Abstract: 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 issues 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=μX_tdt+σX_tdZ_t, where μ is the risk-adjusted drift parameter, and σ is the volatility rate.Z_t denotes the Brownian motion under risk neutral measure.
When the bank is alive, the straight debt has a coupon rate C_s and the write-down debt has a coupon rate C_w. Once the bank suffers from a credit event, the coupon of write-down debt is a automatically reduced by a fraction equal to δ. 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 τ₀, at any short time interval d_t there is a probability λ_dt that the tax rate changes to τ₁. 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 write-down 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.

Key words: tax-rate uncertainty, write-down bond, optimal debt structure