Page 102 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 3: Introduction to Security Analysis

r = Market return Notes
m
= Equity beta
e
However, this model ignores the effect of corporate income taxes.

Considering corporate income taxes:
r = r (1 – t ) + [r – r (1 – t )]
e f c e m f c
where t = corporate tax rate.
c
Once the expected return on equity and on debt are known, the weighted average cost of capital
can be calculated using Modigliani and Miller’s second proposition:

WACC = r E/(E + D) + r D/(E + D)
e d
Taking into account the tax shield:
WACC = r E/(E + D) + r (1 – t )D/(E + D)
e d c
For T = 0 (no tax advantage for debt), the WACC is equivalent to the return on assets, r . r is
a d
calculated using the CAPM:
r + r + [r – r (1 – t )]
d f d m f c
For a levered firm in an environment in which there are both corporate and personal income
taxes and in which there is no tax advantage to debt (T = 0), WACC is equal to r , and the above
a
WACC equation can be rearranged to solve for r :
e
r = r + (D/E)[r – r (1 – t )]
e a a d c
From this equation it is evident that if a firm with a constant future free cash flow increases its
debt-equity ratio, for example by issuing debt and repurchasing some of its shares, its cost of
equity will increase.
r also can be calculated directly by first obtaining a value for the asset beta, a , and then
a
applying the CAPM. The asset beta is:

= (E/V) + d (D/V)(1 – t )
a e c
Then return on assets is calculated as:
r = r (1 – t ) + [r – r (1 – t )]
a f c a m f c
In summary, for the case in which there is personal taxation and in which Miller’s Equilibrium
holds (T = 0), the following equations describe the expected returns on equity, debt, and assets:
r = r (1 – t ) + [r – r (1 – t )]
e f c e m f c
r = r (1 – t ) + [r – r (1 – t )]
a f c e m f c
r = r + [r – r (1 – t )]
d f d m f c
The cost of capital also can be calculated using historical averages. The arithmetic mean generally
is used for this calculation, though some argue that the geometric mean should be used.
Finally, the cost of equity can be determined from financial ratios. For example, the cost of
unleveraged equity is:

r U = [r , L + r , debt(1 – t )D/E]/(1 + D/E)
e e f c
r ,L = b(1 + g)/(P/E) + g
e

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