Cost of Capital

Cost of Capital

Cost of Capital: Cost of Equity, Levering Relations, Bond Yield, Weights and Sources

What the page computes

The weighted average cost of capital is the return a company must earn on its assets to pay the suppliers of its capital what they require: WACC = w_E r_E + w_D r_D (1 − t) + w_P r_P, with the weights of common equity, debt and preferred stock summing to one, r_E the cost of equity, r_D the pre-tax cost of debt, t the tax rate at which interest is deducted and r_P the preferred dividend over its price. The page also prints the composite with the debt at its pre-tax cost. That second figure is the one regulators prescribe as an allowed rate of return, because the income tax is recovered as a separate cost of service; the Surface Transportation Board's yearly railroad cost of capital and the Federal Communications Commission staff's 2013 analysis are both of that form. Every rate is a percent per year and every result carries full precision; the numbers substituted in the printed equations are rounded for display, so a hand product of the displayed figures can differ in the last digit.

Cost of equity

Capital asset pricing model. r_E = r_f + β (market risk premium), with r_f the yield of a long Treasury security and β the slope of the stock's return on the market's. The build-up method adds a size premium, a company-specific premium and a country risk premium; the country premium is added to the cost of equity after multiplication by an exposure factor (1 adds it in full). Each premium is an entered number: the published size-premium tables are proprietary and are not reproduced. The Delaware Court of Chancery's appraisal of The Orchard Enterprises (2012) is a public example of this build-up: a risk-free rate of 3.9 percent, a beta of 1.0, a supply-side equity risk premium of 5.2 percent and a size premium of 6.3 percent; the court rejected a further 1 percent company-specific premium. Those four figures sum to 15.4 percent; the opinion gives 15.3 percent, the figure of the petitioners' expert, and does not explain the difference of 0.1.

Average of the CAPM and a multi-stage discounted cash flow model. The Surface Transportation Board sets the railroad cost of equity as the simple average of the two. The multi-stage model finds the rate r at which the present value of a cash flow forecast equals the market value of the equity: the cash flow grows at a stage-one rate for n₁ years and at a stage-two rate for n₂ years, each amount discounted from the end of its year, and the terminal value at year n₁ + n₂ is the terminal cash flow base, grown through both stages and one more year at the long-run rate g₃, divided by (r − g₃). The Board uses a separate terminal base (income before extraordinary items, on the assumption that depreciation equals capital expenditure in the long run); leave the cell blank to use the cash flow itself. Several companies are averaged with their market values as weights. The default rows are Table 11 of the Board's decision for 2025, which the page reproduces: 11.14, 10.01 and 11.16 percent, 10.88 percent for the industry. With the CAPM figure of 10.65 percent the cost of equity is 10.77 percent, and with the Board's cost of debt and market values the composite before tax is 9.78 percent. The decision prints 9.79 percent because it multiplies components already rounded to two decimals.

Fama-French three factors. r_E = r_f + b (market premium) + s (SMB) + h (HML), with entered loadings and factor premia. The size premium of the build-up is left out of this form because the size factor takes its place.

Dividend growth. A dividend D₁ next year growing at g for ever is worth P = D₁ / (r − g), so r_E = D₁ / P + g.

Beta

Regression. The beta is the least-squares slope of the stock's return on the market's return, R = α + β R_M + ε, over the pasted periods; a third column holding the risk-free return of each period turns both series into excess returns, the form the Board prescribes. The page reports the slope, its standard error s / √S_xx (s² the residual sum of squares over n − 2), the t statistic, the two-sided p-value from the Student t distribution, R² and the 95 percent interval. Price or index levels are converted to simple returns first.

Adjustment toward one. Betas tend to move toward the market value of one over time; data services therefore report two thirds of the regression beta plus one third. The FCC staff report describes the adjustment and tabulates raw and adjusted betas for sixteen carriers.

Levering relations. Debt raises the equity beta. With D/E the debt-to-equity ratio at market value, β_U the unlevered (asset) beta and β_D the debt beta:

Hamada: β_L = β_U [1 + (1 − t) D/E]. A fixed amount of riskless debt; the tax shield is as safe as the debt.
Harris-Pringle: β_L = β_U + (β_U − β_D) D/E. Debt held at a constant share of value continuously; the tax shield is as risky as the assets.
Miles-Ezzell: β_L = β_U + (β_U − β_D) (D/E) [1 − t r_D / (1 + r_D)]. Debt rebalanced to a constant share once a year.

