Question

Consider a world of corporate taxes along with personal taxes on income from shares and on income from bonds.

(i) Prove that the gain from leverage is less than the gain without personal taxes.

(ii) With appropriate tax rates, is it possible that the gain could be negative? If so, provide a numerical example.

Answer 1

Answers-

i)

When we consider the world of corporate taxes and personal taxes on income from shares and bonds the gain from leverage will be lesser than the gain without personal taxes.
This is due to the fact that as the increase in leverage will increase the debt and it will also increase the cost of equity as the investors required rrate of return increases as the risk increases with the increase in debt. This is because of increase in risk pemium to compensate for riskier projects.
The gains without personal taxes is an advantage for shareholders and bond holders of any firm as the investors are not levied taxes on these income and therefore gains more without taxes.
Therefore the  gain from leverage is less than the gain without personal taxes.

ii)

If the EBT ( Earnings before taxes ) is positive then the gain or profit or PAT ( Profit after taxes) cannot be negative as the taxes does not exceed 100 %.

It is possible that the gain can be negative with appropriate taxes. If the company's gain before paying taxes is  negative can leads to negative gains after paying taxes.

This is possible when the EBT are negative then the PAT or Net income will be negative.

For illustration Consider for a firm

EBT = $ 100
Tax rate = 40 % = 0.40
Therefore PAT = EBT x ( 1 - Tax rate ) = $ 100 x ( 1 - 0.40 ) = $ 100 x 0.60 = $ 60

Here we can observe that the taxes are applied on EBT after deducting Interest expenses EBT = EBIT - Interest Expense

Note- This is based the fact that the Corporate Tax rates does nor exceed 100 %