| The Capital Structure is defined as the construction and proportion of financing. It is the kernel research area about how to improve the firm's value by optimizing its capital structure. The research started from the hypothesis about capital structure in 1950s. After the MM theory was proposed by Modigliani and Miller in 1958, it passed long time that the research had been going deeper. Since the pure theory being constructed by Modigliani and Miller in 1958, the scholars have been doing reaserch to adapt to the real word by introducing tax, bankruptcy cost, agency cost, asymmetrical information and corporate control.The paper discusses capital structure from the perspective of tax and bankruptcy cost. The MM theory proposed by Modigliani and Miller in 1958 thinks that under the consideration of positive corporate income tax the firm value reached its maximum when its debt to asset ratio reached 100%. So Modigliani and Miller suggested an optimal capital structure with complete debt. After MM theory, based on the zero-coupon bond pricing model proposed by Merton in 1974, Brennan and Schwartz derived the functional relation of corporate bond and firm value, and provided the first quantitative examination of optimal leverage, where Merton (1974) followed the frame work of BS option pricing theory. In 1973, Black and Scholes provided a perfect option pricing theory. Since the parameters of BS option pricing formula are all observable, it got a widely application and success. Merton (1973) summarized the BS formula, and noticed that not only the frame work provided by Black and Scholes can be used to price option but also can be extended to price corporate bond. Then Merton (1974) extended the BS model to the simple case of pricing zero-coupon bond and its risk structure of interest, based on the MM theory about the independence of the capital structure and the firm value.After having analyzed the limitations of Brennan and Schwartz (1978), Leland (1994) examined the corporate debt values and capital structure in a unified analytical framework. It derived closed-form results for the value of long-term risky debt,yield spreads and the optimal capital structure, when firm asset value followed a diffusion process with constant volatility. And it then established a framework to analyze corporate debt values and capital structure under the conditions of endogenous bankruptcy and exogenous bankruptcy respectively. Leland (1994) defined the total firm valueυ= A + TB ? BC as the modified value of the firm's asset value A, where the firm could benefit from tax saving TB and suffered from bankruptcy cost BC . Although the firm's asset value is observable, the value of tax saving and the value of bankruptcy cost are unobservable, that makes the modified value, the total firm value unobservable. Leland (1994) believed the optimal capital structure rest on the leverage which maximized the unobservable total firm value.Based on the binomial tree method, a new theory of the optimal capital structure is introduced to conquer two logical problems of Leland (1994): 1) What makes the managers to adjust the capital structure actively? Does the total value fit in the managers'motivation of adjusting the capital structure? Who are the owners of the total value of the firm? Following the Kersy theory, it is unimaginable to believe the managers would maximize the total value of the firm, the property right of which is unclear. 2) Even if the managers would act to maximize the total value of the firm, the object of the managers is unobservable, that makes the object of maximizing the managers'interest unreasonable. According to the above logical problems, the optimal capital structure should be the relative ratio between equities and debts when the sum of the two financial instruments value reaches maximum. The hypothesis of rational person suggests that maximizing the benefit of the investors (including stock holders and creditors) would be the activation and object for the managers to regulate the capital structure. Because the relationship between investors and managers belongs to the research area of the principal agent theory, which is the profound field, to simplify our model, the principal agent relation is ignored, and the managers are supposed to act to good purpose of the investors. And we do not take the game relation between stock holders and creditors into consideration. Generally, since the stock holders control the business operation and financial operation of the firm, the stock holders would morally hazard the creditors. The moral hazard is going seriously when the firm is close to bankruptcy, because the stock holders are apt to invest the high-risk investment and it damages the creditors'profit. To prevent the moral hazard, some provisions are included in the composition of debt to limit the high-risk behavior, such as the put provision granted to the creditors if the plan of the raised fund is changed. Besides, the creditors conference and the management system of debt trustee are asked to guarantee the creditors'benefit. But to simplify our model, we neglect the game relation between stock holders and creditors. Thus, the value of equities and debts, which represent the investors'benefit, bear the property right clearly and are observable, so it is reasonable that the managers who state the investors'right would maximize the value of equities and debts.The value of the firm, which is also called as the corporation value, is defined as the total benefit brought by the firm to the investors, or is defined as the total present value of the cash flow that the firm will generate to pay for the investment during the future business operation. Besides the stock holders and the creditors absorb part of the firm's future cash flow, the government also declares part