Weighted Average Cost of Capital



Weighted Average Cost of Capital (WACC)

Updated April 2012

Overview: The weighted cost of capital (WACC) is a measure of the percentage cost to the firm for the capital that the firm raises through long term debt, preferred stock, common stock and retained earnings. WACC regards the existing capital structure, i.e. the capital that has already been raised, as it appears on the firm’s balance sheet. This “historical”, backward, perspective of WACC is opposed to the “marginal cost of capital” (MCC) that regards the percentage cost of future capital to be raised.

The WACC is a significant piece of information for the firm in the planning for future expenditures as it establishes an oft called “hurdle rate” over which the firm must perform in order to remain profitable. That is, if a firm’s WACC is 20%, then it must earn at least that rate (on average) on its future projects. Thus the WACC is the principle part of the discount rate used in the firm’s capital budgeting proposals (with a risk premium usually added on top of WACC).

The calculation of WACC assumes that there is a unique cost related to each of the four components (debt, preferred, common and retained earnings). Each of the four costs is weighted by the proportion of total dollars of the four components as they appear on the balance sheet. And the cost of each component is assumed to be closely related to the expected returns to the investor for the particular component in question.

Component costs are not exactly equal to investor returns (for debt, preferred and common) due to the transaction costs inherent in the firm’s issuing debt (or preferred or common) through a financial intermediary, typically an investment bank. And because the investment bank charges [dearly] for their services, the cost of capital to the firm tends to be higher than the expected return to the investor. Transaction costs can be complex to calculate, with fixed and variable components, consideration for overall magnitude of the transaction as well as costs based on the quality of the relationship between the parties involved.

For academic purposes, we express transaction costs either as a fixed percentage of the total transaction or a fixed dollar amount per unit instrument. In either case, the net amount received by the firm from the sale of a bond (or share of stock) is equal to the “street price” (the closing retail price paid by the investor) minus the transaction cost. A synonymous expression of this model is “Close minus Transaction Cost equals Net to the Firm”.

Methodology of calculation:

Debt: As Rodriguez’s Model is used to calculate the expected return to the investor, it may also be used, with some modification, to calculate the pre-tax cost of debt to the firm. The input variables are 1) annual coupon payments on the bonds, 2) face value of the bond (assumed to be $1000), 3) net value of the bond received by the firm, and 4) number of years to maturity. The output, Kdb, represents the pre-tax cost of debt to the firm.

Further, in the case debt (and debt alone of the four components), because of the pre-tax nature of interest expenses, the firm enjoys a tax benefit that helps to mitigate the costs of debt. Hence, the effective after-tax cost of debt is considerably less than the pre-tax expected return to the investor. To calculate the After Tax Cost of Debt, the pre-tax cost of debt is multiplied by “one minus the tax rate”, where the firm’s estimated tax rate is assumed from the income statement as the proportion of Income Before Tax that is paid as taxes.

Preferred Stock: Gordon’s Model for the expected return on preferred stock is used to calculate the cost of preferred to the firm for reasons consistent with the logic previously described for debt. The input variables are 1) annual dividends and 2) net price received by the firm. The output is the cost of preferred to the firm. Note that because dividends are paid after taxes, the calculated cost of preferred is also on an after-tax basis and does not have to be converted as was done with debt (above).

Common Stock: Gordon’s Model for the expected return on common stock is used to calculate the cost of common to the firm. The input variables are 1) last year’s dividends, 2) net price received by the firm, and 3) expected growth rate of dividends. In this version of Gordon’s Model, next year’s dividends are estimated as last year’s dividends “bumped up” by the growth rate. The output is the after tax cost of common to the firm.

Retained Earnings: The cost of retained earnings to the firm is theoretically the same as the expected return to the common stock investor on the grounds that the investors “own” the retained earnings. Therefore the cost to the firm of using those earnings is the opportunity cost to the investor. Hence, we use the same model as with common, with the same inputs with the following exception: Rather than using the net price received by the firm, we use the retail closing street price paid by the investor. The output is the cost of retained earnings to the firm.

Weighted Average: Once the four after-tax component costs have been determined, the individual costs are “weighted”, i.e. multiplied by the proportion of the total value, on the balance sheet. These “weighted costs” are aggregated to derive a final weighted average cost of capital (WACC).

Here are the steps related to calculating the WACC.

1. Calculate the component costs of Debt, Preferred, Common, and Retained Earnings, given:

a. bonds: XYZ 12s2020 close @ 120

b. preferred: pays $1.25 div/qtr, closed @ $41.00/share

c. common: div (ttm) =$6.00, expected growth in div=5% closed @ $48.00

d. effective corporate tax rate: from the Income Statement (taxes / Inc B/T)

e. transaction costs : $4 / Bond; $1 /share for Preferred; 2% Common

Steps:

1. a) Calculate Before tax cost of Debt, using Rodreguez's Model, where

PMTS = 12% of Face Value = $120

Face Value = $1000

Street Price = 120% of Face Value, or 1.20 x $1000 = $1200

Vb = Net to the Firm= Street price - transaction costs, or $1200 - 4 = 1196

n=no of yrs to maturity = 2020-2012 = 8 Income Statement

Thus, Kdb (B/T) = .0845 Inc B/Tax $91,000

and "Before Tax Cost" (1- tax rate)= "After Tax Cost", Taxes 27,300

where "Tax Rate"= taxes / income before tax tax rate = .30

So, Kdb (A/T), cost of debt after taxes = .0591

1. b) Calculate cost of Preferred, using Gordon's Model, where

D = (1.25 x 4 qtrs) = $ 5.00 / yr

and Street Price = 41.00, trans = 1.00, Net to firm = 40.00,

so D/P, cost of preferred = .1250

1. c) Calculate cost of Common, using Gordon's Model, where

D1 = D0 (1 + g), or, D1 = (6.00) (1 + .05) = $ 6.30

and Street Price = 48.00, trans =2% so "Net to firm" = 48 x .98 = 47.04

So, Ke, cost of common = .1839

1 d) Calculate the cost of Retained Earnings, using Gordon's Model,

D1 = D0 (1 + g), or, D1 = (6.00) (1 + .05) = $ 6.30

and Street Price = 48.00

So, Ke, cost of common = .1813

2. Calculate the Weighted Average Cost of Capital (WACC) using the following

values from the balance sheet and the shortcut kiwi method:

a) $ cost (K) extension

debt 513,000 x .0591 = 30318

pref 234,000 x .1250 = 29250

comm. 122,000 x .1839 = 22436

ret earng 600,000 x .1813 = 108780

total $1,469,000 190784

b) 190784/1469000 = .1299

WACC = 12.99%

[Note to editor: This example may be updated to account for “years to maturity” by changing the “year OF maturity”, first in the bond listing, and then in the “year to maturity” calculation.]

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