Estimated costs of equity for utilities are, like interest rates, very low by historical standards. A standard capital asset pricing model (CAPM) value might be 9 percent,¹ although some analysts might argue for much lower values.² Discounted cash flow (DCF) methods may produce a wider range of answers, due to variations in the growth rates selected, but many of those answers will be low by historical standards, too.³

These low findings are based in part on problems with the underlying models. For example, the CAPM long has been known to underestimate the cost of equity of low-beta stocks and to overestimate the cost of equity of high-beta stocks.⁴ However, often there is a more fundamental problem that rate regulation in North America usually overlooks: a material mismatch between the capital structure at which the cost of equity is estimated and the ratemaking capital structure to which it is applied.⁵ A material capital structure mismatch, which occurs frequently, can lead to material misestimates of the appropriate allowed return on equity, perhaps on the order of 2 percentage points. That is, a 9 percent estimate of the cost of equity can imply an allowed rate of return on equity of 11 percent.

Effect of Debt On Equity Risk

Let's start with the basics. Companies raise money for investment by issuing securities. Different securities have different claims on the firm's earnings, and if necessary, on its assets. Debt has a senior claim on a specified portion of the earnings. Common equity, the most junior security, gets what's left after everyone else has been paid.

The company's overall risk depends on the business it's in. When a company uses (reasonable amounts of) debt, the company's overall risk falls on a fraction of its capital, the common equity.⁶ Since equity bears more risk, investors require a higher rate of return on equity than on debt. Except at extreme debt levels, the overall risk of the firm does not change materially due to the addition of debt. The various securities just divvy that risk up.

Modern models of the cost of equity assume risk consists of a stock's sensitivity to one or more economic factors that affect asset values generally. Suppose changes in some market-wide economic factor normally produce fluctuations in the market value of a company's assets of plus or minus (+/-) 2 percent. At 100 percent equity, these changes produce fluctuations of +/-2 percent of the market value of the company's equity, too. But at a 50-50 market-value, debt-equity ratio, the same asset-value fluctuations produce equity-value fluctuations of +/- 4 percent. At a 75-25 market-value debt-equity ratio, these fluctuations become +/- 8 percent of the market value of the company's equity. Figure 1 illustrates this point for debt-equity ratios of 0-100, 25-75, 50-50, and 75-25. Higher risk means a higher required rate of return, so the cost of equity goes up at an ever increasing rate as a company adds debt, which offsets the lower cost of debt. In short, there is no magic in financial leverage.

This result should be familiar to anyone who owns a home. When housing prices go up or down, the effect on the owner depends in part on how big the mortgage is. Figure 2 shows this effect for mortgages that are 0 percent, 20 percent, 50 percent, and 80 percent of the dwelling's initial purchase price. The figure assumes the purchase price of a home is $100,000, and that a year later housing prices in the area are expected to vary within a range of plus or minus 10 percent of today's price. The impact on the homeowner's net worth depends on the size of the mortgage. With no mortgage, a +/-10 percent change in the dwelling's price translates into a +/-10 percent change in the owner's equity. With a mortgage of 50 percent of purchase price, this range doubles to +/-20 percent. With a mortgage of 80 percent of purchase price, the +/-$10,000 in the home's value becomes +/-50 percent of the owner's initial $20,000 in equity.

Implications for Rate Regulation

Nearly half a century of financial research on the effects of capital structure on the value of the firm⁷ and the resulting literature have explored the effects of risk, corporate taxes, personal taxes, financial distress, the signals companies send investors through the ways they raise capital, and possible divergences of interests between managers and shareholders. We believe it is fair to say that no single theory has emerged as "the answer" to how capital structure affects the value of a firm.

Empirical as well as theoretical research has been done. For most industries, modest amounts of debt appear to add some value to the firm. However, companies display a wide range of intra-industry capital structures, and the most profitable firms in an industry tend to use the least debt, a finding that holds internationally as well as in the United States. The most profitable firms are the ones that could make best use of the corporate tax shields that interest expense provides,⁸ and presumably these firms tend to be the best managed (why else are they the most profitable?). The fact that these firms do not use more debt implies that the corporate tax advantage of debt must be offset by other costs. The upshot of such research is that the value of a firm is not very sensitive to the debt ratio over a broad middle range of capital structures.

What does this mean for the cost of capital? Standard practice uses the after-tax weighted-average cost of capital as the discount rate in determination of the value of a project or a firm.⁹ If the value of the project or the firm is independent of capital structure over a broad middle range, as the research demonstrates, so too must be its after-tax weighted-average cost of capital.¹⁰

The result is illustrated in Figure 3. Here the after-tax weighted-average cost of capital is shown essentially as flat between market-value capital structures of about 30 and 55 percent debt. If the overall cost of capital is essentially constant as the proportion of risk-bearing equity shrinks, the risk and cost of equity must rise at an ever-increasing rate-just what the risk discussion in the previous section predicted. But the finding that the after-tax weighted-average cost of capital essentially is flat tells us just how fast the cost of equity increases with debt. The figure shows this effect in the cost-of-equity curve.¹¹

Market-value equity ratios typically are higher than book-value debt ratios for utilities today. Suppose an analyst examines a sample of firms in this industry and estimates a 9 percent cost of equity at the sample's 34 percent market-value debt ratio. Then (estimation errors aside) she would have found an 11 percent cost of equity had the sample had a 53 percent debt ratio, because the sample's equity holders would have been bearing much more financial risk at the higher debt ratio.¹² That, in turn, means that if the capital structure used to set rates were 53 percent debt, the allowed rate of return on equity should be 11 percent, not 9 percent.

