为解决中小企业融资难问题，我国推出了一新型融资模式—担保换股权。利用该模式，中小企业可获得贷款担保。为此本文研究中小企业在该模式下的最优投资与融资。首先在项目收益流服从几何布朗运动下，利用均衡定价方法给出债券、股权和担保成本的定价；然后利用实物期权方法导出最优投资时机满足的代数方程；最后分析了最优贷款规模。我们获得了定价的显式解；确定了最优投资时机、最优生产规模和最优资本结构的相互关系；解释了这一新型融资模式的优势。经济分析表明：最优融资规模与项目风险呈U型关系；风险较小时，企业会加速投资同时扩大债务融资比例减少股权比例。与纯股权融资的企业和无融资约束的杠杆企业相比，该模式显著提高了企业的生产规模；与纯股权融资的企业相反，最优生产规模与投资时机随项目风险的增大而增大。研究结果对中小企业的投融资决策具有指导意义，也为今后对担保换股权和担保换期权的比较研究起到借鉴作用。
To solve the financing problem of SMEs, a new financing model has been introduced, which is the equity-for-guarantee swap (EGS). In this paper, the optimal investment and financing decisions of a firm that uses a financial derivative, equity-for-guarantee swap (EGS) are studied, in an emerging market. With this swap, the entrepreneur obtains a loan from a banker guaranteed by an insurer, after granting the insurer a fraction (guarantee cost) of his equity.
First, the price of equity and debt and the guarantee cost are provided based on equilibrium pricing rules. Second, in a real-options framework, the algebraic equations about the optimal investment timing and the optimal production scale respectively are derived. Finally, the optimal size of the loan is analyzed. In this paper, the analytical solutions of the pricing of the firm's securities and the guarantee cost are firstly obtained. Then, the relationships among the optimal investment timing and the optimal investment scale and the optimal financing structure are determined. In the end, the advantage of this financing model is shown. Economic analysis indicates that there is an U-shaped relation between the optimal production scale and the project risk. When the risk is smaller, the enterprises will accelerate the investment and increase the proportion of debt financing. Compared with the enterprises with all-equity financing and the enterprises with no financing constraints, the new financing model significantly increases the production scale of the firm. In contrast to the enterprises with all-equity financing, the optimal production scale and the optimal investment threshold all increase with the project volatility. The results in the paper have an import influence on the investment and financing decisions of small and medium-sized enterprises. At the same time, the comparative research between the option-for-guarantee swap and the equity-for-guarantee swap will be promoted in the future.
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