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Cost Of Capital Basics

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Market Value Of Invested Capital


Present value


Future value


Market value of invested capital


k             = Discount rate (generalized)


k.            = Discount rate for common equity capital (cost of common equity capital)


Unless otherwise stated, it generally is assumed that this discount rate is applicable to net cash flow available to common equity.


ke(pt-          ~ Cost of equity prior to tax effect


kp             = Discount rate for preferred equity capital


kg            = Discount rate for debt (net of tax effect, if any)


(Note: For complex capital structures, there could be more than one class of capital in any of the preceding categories, requiring expanded su bscripts,)


kd!vV          = Cost of debt prior to tax effect


km            ~ Discount rate for equity capital when net income rather than net cash flow i;


the measure of economic income being discounted


c             = Capitalization rate


c.            = Capitalization rate for common equity capital. Unless otherwise stated, if


generally is assumed that this capitalization rate is applicable to net cash flow available to common equity.


c„,            = Capitalization rate for net income


cv             = Capitalization rate for preferred equity capital


cd             = Capitalization rate for debt


(Note: For complex capital structures, there could be more than one class of capital in any of the preceding categories, requiring expanded su bscripts,)


t             = Tax rate (expressed as a percentage of pretax income)


R             ~ Rate of return


Rf            = Rate of return on a risk-free security


E(R)         = Hxpected rate of return


: Expected rate of return on the "market" (usually used in the context of a market for equity securities, such as the New York Stock Exchange [NYSE] or Standard & Poor's [S&PJ 500) : Expected rate of return on security i


■■ Beta (a coefficient, usually used to modify a rate of return variable) : Levered beta : Unleveredhefa : Risk premium : Risk premium for the "market" (usually used in the contest of a market for equity securities, such as the NYSE or S&P 500) : Risk premium for "small" stocks (usually average size of lowest quintiie or decile of NYSE as measured by market value of common equity) over and above RPm


■■ Risk premium for unsystematic risk attributable to the specific company : Risk premium for the rth security : Risk premium associated with risk factor 1 through n for the average asset in the market (used in conjunction with arbitrage pricing theory) : Weighted averaged cost of capital = Expected economic income (in a generalized sense; i.e., could be dividends, any of several possible definitions of cash flows, net income, etc.)
r          = Net income (after entity-level taxes)


CFe       - Net cash flow to equity


CFf       - Net cash flow to the firm (to overall invested capital, or entire capital structure, including all equity and long-term debt) = Payment (interest and principal payment on debt security) = Dividends -Tax (in dollars)


-   Gross cash flow (usually net income plus noncash charges)


-   Earnings before taxes


-   Earnings before interest and taxes = Earnings before depreciation, interest, and taxes ("Depreciation" in this context usually includes amortization- Some writers use EBITDA to specifically indicate that amortization is included.)


- Earnings before interest, taxes, depreciation, and amortization


: The i\h period or the i\h variable in a series (may be extended to thej'th variable, the kth variable, etc.)


: The number of periods or variables in a series, or the last number in a series : Infinity : Period^, the base period, usually the latest year immediately preceding the val uation date


W  = Weight


We = Weight of common equity in capital structure Wp ~ Weight of preferred equity in capital structure Wd ~ Weight of debt in capital structure (Note: For purposes of computing a weighted average cost of capital [WACC], if assumed that preceding weightings are at market value.)


g = Rate of growth in a variable (e.g., net cash How)


Sum of (add all the variables that follow)


Product of (multiply together all the variables mat follow)


Mean average (the sum of the values of the variables divided by the number oi


Geometric mean (the product of the values of the variables taken to the roof of th number of variables)


py.NCF,   t   NCF2


+•••+


NCFn


where:


Present value


Net cash flow (or otlier measure of economic income) expected in
each of the periods 1 through n, n being the final cash flow in the
life of the investment.

