 In tax optimal capital structure, let's see whether there is any limit of using debt in order to obtain any tax shield. We know that a firm can receive full tax benefit of leverage without using 100% debt financing in its operations. And for that purpose, a firm must have taxable earnings to obtain tax savings. This means there is a limit of using debt in order to have tax shield of debt. And that limitation is the taxable earnings or the profitable earnings, which means that earnings before interest and tax of a particular firm should be positive in order to go for the tax saving. A firm with interest payment beyond earning before interest and tax pays no taxes because there is no taxable profit so no immediate tax shield can be there from the excessive leverage. The optimal leverage from tax saving perspective is the point where the interest payments of a firm are equal to its earnings before interest and taxes. Let's see tax savings with different amounts of leverage. Assume that a firm with earning before interest and tax of $1000 and a corporate tax rate of 35%. We have three scenarios where in one scenario we have no leverage, in the other we have high level of leverage and in the third we have excessive leverage. We have a bit of $1000 for all the three scenarios. We have no debt in the case of no leverage and 1000 interest expense which is equal to the a bit of $1000. This is the case of higher leverage and we have $1100 as interest expense which is greater than the amount of a bit and this is the case of excessive leverage. If we see the net income, we have net income of $650 in first case, zero income in higher leverage case and negative $100 income or the loss of $100 in the excessive leverage case. So when we see the tax savings from the leverage, there is no tax saving in the case of no leverage and full tax saving of $350 in case of higher leverage and we have no tax saving on the excessive leverage where we have extra interest of $100 because we have no extra profit against this $100. So we see that there is in the case of no leverage, the firm is owing a tax of $350 on the full amount of a bit and at higher level of leverage with interest payment equal to $1000, full earning of $350 can be shielded from taxes and with excessive leverage, the interest payments are going beyond a bit. So the firm has a net operating loss of $100. This means there is no tax to pay. In this case, no increase in tax savings on excessive interest payments are there. In other graph, we see that the firm for a bit with certainty and interest payment of same amount can maximize the tax savings as we are seeing in the case of $1000 of a bit where interest expense is equal to this amount and where the firm cannot predict the interest, the abit very precisely then abit with uncertainty has greater vulnerability of exceeding a higher interest expense over the abit. So that we are seeing here as a consequence is that the tax savings for higher interest falls possibly reducing the optimal level of interest payments. Is there any low leverage puzzle? Let's see what does it mean. A study of S&P's 500 firms from 1975 to 2015 shows interest expense of leveraged firm well below its taxable income. This means that these firms were mainly under leveraged. Why this thing happened or why these firms could not exploit fully the option of debt financing when talked to the managers, many of them have had consensus on few things like they said that debt financing has other costs preventing firms from using interest tax shield fully and why this was the cause because the higher debt level increases the probability of bankruptcy and debt payments must be paid to avoid bankruptcy That means that the payment of interest and debt is a legal obligation of the firm but to pay dividend is not a legal restriction or binding on the firm for its equity holders. So the costly bankruptcy may offset the tax advantages of the debt. So we see while solving this low leveraged puzzle that the probability of the riskiness of bankruptcy is the main cause that prevent a firm using the debt at a full level because the cost of bankruptcy may go beyond the benefit of the tax debt advantage.