unsystematic risk exposure. Since poor returns on some stocks will be offset by good returns on others, the total risk exposure of a well-diversified portfolio is due only to market risk.) Accordingly, the CAPM states that investors should only be rewarded for systematic risk. This depends on the market risk premium and the firm's sensitivity to movements in the market. We examine different proxies for the risk-free rate, the market risk premium, and the measure of systematic risk (beta).

Risk-Free Rate

Theoretically, the risk-free rate should be a default-free return that represents compensation for the pure time value of money. Textbooks often use an average of historical T-bill rates as a proxy for the risk-free rate. Firms and analysts tend to use current interest rates on long-term treasuries to match the time horizon of their investments. Bruner, Eades, Harris, and Higgins reported that 70 percent of firms use treasury maturities of 10 years or longer.29 The spread between short-term and longer-term yields has averaged about 1.5 percent and is currently 3.21 percent,30 so the choice of maturities can have a significant impact on the cost of equity estimate.

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