Cost of capital applicable to (he defined stream of net cash flow


PV =


NCF,


/here:


= Present \>i


'\ = Net cash flow expected in (he first period immediately following the valuation date


tion rate c = k- /here:


c = Capitalization rate


k = Discount rate (cost of capital) for the subject investment g = HKpecied long-term sustainable growth rate in the cash flow available to the subject investment


py_NCF0(l + g) k-g


ye:


NCF0 = Net cash flow in period 0, the period immediately preceding the valuation


date k        = Discount rate (cost of capital) g        = Expected long-term sustainable growth rate in net cash flow to investor


py=      NCF^        |      NCF2       ,             ,    NCF»


(l + k)"5    (l + k)15           (l + kf-05


where:


ftesent value


Net cash flow7 (or other measure of economic income) expected in each of the
periods 1 through n, n being the final cash flow in the


life of the investment

Cost of capital applicable to the defined stream of net cash flow


pv=NCFla+kr_


w


PV     - Present value


ATCFj - Net cash flow expected in the first period immediately following th


valuation date k        = Discount rate (cost of capital)


g        = Bspected long-term sustainable growth in net cash flow


NCFn(l + g)(l + k)0-5


PV=   NCFi   |   NCF2   |     |    NCF*     k-g


(l + k)u5    (1 + kf5            (l + kf-05            (l + k)*


w


Net cash flow7 expected in each of the periods 1 through n, n being


the last period of the discrete cash flow projections


Discount rate (cost of capital)


Expected long-term sustainable growth rate in net cash flow, starting


with the last period of the discrete projections as the base year


(X x we) + (t,x wv) + (kdi7Hn -1] x wd)


where:


WACC  ~ Weighted average cost of capital


ke        = Cost of common equity capital


W..      = Percentage of common equity in the capital structure, at market value


kp        = Cost of preferred equity


WTr       = Percentage of preferred equity in the capital structure, at market value


kdlvt)      ■=■ Cost of debt (pretax)


/         = Tax rale


W,,      = Percentage of debt in the capital structure, at market


where:


= Expected (market required) rate of return on security i RF      = Rate of return available on a risk-free security as of the valuation date RPm  ~ General equity risk premium for the '"market" RPs   ~ Risk premium for small size RPU   = Risk premium attributable to the specific company or to the industry (the u stands for unsystematic risk, as defined in Chapter 5)


An additional component may be a factor for industry risk.


5>


X =


w


x = Mean average


R, = Return for the ith period (the returns measured for each period are actually


excess returns, that is, the difference between the equity market return and the Treasury obligation income return for the


n = Number of observation periods


G =


-i


Sometimes also written as:


G = Jf[(X + Rt)-l


where:


G = Geometric average


RL = Return for the ilh period (the returns measured for each period are actually excess returns, that is, the difference between the equity market return and the Treasury obligation income return for the period) n = Number of observation periods


£(/?,)


e:


return (cost of capital) for an individual security : Rate of return available on a risk-free security (as of the valuation date) : Beta


: Equity risk premium for the market as a whole (or, by definition, the equity risk premium for a security with a beta of 1.0)


E(Rl)=Rf + B(RPm) +


w


j = Expected rate of return on


= Rate of return available on a risk-free security as of the valuation date ,   = General equity risk premium for the market = Risk premium for small size


= Risk premium attributable to (he specific company (u stands for unsystematic risk)


This is the formula to go from a levered capital structure to the for an unlevered capital structure (100% equity).


that would be a


B =


B,


l + (l-t)Wd/We


w


Beta


■ Beta levered


■ '.Fax rate for the company


■ Percent debt in the capital structure


■ Percent equity in the capital structure


BL = Btt0. + (l-t)WttfWe)


where the definitions of trie variables are (he same as in the formula for computing unlev­ered betas


k=NCF0(l + g) | PV


where:


Present value


Net cash flow in period 0, the period immediately preceding the valuation


Discount rate (cost of capital)


Expected long-term sustainable growth rate in net cash flow to investor



NCF10(l + g3)
pv = Y[NCFoa + g1T]   ^[NCF5(X + g2r5]                    k-g3


(i+ky


(X + kf


d + kT


Net cash flow (or dividend) in the immediately preceding year Expected net cash flow (or dividend) in the fifth year Expected net cash flow (or dividend) in the tenth year Expected growth rates in NCF (or dividends) through each of stag 1, 2, and 3, respectively Cost of capital (discount rate)