The finding that the after-tax weighted-average cost of capital is essentially flat for companies in the industry's middle range of capital structures provides a ready three-step procedure to use in rate hearings:

1. Calculate the after-tax weighted-average cost of capital of a sample of companies not in financial difficulty,¹³ using each company's market-value capital structure and its current after-tax market cost of debt;¹⁴
2. Take the average of these values as the industry's after-tax weighted-average cost of capital; and
3. Calculate the regulated company's allowed rate of return on equity as the cost of equity that produces the same after-tax weighted-average cost of capital at the ratemaking capital structure, again using the company's current after-tax market cost of debt.

The result will be the cost of equity found by the analyst, estimation problems aside, if the sample's market-value capital structure had been equal to the ratemaking capital structure. That value is the appropriate allowed rate of return on equity at the ratemaking capital structure.

Differences between the market-value capital structures of the sample companies and the capital structure used to set rates can be large. If so, there will be equally large differences in the amount of financial risk-hence, the costs of equity at the different capital structures. Failure to take these differences into account is likely to lead to allowed rates of return on equity that are materially below the costs of equity that utility shareholders actually require.

Endnotes:

1. Recall that the CAPM estimates the cost of capital as the sum of (1) the risk-free interest rate plus (2) the product of the stock’s beta and the market risk premium. If the long-term risk-free rate is set at 5 percent, the market risk premium at 6.5 percent, and the beta at 0.6, the result is 8.9 percent. (Recall also that beta measures the sensitivity of the stock’s returns to the market’s returns, and that the average beta is 1.0, indicating an average-risk stock.)
2. For example, a 5 percent value for the long-term risk-free rate, a market risk premium 
   of 5.5 percent, and a beta of 0.5 produce a CAPM cost-of-equity estimate of 7.8 percent. Use of a short-term interest rate, although uncommon in rate regulation, currently would produce even lower estimates for the cost of equity.
3. Recall that the basic DCF method estimates the cost of equity as the sum of (1) the forecasted dividend yield plus (2) the growth rate.
4. See, for example, Fischer Black, Michael C. Jensen and Myron Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” in M. Jensen (ed.) Studies in the Theory of Capital Markets, New York: Praeger (1972) 79-121; Eugene F. Fama and James D. MacBeth, “Risk, Returns and Equilibrium: Empirical Tests,” Journal of Political Economy 81 (1973), 607-636; and Robert H. Litzenberger, Krishna Ramaswamy and Howard Sosin, “On the CAPM Approach to Estimation of 
   a Public Utility’s Cost of Equity Capital,” The Journal of Finance 35 (1980) 369-387.
5. Countries such as Australia, the United Kingdom, and New Zealand have implemented rate regulation much more recently than Canada or the United States. Their procedures, developed with the advantage of access to modern financial research, focus primarily on the overall market cost of capital rather than the separate costs of debt and equity. This approach avoids the problems raised in this article.
6. At excessive debt levels, debt starts to bear risks ordinarily borne by equity. We ignore this possibility for now, but recognize it in the next section.
7. The modern literature begins with Modigliani and Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review, 
   48: 261-297 June 1958). Hundreds of papers have explored the theoretical and empirical aspects of the issue since that time.
8. One advantage of debt is that it reduces corporate taxes on operating income, an advantage offset to a degree by the higher personal taxes on interest versus capital gains (and currently, dividends).
9. See, for example, Brealey and Myers, Principles of Corporate Finance, New York: McGraw-Hill/Irwin, 7th ed. (2003), Chapter 19. The after-tax weighted-average cost of capital is applied to the all-equity cash flows generated by the firm or project.
10. The decline in firm or project value at high debt ratios is due to a combination of increases in the weighted-average cost of capital and other costs. In principle, both capital budgeting and rate regulation could model the pure cost-based part separately. But this is not done in ordinary practice. Treating the weighted-average cost of capital estimated at normal capital structures as flat when debt becomes excessive is an easy, practical approach to recognizing both effects. (We understand that the next edition of Brealey and Myers, op. cit., may recommend this practice, too.)
11. The rate at which the cost of equity increases is mitigated by increases in the after-tax cost of debt as higher debt ratios force debt to bear an increasing proportion of the firm’s risk.
12. These precise values depend on the precise cost of capital curves assumed in Figure 3, but the basic conclusion holds for any set of cost of capital curves consistent with the research on the effects of capital structure on the value of the firm.
13. Companies in financial distress will be beyond the middle range of capital structures. A ready practical procedure to avoid such companies is to exclude from the 
    sample any companies without investment-grade debt.
14. The after-tax cost of debt is the current yield to maturity times the quantity, one minus the corporate tax rate. The market value of equity is price per common share times the number of outstanding common shares. Unless the company’s embedded interest rates are far from current market values, analysts typically use the book value of debt in such calculations. Preferred stock should be treated like debt, except that its current yield is already after-corporate-tax.