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Units, Constants and Useful Formulas
Capital Structure
-----------------
Cost of Equity
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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:
r_{E} = r_{RF} + β(r_{M} - r_{RF})
Where
r_{RF} = Risk free interest rate (for example the YTM for a 10 yr
Treasury bond).
β = The stock's volatility.
r_{M} = The market's expected rate of return.
The β quoted is normally the levered β. β_{L}. Levered means debt
+ equity financing. Unlevered means equity only. To get the
unlevered β we can use the HAMADA Equation:
β_{U} = β_{L}/{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
r_{E} = (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,
V_{L} = V_{U} + TD
where,
D = Value of debt.
T = Tax rate.
Proposition 2:
Relationship between Leveraged and Unleveraged Cost of Equity:
r_{L} = r_{U} + (D/E)(r_{U} - r_{D})(1 - T)
where,
r_{L} = Leveraged cost of Equity
r_{U} = Unleveraged cost of Equity
r_{D} = 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 r_{D}. 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:
r_{DT} = r_{D}(1 - T)
Alternatively, we can calculate r_{D} from the CAPM as
r_{D} = r_{RF} + β_{D}(r_{M} - r_{RF})
To get β_{D} 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)}r_{E} + {D/(E + D)}r_{D}(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.
r_{D} from Debt Cost of Capital calculation.
r_{E} from Cost of Equity calculation or Modigliani-Miller Equation.
T = Corporate tax rate.
Corporate Cost of Capital
-------------------------
CCC =[W_{D}r_{D}(1 - T) + [W_{E}r_{E}]
Where:
W_{D} = % of Debt
W_{E} = % of Equity
r_{D} = Cost of debt (%)
r_{E} = 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