Federal Reserve's imputed cost of equity capital: A survey, The

Chicago Fed Letter, Jul 2001 by Green, Edward J, Lopez, Jose A, Wang, Zhenyu

The U.S. Federal Reserve System provides services to depository financial institutions through the twelve Federal Reserve Banks. U.S. federal legislation, contained in the Monetary Control Act of 1980, requires the Federal Reserve Banks to price their services at a level that fully recovers their costs. The act specifically requires imputation of various costs that the Federal Reserve Banks do not actually pay, but that they would pay if they were commercial enterprises. Prominent among these imputed costs is a cost of capital, that is, a proxy for the cost of the debt and equity liabilities that a commercial enterprise would have to issue in order to finance its assets. The Federal Reserve has complied with the act by adopting an imputation formula for the overall cost of capital that combines separate imputations of costs of debt and equity. This Chicago Fed Letter provides a survey of the economic and statistical issues in imputing a cost of equity capital to the Reserve Banks and suggests a revised approach for doing so.1

Shortly after the Monetary Control Act was passed, the Federal Reserve formulated a Private Sector Adjustment Factor (PSAF) to quantify the costs that must be imputed to comply with the act. Currently, the Federal Reserve is considering possible revision of the PSAF. The goal is to adopt an imputation formula that will:

1. Provide a conceptually sound basis for economically efficient pricing;

2. Be consistent with actual Reserve Bank financial information;

3. Be consistent with economy-wide practice, and particularly with privatesector practice, in accounting and applied financial economics; and

4. Be intelligible and justifiable to the public, and replicable from information that can be obtained by the public.

The cost of equity capital used in the current implementation of the PSAF is estimated from a comparable accounting earnings (CAE) method. For each holding company (HQ in the specified peer group (currently, the largest 50 HCs by asset size), the estimate is calculated as the return on equity (ROE), defined as ROE = (Net income) / (Book value of equity). The individual ROE estimates are averaged to determine the average HC peer group ROE for a given year. For example, if the values of ROE for firms in the peer group were currently distributed uniformly between 15% and 25%, then the average ROE adopted for purposes of the PSAF would be 20%. A further complication is that, in order to smooth year-to-year fluctuations, the CAE estimate actually used in the PSAF for a given year is the average over the previous five years of these firm-average ROE measures.

The CAE method has been criticized for being "backward looking" since past earnings may not be a good forecast of expected earnings due to cyclical changes in the economic environment. As a firm makes its way through the business cycle, its earnings may rise above or fall below the trend line that might more accurately reflect sustainable economic earnings. A high ROE in the past does not necessarily imply that a firm's future ROE will remain high. A declining ROE might be evidence that the firm's new investments have offered a lower ROE than its past investments. The best forecast of future ROE in this case may be lower than the most recent ROE.

Therefore, one focus of efforts to meet the criteria for a revised PSAF is to take account of the scientific -view that financial asset prices reflect market participants' assessments of future stochastic revenue streams has received strengthened statistical corroboration and general public acceptance. Quantitative models that reflect this view, rather than the backward-looking assessment implicit in the CAE method, have come into widespread use in investment banking and also for regulatory rate-setting in utility industries. We suggest an imputation formula that would average the estimated costs of equity capital from two such models, discounted cash flow (DCF) model and a capital asset pricing model (CAPM), together with the estimates from the CAE method. We show that the proposed approach would have provided stable and sensible estimates of the cost of equity capital for the PSAF over the past 18 years.

The theoretical foundation of corporate valuation is the DCF model, in which the stock price equals the discounted value of all expected future dividends. It is difficult to project expected dividends for all future periods. To simplify the problem, financial economists often assume that dividends grow at a constant rate, which they estimate from accounting statements. They assume that reinvestment of retained earnings generates the same return as the current ROE. The assumption of a constant dividend growth may lead financial analysts to unreasonable estimates of the cost of capital. However, the DCF model with multi-stage growth gives an economically meaningful and statistically robust estimate. We therefore recommend the implementation of the DCF model with multi-stage dividend growth rates for the cost of equity capital used in the PSAF.