Appendix I to Part 504 - Procedures for the Computation of the Real Cost of Capital

Appendix I to Part 504 - Procedures for the Computation of the Real Cost of Capital

(a) The firm's real after-tax weighted average marginal cost of capital (K) is computed with equation 1.

The terms in equation 1 are defined as follows:

W_d = Fraction of existing capital structure which is debt.

W_p = Fraction of existing capital structure which is preferred equity.

W_e = Fraction of existing capital structure which is common equity and retained earnings.

R̂_d = Predicted nominal cost of long term debt expressed as a fraction.

R̂_p = Predicted nominal cost of preferred stock expressed as a fraction.

R̂_e = Predicted nominal cost of common stock expressed as a fraction.

INF = Percentage change in the GNP implicit price deflator over the past 12 months expressed as a fraction.

f_d = Flotation cost of debt expressed as a fraction.

f_p = Flotation cost of preferred stock expressed as a fraction.

f_e = Flotation cost of common stock expressed as a fraction.

t = Marginal federal income tax rate for the current year.

(b) Information on parameters used in Equation

1.

(1) The parameters used in equation 1 will be the best practicable estimates. They will be obtained from the firm, accepted rating services (e.g., Standard & Poors, Moody's), government publications, accepted financial publications, annual financial reports and statements of firms, and investment bankers.

(2) The predicted nominal cost of debt (R̂_d) may be estimated by determining the current average yield on newly issued bonds - industrial or utility as appropriate - which have the same rating as the firm's most recent debt issue.

(3) The predicted nominal cost of preferred stock (R̂_p) may be estimated by determining the current average yield on newly issued preferred stock - industrial or utility as appropriate - which has the same rating as the firm's most recent preferred stock issue.

(4)

(A) The predicted nominal cost of common stock (R̂_e) is computed with equation 2.

Eq 2 R̂_e = R̂_f + B × R̄_m

where:

R̂_f = The risk free interest rate - the average of the most recent auction rates of U.S. Government 13-week Treasury Bills,

B = The “beta” coefficient - the relationship between the excess return on common stock and the excess return on the S&P 500 composite index, and

R̄_m = The mean excess return on the S&P 500 composite index - the mean of the difference between the return on the S&P 500 composite index and the risk free interest rate for the years 1926-1976 as computed by Ibbotson and Sinquefield(1) - 9.2%

(B) The “beta” coefficient is computed with regression analysis techniques. The regression equation is Equation 3.

(R_e^t − R_f^t) = A + B(R_m^t − R_f^t) + e^t

Eq. 3

where

R_ft = The risk free interest rate in month t - the average of the yields on 13-week treasury bills auctioned in month t.(2)

A = A constant which should not be significantly different than zero.

e^t = The error in month t.

PRCC_t = Closing market prices of the firm's common stock at the end of month t fully adjusted for splits and stock dividends.

DIVRATE_t = The sum of the dividends paid in the fiscal year which contain month t.

V_sp,t = The market value of “one share” of the S&P 500 composite index at the end of month t.

D_sp,t = The estimated monthly income received from holding “one share” of the S&P 500 in month t.

The regression analysis is done with sixty months of data. The first month (t = 1) is sixty months before the month in which the firm's current fiscal year started. The last month (t = 60) is the last month of the past fiscal year.

(5) Where the parameters specified above are not obtainable, alternate parameters that closely correspond to those above may be used. This may include substituting a bond yield for nominal cost of preferred stock where the former is not available. Where the capital structure does not consist of any debt, preferred equity, or common equity, an alternate methodology to predict the firm's real after-tax marginal cost of capital may be used.

Example of using alternate parameters that closely correspond to those above are:

(A) In the case of industrials, who do not typically issue preferred stock, the predicted nominal cost of preferred stock (R̂_P) can be estimated by determining the current average yield on newly issued industrial bonds which have the same rating as the firm's most recent debt issue.

(B) If necessary, the following assumptions can be made to determine the nominal cost of debt or preferred stock and their flotation costs.

(i) Where a company issued privately placed debt that was not rated, the rating, applied to preferred stock could be used to determine the cost of debt and its flotation cost.

(ii) Where a company issued privately placed preferred stock that was not rated, the rating applied to debt could be used to determine the cost of preferred stock and its flotation costs.

(iii) In the case where all issues were privately placed, the current average yield on all newly issued debt or preferred could be used to determine the cost of debt or preferred respectively, and an average flotation cost, for debt or preferred, could be used.

(C) Evidence Requirements. Copies of this calculation with notations as to the source of the data must be submitted.

Footnotes

(1) Ibbotson, R.E. and R.A. Sinquefield, Stocks, Bonds, Bills, and Inflation, Charlottesville, Va.: The Financial Analysts Research Foundation, 1977, cited by Ernst & Whinney, Costs of Capital and Rates of Return for Industrial Firms and Class A&B Electric Utility Firms, June 1979, p. 3-8.

(2) As an option, R_f t can be developed with the following equation:

where:

D^t = The average annual yield on three month U.S. Treasury bills reported in the Survey of Current Business auctioned in month t - which is reported using the bank discount method.

N = Number of days to maturity.

[46 FR 59920, Dec. 7, 1981]