Utilities and regulators are stuck in a rut, treating rate-base assets in a traditional way and depreciating their value according to a straight-line calculation. But alternative accounting...

## Measuring Return on Equity Correctly

Why current estimation models set allowed ROE too low.

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:

- 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} - Take the average of these values as the industry's after-tax weighted-average cost of capital; and
- 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