Each relation implies a weighted average: with CAPM costs, Hamada gives WACC = r_U (1 − t D/V) for riskless debt, Harris-Pringle gives WACC = r_U − t r_D D/V and Miles-Ezzell gives WACC = r_U − t r_D (D/V) (1 + r_U) / (1 + r_D), where r_U is the unlevered cost of capital. The test script proves the three relations against these identities. When the method has no beta (dividend growth, multi-stage, entered) the same relations are applied to the returns: r_E = r_U + (r_U − r_D) k, with k the bracketed leverage term of each relation.

Pure-play beta. For a division or project whose risk differs from the company's, the betas of comparable listed companies are unlevered at their own debt-to-equity ratios and tax rates, averaged, and the mean is relevered at the structure entered on the page. The result is the hurdle rate of the division. With a target structure and the box checked, an entered or regressed company beta is treated the same way: unlevered at the company's present market-value structure and relevered at the target.

Cost of debt

The cost of debt is the yield at which the company could borrow today, not the coupon of old debt. Three entries: the market yield itself; the risk-free rate plus the spread of the company's rating class (the synthetic-rating approach, with the spread entered because the published spread tables are proprietary); or the yield to maturity of an outstanding bond. Flotation costs, in points of yield, can be added as the Board does.

Yield to maturity. With c the coupon per period per 100 of face, i = y/m the yield per period, v = 1/(1 + i), n the number of whole periods after the next coupon and w the fraction of a period from settlement to the next coupon, the price plus accrued interest is [c + c a_n + 100 vⁿ] discounted over the part period, where a_n = (1 − vⁿ)/i. The Treasury discounts the part period at simple interest, dividing by (1 + w i) (31 CFR Part 356, Appendix B, section II); the market practice for corporate bonds is compound interest, multiplying by v^w. The accrued interest is (1 − w) c. The yield is found by bisection on the price, which falls steadily as the yield rises. The default is the Treasury's own example: an 8¾ percent 30-year bond at a yield of 8.84 percent is priced at 99.057893. The quoted yield is compounded m times a year; the effective annual yield is printed beside it.

Weights

The weights are market values: share price times shares for the equity, the market value of the debt (book value is a common stand-in when the debt trades near par) and of the preferred stock. A target structure can be entered instead when the present structure is not the one the company intends to keep.

Real and nominal rates

A nominal rate discounts cash flows that include inflation, a real rate discounts constant-dollar flows, and the two must not be mixed. The exact conversion is real = (1 + nominal)/(1 + inflation) − 1, the form OMB Circular A-94 gives as the precise estimate; nominal less inflation is the approximation.

Sensitivity table and capital structure schedule

The sensitivity table varies the beta (or, without a beta, the cost of equity) at the base structure and the debt share. In each cell the beta is unlevered at the base structure and relevered at the column's debt share with the chosen relation; the pre-tax cost of debt is held at its base value, so the table isolates the leverage relation and the tax factor. The schedule removes that simplification: each row carries its own cost of debt, entered, which rises with leverage as the default illustrates, and the WACC then passes through a minimum. The schedule is an illustration of the trade-off under the entered costs; it does not model distress costs and is not a prediction of an optimal structure.

Adjusted present value

The unlevered cost of capital r_U printed on the page is the discount rate of the adjusted present value method, in which the operating cash flows are discounted at r_U and the interest tax shields are valued separately. It is the better route when the debt follows a repayment plan rather than a constant share of value.

Federal discount rates

A federal agency does not discount at a private cost of capital. OMB Circular A-94 sets a real rate of 7 percent for the base-case benefit-cost analysis of public investments and regulations and, in its Appendix C, revised each year, the nominal and real Treasury rates for cost-effectiveness and lease-purchase analysis (for calendar year 2026: nominal 3.4 to 4.1 percent and real 1.1 to 2.0 percent from 3 to 30 years). The Appendix C rates are entered on the page, with the 30-year values of 2026 as defaults.

What is not covered

No market data are supplied: the risk-free rate, the market premium, the size, country and factor premia, the rating spread and the betas of comparables are entered. Costs of distress, personal taxes, convertible securities, leases, and the iteration between value and weights in a valuation are outside the page.