of the firm's future cash flow by compulsive tax. And if the firm is bankrupted, the latent buyer of the liquidated asset gains his discount income by auction. So the future cash flow generated by the firm will be occupied by the 4 types of claimers: the creditors, the stock holders, the government and the latent buyer of the liquidated asset. Each part of the future cash flow owned by different claimers is stochastic, and can be treated as some special options whose underling asset is the value of the firm. At maturity day, if the value of the firm will be larger than the face value of the debt, the creditors will receive the fixed face value, the government will levy a tax on the surplus value over the face value of the debt, the stock holders will claim the surplus value after the tax, and the value of the latent buyer will get nothing. But if the value of the firm will be less than the face value of the debt, that means the bankruptcy of the firm, the latent buyer will benefit from the discount sale of the firm's asset, the creditors will obtain the liquidation value, and the stock holders and the government will get nothing. So, the value of each 4 types of claimers can be priced by the framework of option pricing. According to the law of one price, the sum of the 4 claimers'value equals to the value of the firm ( A0 = D0 + S 0 + TB0 + BC0). From the perspective of the present value and the static state, the value of the firm can be divided to the 4 types of claimers. The creditors, the stock holders, the government and the latent buyer obtain their separate part value of the firm respectively.Since the motion of the firm's value At is decided by the business operation, under the hypothesis of the perfect market, it follows a Geometric Brown Motion with the start point of A0 , constant drift term and constant volatility. The motion of the firm's value has nothing to do with the financial operation, that means the firm's value is independent of the capital structure. At the preset motion of At , the CFO adjusts the capital structure by financial operation to maximize the investors'value, or maximize the value of the equities and debts. Because the influence of tax saving and bankruptcy contradicts each other, the maximum value of the equities and the debts can be found by adjusting their relative proportion. Here, we ignore the inner structure of the firm's debts, which not only come from the indirect financing of bank, but also come from the direct financing of financial market. Usually, the bank lending is short term and adapts to complement liquidity of the firm, and the bond from financial market is long term and adapts to long-term investment. But whether the debts come from bank or financial market, its yield rate is determined by the firm's credit rank. Here, to simplify our model, we mix the indirect and direct debts, and treat them as a general bond.After the rationality of the object function is explained, the sensitive analysis about the parameters of the model is made, and two conclusions are drawn. First, the drift term of the firm's valueμis irrelevant to the results, that represents the model's compatibility to the risk-neutral pricing model. This characteristic is very important and makes the model adapt to the situation of bear market. Secondly, if the firm has been sticking to the optimal capital structure, the increase of the risk free interest rate r f suggests an increase proportion of debt, that contradict our traditional opinion. Usually, we believe that the increase of the risk free interest rate means the increase of the lending rate of bank and the increase of the debt cost to the firm, so the firm should decrease the liability. This is because that people only notice the bebt cost,but ignore the fact that the increase of risk free interest rate results in the increase of the tax.After the optimal capital structure of the firm is confirmed, a empirical research about 146 listed companies is made from data collection, parameters setting and result analysis. The net financial debt, which is the difference of the financial debt from the financial asset, is used as the creditors'value. And some important conclusions are drawn. First, most of the listed companies in China are dominate on equity financing and are lack of debt financing. That's because of the limited improvement on inner claimers'value by choosing optimal capital structure. Secondly, the improvement that most of the firms can gain is less than 2%, but also a few companies have a notable improvement. So the model can act as a guider for the firms to maximize the investors'value by debt financing. Innovations of this paper:1,It is unreasonable for Leland model to optimize the capital structure by maximizing the total value of the firm, so we provide another analyzing framework of the optimal capital structure. The future cash flow generated by the firm will be occupied by the 4 types of claimers: the creditors, the stock holders, the government and the latent buyer of the liquidated asset. Each part of the future cash flow owned by different claimers is stochastic, and can be treated as some special options whose underling asset is the value of the firm.2,We both consider the value added tax rate and the corporate income tax rate, and it makes our model fit the situation in China better.3,We choose the binomial tree method to discount the firm asset. It can price all kinds of asset indiscriminately, without considering whether it is stock value, bond value, tax value or firm value.4,A empirical research about 146 listed companies is made from data collection, parameters setting and result analysis.Then we compare the current capital structure in listed companies and the optimal capital structure in our model.
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