税率不确定性下的减记型二级资本债设计及银行最优债务结构

Designing of Write-down Bond and Optimal Debt Structure of Bank Under Tax-rate Uncertainty

考虑了税率不确定下减记型二级资本债（减记债）设计和银行最优债务结构问题。假设银行的融资方式为股权,普通债和减记债,在税率不确定环境下,利用动态规划方法,解析地得到了银行证券的价值和银行最优债务结构。分析了税率不确定性对银行融资决策的影响。结论表明：普通债的最优券息是减记比例的凸函数,随着减税而减少,随着减税时间点的增加而增加。减记债最优券息随着减记比例先增后减,受减税和减税时间点的影响是不确定的。此外,银行总价值和最优杠杆率随着减记比例先增后减。本文也为我国“营改增”政策的可行性提供了理论依据。同时,从银行总价值最大化和税率效应角度为金融决策者如何灵活地选择适当的减记比例提供了理论参考。

In the recent financial crisis, many banks have experienced financial distress, under which they were not able to raise significant new funds from the market through a conventional approach. To solve such kind of problems, two new interesting classes of debt with loss-absorbing features, write-down debt and contingent convertibles （CoCos）, have drawn much attention of researchers and regulators. According to the statistics, the 50 percent of debt with loss-absorbing features issued in Europe is write-down debt. For example, RaboBank issues 2.0bn USD write-down debt with perpetual term in November, 2011, Barclays issues 3.0bn USD write-down debt with ten years maturity in November, 2012 and Credit Suisse is- sues 2.5bn USD write-down debt with ten years maturity in December, 2013. The banks in China have stepped up issuance： from nothing in 2012 to RMB 385 bn yuan of the write-down debt with 10 years maturity by December 2014. The maturity of the write-down debt is long-term or perpetual, however, the tax rate will change during the maturity of debt. For example, the average of corporate statutory tax rates has fallen from 31.4% to 25.9% over the 1999 - 2008 period. So, the impact of tax-rate uncertainty on bank＇ s financing policy is important. In this paper, the designing of write-down bond and the optimal debt structure of bank under tax-rate uncertainty are considered. It is assumed that the capital structure of bank is composed are considered equity, straight debt and a write-down debt. The before-tax cash flow x dynamics is described by the following geometric Brownian motion dX t = μXtdt ＋ σXtdZt , where μ is the risk-adjusted drift parameter, and σ is the volatility rate. Zt denotes the Brownian motion under risk neutral measure. When the bank is alive, the straight debt has a coupon rate Cs and the write-down debt has a coupon rate Cw. Once the bank suffers from a credit event, the coupon of write-down debt is a automatically reduced by a fraction equal to 3. The write-down debt can be written down only once. When the bank defaults, two bondholders gain the remaining value of bank by equal priority rule. We assume that the tax rate follows a Poisson process. Given an initial tax rate r0, at any short time interval d, there is a probability λdt that the tax rate changes to r1. We examine how the bank chooses the optimal debt structure and the optimal write-down scale under tax-rate uncertainty. Firstly, according to the dynamic programming, the value of securities of bank under tax-rate uncertainty is provided analytically. Secondly, the optimal debt structure of bank is also conidered and the closed-form expression is given. Lastly, numerical analyses and implications are provided. In our numerical analyses, the base parameter values are similar to Andrikopoulos and Fedele et al （2011）based on empirical evidence. Our results show that the optimal coupon of straight bond is convex function of write-down scale,increases with the expected time to occur a tax cut, and a tax-rate cut reduces the optimal of straight bond. The optimal coupon of write-down bond first increases and decreases with write-down scale and the impact of the tax cut and the expected time to occur a tax cut on it is ambiguous. It is also found that the total value and the optimal leverage are first increases and decreases with writedown scale. The theory basis is provided for the feasibility of replacing the business tax with a value-added tax. What＇s more, reference about how the decision maker flexibly chooses the appropriate write-down scale is provided by maximizing total value and the effect of tax-rate.