Research On Start-up Financing Decision Based On Real Option

Venture capital investment and financing decision-making is one of the hot issues in current financial research.Long-term practical experience shows that the venture capital process may be affected by emergencies,so economic variables may jump.Based on the jump diffusion model under the assumption of random jump amplitude,we study the optimal contingent payment and investment decision,and compare it with the results under the constant case;Based on the jump diffusion model with the jump size obeying normal distribution and exponential distribution,this paper research the optimal investment decision and its comparison under the mutual influence of entry and exit decision.The details are as follows:First,consider impact of emergencies,we assume that the profit flow of entrepreneurial firm is subject to a jump-diffusion model with a constant jump size,and study the optimal contingent payment and financing decision-making problems;further assume the jump size is a random variable and compare with relevant results under a constant case.Applying real option ideas and Ito’s lemma to derive differential equations that satisfy the value of investment opportunities,explicit expressions of investment opportunity values,investment thresholds,and optimal contingent payments are shown under different contingent payment types,this paper prove the optimal investment timing is independent of the type of contingent payment.Numerical simulation gives the contingent payment value and payment amount at the optimal decision,which indicate contingent payment at hit is more valuable than contingent payment at term from the perspective of payment date.Compared with the case of normal random jump size,jump-diffusion models with constant and exponential random jump size underestimate the value of investment opportunities.In addition,entrepreneurs tend to wait under the jump-diffusion model with random jump size,and under the exponential distribution assumption invest later.Secondly,under the jump diffusion models with normal random jump size and exponential random jump size,respectively,the optimal investment decision under the mutual influence of entry and exit investment decisions is studied when exit is restricted and unrestricted on time.Using the real option approach and Ito’s lemma to derive the display expression of entry threshold,exit threshold,optimal ownership after expansion,expected cash multiple and adjusted cash multiple when exiting without time restriction.Then we study the optimal investment decision when there is an exit time restriction correspondingly.The numerical results show that the jump-diffusion model with random jump size promotes investment,but at the same time investor withdraw capital earlier,acquire less equity,and perform poorly(adjusted cash multiple is small).Therefore,under the influence of emergencies,the jump-diffusion model with random jump size has a negative impact on investment decisions.In addition,probability that investors need a higher premium to reach an exit agreement become bigger,and the impact of the exponential case is more significant.