运营滞后与信用担保互换下的项目投资决策模型

在项目投资面临运营滞后以及债务融资约束的情形下，基于实物期权框架构建了企业家签订信用担保互换契约的两阶段投资决策模型。运用动态规划以及均衡定价方法，给出了企业家股权及期权价值的显示表达，得到了两个阶段担保成本满足的代数方程，并进一步分析了运营滞后和信用担保下企业家的最优投资决策问题。数值结果表明：外部运营时滞会提高杠杆率，导致企业家提前投资，同时会提高企业家第一阶段债务融资的担保成本，但会降低第二阶段债务融资的担保成本；随第一阶段投资额度逐渐增大，企业家的最优投资水平呈U型变化，第一阶段债务融资时的担保成本单调递减，而第二段债务融资时的担保成本呈现倒U型；企业家两个阶段的融资缺口对项目最优投资水平、最优破产水平以及担保成本有显著影响。

An Investment Decision-making Model under Implementation Lag and Equity-for-guarantee Swap

Most capital projects involve significant time to completion before they start generating cash flows, and this time lag is known in the literature as ‘implementation lag’. On the other hand, entrepreneurs always encounter financing problems and it is difficult or even impossible for them to obtain loans directly from banks. To overcome such financing constraints, equity-for-guarantee swap is introduced by entrepreneurs, where a bank lends at a given interest rate to a lender and once the lender defaults on the loan, the insurer must pay all the outstanding interest and principal to the bank instead of the lender. At the same time, the lender must allocate a fraction of the lender's equity to the insurer, which is called the guarantee cost.
Inspired by the composition of the implementation lag and financing constraints of the project investment in practice, an optimal investment decision-making model is constructed by real options theory. First, it is assumed the cash flow of the project is described by the Geometric Brownian Motion. Second, entrepreneur wants to implement the project by two stages, with some elapsed time between the two stages, before it can realize any benefits from the project. In the first stage, the entrepreneur invests a fraction θ of the total investment cost (orθI) and receives a fraction θ of the total set of assets of the project. In the second stage, the entrepreneur pays the remainder of the investment cost, or (1-θ)I, and receives the remaining fraction of the assets. Third, to overcome financing constraint, equity-for3guarantee swap among an entrepreneur, a lender (bank), and an insurer is introduced. The insurer must pay all the loss from the borrower's default and so the lender's asset is risk-free. So, the value, denoted by D^guar(x), of the insurer's compensatory payment to the lender, must satisfy the following equation (1-τ_i)D^guar(x)=(1-τ_i)c/r-D(x), where(1-τ_i)c/r is the value of risk-free debt, D(x) is the value of risk debt. To make the swap fair, an insurer's compensatory payment should be equal to the present value of an SME's equity allocated to the insurer at the investment time. That is φE(x)=(1-τ_f)D^guar(x),where φ is the guarantee cost. At last we give the value of corporate securities and give the algebraic equations of the guarantee costs by the method of dynamic programming and equilibrium pricing. The impact of implementation lag and equity-for-guarantee swap on the entrepreneurs' investment policy and default decisions is explored.
In our numerical analysis, the base parameter values are taken from Sarkar and Zhang (2015) and Gan et al. (2016) based on empirical evidence. The results show that:Implementation lag will increase leverage of the project, leading entrepreneur investment earlier, and it will rise the warranty costs of the first phase and reduce warranty cost of the second phase; When first phase investment proportion increases, optimal level of investment entrepreneurs U-shaped, warranty costs of the first stage decrease, and the cost of second stage incurs an inverted U-shape; Scale of financing have a significant impact on the level of investment, the level of bankruptcy and warranty costs. Our study enriches the application of real options theory on financing constraint.