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。
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 Dguar(x), of the insurer's compensatory payment to the lender, must satisfy the following equation (1-τi)Dguar(x)=(1-τi)c/r-D(x), where(1-τi)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-τf)Dguar(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.
[1] Mcdonald R, Siegel D. The value of waiting to invest[J]. Quarterly Journal of Economics, 1986, 101(4):707-727.
[2] DixitA K, Pindyck R. Investment under uncertainty[M]. Princeton, NY:Princeton University Press, 1994.
[3] Childs P D, Mauer D C, Ott S H. Interactions ofcorporate financing and investment decisions:the effects of agency conflicts[J]. Journal of Financial Economics, 2005, 76(3):667-690.
[4] Mauer D C, Sarkar S. Real options, agency conflicts, and optimal capital structure[J]. Journal of Banking and Finance, 2005, 29(6):1405-1428.
[5] Shibata T, Nishihara M. Investmenttiming under debt issuance constraint[J]. Journal of Banking and Finance, 2012, 36(4):981-991.
[6] Shibata T, Nishihara M. Investmenttiming, debt structure, and financing constraints[J]. European Journal of Operational Research, 2015, 241(2):513-526.
[7] Shibata T, Nishihara M. Investment-based financing constraints and debt renegotiation[J]. Journal of Banking and Finance, 2015, 51(2):79-92.
[8] Andrikopoulos A. Irreversible investment, managerial discretion and optimal capital structure[J]. Journal of Banking and Finance,2009, 33(4):709-718.
[9] Hori K, Osano H. Investment timing decisions of managers under endogenous contracts[J]. Journal of Corporate Finance, 2014, 29:607-627.
[10] 杨金强, 杨招军. 部分信息下实物期权的定价和风险对冲[J].中国管理科学, 2011, 19(4):9-16.
[11] 谷晓燕. 基于实物期权的研发项目动态投资决策模型[J].中国管理科学, 2015, 23(7):94-102.
[12] 周艳丽, 吴洋, 葛翔宇. 一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟[J].中国管理科学, 2016, 24(6):19-28.
[13] 甘柳, 杨招军.最优长期合同下的企业投融资决策[J]. 控制理论与应用, 2016, 33(11):1483-1491.
[14] 甘柳, 罗鹏飞, 杨招军.特质管理者决策下的企业投融资研究[J].系统科学与数学, 2016, 36(11):1995-2006.
[15] Alvarez L H R, Keppo J. The impact of delivery lags on irreversible investment under uncertainty[J]. European Journal of Operational Reasearch, 2002, 136(1):173-180.
[16] Sarkar S, Zhang Chuanqian. Implementation lag and the investment decision[J]. Economics Letters, 2013, 119(2):136-140.
[17] Agliardi E, Koussis N. Optimal capital structure and the impact of time-to-build[J]. Finance Research Letters, 2013, 10:124-130.
[18] Sarkar S, Zhang Chuanqian. Investment policy with time-to-build[J]. Journal of Banking and Finance, 2015, 55:142-156.
[19] 杨兆廷, 李吉栋. "担保换期权"与高新技术中小企业融资[J]. 管理世界, 2008, 10:167-179.
[20] 盛世杰, 周远游, 刘莉亚. 引入担保机构破解中小企业融资难:基于期权策略的机制设计[J]. 财经研究, 2016, (06):63-73.
[21] Yang Zhaojun, Zhang Hai. Optimal capital structure with an equity-for-guarantee swap[J]. Economics Letters, 2013, 118(2):355-359.
[22] Zhang Chunhong, Yang Zhaojun. Two new equity default swaps with idiosyncratic risk[J]. International Review of Economics and Finance, 2015,37:254-273.
[23] Wang Huamao, Yang Zhaojun, Zhang Hai. Entrepreneurial finance with equity-for-guarantee swap and idiosyncratic[J]. European Journal of Operational Research, 2015, 241(3):863-871.
[24] Xiang Hua, Yang Zhaojun. Investment timing and capital structure with loan guarantees[J]. Finance Research Letters, 2015, 13:179-187.
[25] Gan Liu, Luo Pengfei, Yang Zhaojun. Real option, debt maturity and equity default swaps under negotiation[J]. Finance Research Letters, 2016, 18:278-284.
[26] Goldstein R, Ju Nengjiu, Leland H. An EBIT-based model of dynamic capital structure[J]. Journal of Business, 2001, 74(4):483-511.
[27] Margsiri W, Mello A S, Ruckes M E. A dynamic analysis of growth via acquisition[J]. Review of Finance, 2008, 12(4):635-671.
[28] Leland H. Agency costs, risk management, and capital structure[J]. Journal of Finance. 1998, 53(4):1213-1243.
