
An Investment Decisionmaking Model under Implementation Lag and Equityforguarantee Swap
GAN Liu, LUO Pengfei, YANG Zhaojun
2018, 26 (3):
2232.
doi: 10.16381/j.cnki.issn1003207x.2018.03.003
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, equityforguarantee 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 decisionmaking 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 (1θ)I, and receives the remaining fraction of the assets. Third, to overcome financing constraint, equityfor3guarantee 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 riskfree. So, the value, denoted by D^{guar}(x), of the insurer's compensatory payment to the lender, must satisfy the following equation (1τ_{i})D^{guar}(x)=(1τ_{i})c/rD(x), where(1τ_{i})c/r is the value of riskfree 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)=(1τ_{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 equityforguarantee 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 Ushaped, warranty costs of the first stage decrease, and the cost of second stage incurs an inverted Ushape; 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.
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