 Recapitalization refers to a process whereby a firm changes its capital structure and a leveraged recapitalization refers to a process whereby a firm issues new debt, raises certain amount of cash and uses that amount of cash in order to pay dividend to its shareholders or repurchase some of its shares from the existing shareholders. Now it is assumed that this leveraged recapitalization also provides some tax benefits to the firm's shareholder. Let's see that how this tax benefit can be computed for the firm's shareholder as a result of such transaction. We assume that the firm has outstanding shares of 20 million whereas the share market price is $15 each, the firm at present has no debt in its capital structure but the firm plans to borrow new debt at the amount of $100 million and the corporate tax rate is 35%. Now the question arises that would there any boost in the stock price and the benefit to the shareholders of this particular firm using the given scenario. Now as the firm is unlevered so the value of this unlevered firm is the product of its number of shares and the share market value which is equal to $300 million and the firm if goes for the issuance of new debt then there would be the interest payment and accordingly the interest tax shield will be there. The present value of this interest tax shield is simply the product of corporate tax rate and the debt value. The present value is equal to $35 million. So the levered firm's total value is now the sum of the unlevered firm's value and the resulting present value the interest tax shield. Now adding 35 million of the interest tax shield to the unlevered firm's value of the 300 million the levered firm's value comes to $335 million. On the other side if we determine the value of levered equity in this particular firm then the levered equity of this particular firm is the difference between the value of the levered firm and the amount of the debt and the value is equal to the $235 million. So the debt has reduced the value of the levered equity as a result of leverage. Now we see that there is an increase in the firm value by 35 million but on the other hand there is a decline in the equity value by Rs. 65 million. Now the question arises would there exist any benefit to the shareholders of this particular firm under these circumstances. Let's see is there any. The value of levered equity as we have seen is equal to $235 million and as a result there is a share repurchase by the firm to the tune of $100 million. So this has increased the value of the equity by Rs. 335 million although there has been a decline in the number of shares but the amount of 100 million is gone to the shareholders pocket. So there is total value of the levered equity as a result of this transaction is now $335 million but the value of this equity when the firm was unlevered was $300 million. So we see that as a result of this leveraged recapitalization or the leveraged recap the value of unlevered equity has increased by $35 million. Now this was the total amount analysis. Let's see this increment in form of share purchase or share price in the market. Now how again can be determined as a result of this share repurchase? We see that the firm has outstanding shares of 20 million. The repurchase occur for 6.667 million because this repurchase occur at a market price of $15 using the amount of $100 million. So the repurchase occur for 6.667 million. The remaining shares are 13.33 million but these 13.33 million shares are worth for the market value of $335 million. This gives a new market price per share of $17.625 per share. This means that there is a per share gain as a result of this share repurchase transaction and that share per share gain is the difference between the share repurchase price of $17.625 and the existing share price of $15. So the gain is $2.625 per share. This means that the total gain to the remaining equity shareholders is the product of 13.33 million shares multiplied by the per share gain of $2.625 and this gives the total gain for the remaining equity shareholders by Rs.35 million. Now if there is no arbitrage pricing, what will happen? Let's see an example that if there is any arbitrage opportunity, the shareholders are required to buy $15 before the repurchase transaction and immediately sell these shares at the price afterwards which is $17.265 each share. This means that this would increase the share price by the value of interest tax shield and this would set the new share price at $16.75 each. And this also gives a gain of $1.75 for both of the shareholders. For the shareholders who are entering their shares at $16.75 and for the shareholders who are holding their shares at existing share price of $15 each. So the benefit of interest tax shield goes to all of the 20 million shares who are the original shares issued by the firm. To determine the total benefit we need to multiply the 20 million shares with the differential gain of $1.75 each share and it gives a total gain of $35 million that we see that the total gain of $35 million is going towards both of the shareholders who are selling their shares to the firm back and those who are holding their shares with themselves. Now how this recapitalization with the help of leverage can be analyzed using the market value balance sheet. We see that this recapitalization can be analyzed using the market value balance sheet assuming that the market value of the firm is equal to the market value of its assets. This means that the firm's assets now must include the interest tax shield as a new asset. Now this analysis can be done in three steps. At first we see that there is an announcement of recapitalization and as a result the investors will anticipate an interest tax shield to the tune of $35 million and that will also be increased in the value of the firm's assets. The second step is the issuance of debt by $100 million by the firm. This will increase both the firm's assets in the form of cash and firm's obligation in the form of debt on its liabilities side and the third step to analyze is the utilization of the proceeds of the debt to repurchase the shares. This will decline the company's cash on the assets side and on the liabilities side it will reduce the number of firms existing outstanding shares. Now all of these three steps can be analyzed using the market value balance sheet of the firm. We have the market value balance sheet where the firm has the original assets when the firm is an unleavoured firm of $300 million and there is initially no cash and interest tax shield in the firm's total assets and for liabilities we have no debt so to determine the firm's equity we need to deduct the value of liabilities from the total assets and the equity is the same amount of $300 million. The firm has 20 million outstanding shares, the per share value is now $15 each. As a step one when the recapitalization is announced and there is an anticipation of interest tax shield, this is added to the firm's assets as a new asset it raises the total asset to the amount of $235 million so with no debt till now the equity is also equal to the amount of total assets and having 20 million shares the new share price is $16.75 each so the share price has been risen as a result of recapitalization announcement and as a at a second stage where the firm issues a debt there is a cash proceed of $100 million so the total asset are now $435 million but now there is debt in the liabilities side so the equity is the difference between total assets and the debt which is now $335 million dividing this equity over the 20 million shares again we have a share price of $16.75 each now see that again we have in the third step when there is a repurchase of the firms issued shares there is an outflow of cash that reduces the firm assets to the tune of $335 so this is the new value of the firms total assets at the time of share repurchase but they exist continually the amount of debt so the equity of the levered firm is now $235 million but remaining outstanding shares are $14.03 so the price remains constant at $16.75 each this shows two types of conclusion here that although the leverage reduces the total market value of the firm's equity that we see which is now $235 a million dollars but the share holders capture benefit of the interest tax shield that we see these benefits are a per share $1.75 million that is increment from $15 and a new price is $16.75 dollars each and this benefit is due to the interest tax shield so we see that although the leverage reduces the firm's total value and accordingly the total market value of the equity yet it it allows the share holders to gain benefit of the interest tax shield