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Last modified: January 26, 2018

Capital Structure
-----------------

Cost of Equity
--------------

Equity investors incur an opportunity cost in owning the 
equity of the company and they therefore demand a rate 
of return comparable to what they could earn by investing 
in securities of comparable risk.

The cost of equity is the rate of return required to persuade an 
investor to make a given equity investment.  The COE can be
determined using the Capital Asset Pricing Model (CAPM).

Security Market Line:

rE = rRF + β(rM - rRF) 
                 
Where 

rRF = Risk free interest rate (for example the YTM for a 10 yr
      Treasury bond).
β = The stock's volatility.
rM = The market's expected rate of return.

The β quoted is normally the levered β. βL.  Levered means debt 
+ equity financing.  Unlevered means equity only. To get the 
unlevered β we can use the HAMADA Equation: 

βU = βL/{1 + (1 - T)(D/E)}

The COE can also be calculated from the Discounted Cash Flow
(Dividend Discount Formula) method as: 

P(0) = Curent stock price
D(1) = Next year's dividend
G = Projected growth

rE = (D(1)/P(0)) + G

The DCF and SML should produce similar results.  Generally, 
the average of the two is used. 

Modigliani and Miller 
---------------------

Proposition 1:

The market value of a firm is determined by its earning power and 
the risk of its underlying assets, and is independent of the way it 
chooses to finance its investments or distribute dividends.  The basic 
idea is that, under certain assumptions, it makes no difference 
whether a firm finances itself with debt or equity.  Thus,

VL = VU + TD

where,

D = Value of debt.
T = Tax rate.

Proposition 2:

Relationship between Leveraged and Unleveraged Cost of Equity:

rL = rU + (D/E)(rU - rD)(1 - T)

where,

rL = Leveraged cost of Equity
rU = Unleveraged cost of Equity
rD = cost of debt (see next section).
D/E = Debt to Equity ratio.

Therefore, a higher debt-to-equity ratio leads to a higher required 
return on equity, because of the higher risk involved for equity
holders in a company with debt.

Both of these propositions hold if the no transaction costs exist, 
individuals and corporations borrow at the same rates and 
corporations are taxed at the rate on earnings after interest  In
reality these situations do not exist.  The implication is that the
capital structure does matter and tells us where to look in order
to optimize the capital structure of a company.

Debt Cost of Capital
--------------------

The cost of debt capital is the return demanded by investors in 
the company's debt.

It is not uncommon for firms to use yield on their debt as an 
approximation for their debt cost of capital rD.  For example, the 
expected yield on a 10 year non-callable bond issue might be 
used to determine cost of debt.

Debt provides valuable tax shields.  The after-tax cost of debt 
is:

rDT = rD(1 - T)

Alternatively, we can calculate rD from the CAPM as

rD = rRF + βD(rM - rRF) 

To get βD we can refer to published tables that show β's by 
rating and maturity. 

Weight Average Cost of Capital
------------------------------

The WACC or simply the company's cost of capital is the rate 
that a company is expected to pay on average to all its security 
holders to finance its assets.  It is dictated by the external 
market and not by management. The WACC represents the 
minimum return that a company must earn on an existing 
asset base to satisfy its creditors, owners, and other providers 
of capital, or they will invest elsewhere.

Companies raise money from a number of sources.  Different
sources of finance, are expected to generate different returns. 
The WACC is calculated taking into account the relative weights 
of each component of the capital structure. 

WACC(%) = {E/(E + D)}rE + {D/(E + D)}rD(1 - T)

where

E = Market Cap (market value of equity).
D = Market value of outstanding debt.  This can be found by 
    multiplying the amount outstanding for each bond issue by 
    the corresponding price.
rD from Debt Cost of Capital calculation.
rE from Cost of Equity calculation or Modigliani-Miller Equation.
T = Corporate tax rate.

Corporate Cost of Capital
-------------------------

CCC =[WDrD(1 - T) + [WErE]

Where:

WD = % of Debt
WE = % of Equity 
rD = Cost of debt (%)
rE = Cost of equity (%)
T = Marginal tax rate (%)

Enterprise Value and Net Debt
-----------------------------

EV = E + D - Excess cash

Net Debt = Debt - Excess cash and short term investments

 

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