Capital Structure Theories^277PVINTS =
=Thus the formula for PVINTS in the case of a positive personal tax rate for lenders
and no personal tax rate for shareholders can be written as follows:PVINTS =
Corporate tax rate Lender s Personal tax rate Interest
Cost of debt Lender s Personal tax rate
¥
' )
( 1 ' )
- =
= ...(17)
The total earnings of a firm will be distributed either as interest income or equity
income. The personal tax rate on interest income is Tpb and on equity income Tpe. Tpe
is unlikely to be equal to Tpb. mostly it will be less than Tpb, and in extreme cases it
will be equal to zero. Comparing the income tax shields in Tables we can see that
corporate borrowings is advantageous if
(1 - Tpb) > (1 - Tpe)(l - T)
Thus a firm should stop borrowing when (1 - Tpb) becomes equal to (1 - Tpe) (1 - T).
In practice, the finance manager will find it difficult to arrive at the numerical values
of Tpb and Tpe since the firm will have a large number of shareholders and debt holders
in different tax brackets.
How does leverage affect the firm value when the personal tax rates of shareholders
and debt-holders differ? We have already shown that the value of the firm will be
reduced when the personal tax rate of lenders is higher than that of shareholders.
Miller has provided a formal answer to this question. As we know, the interest tax
shield (INTS) which is the gain from leverage is the difference between the value of
the levered and unlevered firm, and is also given by the product of the corporate tax
rate and the amount of debt under the assumption of perpetual debt and no personal
taxes:
INTS = kdDT
PVINTS = kdDTlkd
PVINTS = Vt ñ Vu = TD ...(18)
Miller introduced personal taxes in the model and modified it.í In the unlevered firm
where equity income is taxed at Tpe personal tax rate, the shareholderís earnings will
be:
X (1-T) (1-Tpe) ...(19)
and when we discount these earnings at the pure-equity capitalisation rate, k~, the
value of the unlevered firm will be:
- =