Optimal venture capital entry–exit strategy with jump–diffusion risk

This paper introduces a double exponential jump–diffusion process to model the pre-expansion value of a start-up firm. Within this framework, we present a dynamic model for studying the entry and exit decisions of venture capitalists (VCs). The model returns an analytical solution for the entry trigger, a semi-analytical solution for the exit trigger, the post-money optimum ownership, the (raw) cash multiple and a new time-adjusted version. Significantly, we uncover a direct correlation between the optimal premium upon exit through the trade sale (M&A) and the start-up firm’s value during the M&A offer. Additionally, we theoretically demonstrate that the exit trigger is larger than the value of the start-up firm when the VC makes a M&A offer to the buyer. Our numerical analysis discusses the following empirical implications: (i) postponing the M&A offer results in an increased optimal premium, leading to a strategically delayed divestment. This delay corresponds to an amplified (raw) cash multiple but triggers a notable decrease in the adjusted cash multiple; (ii) considering jump risk enhances the expected investment performance; (iii) the post-money optimum ownership is not influenced by jump risk; (iv) greater uncertainty associated with jump intensity and volatility prompts delayed entry and exit decisions, producing larger cash multiples; (v) a higher VC’s optimism leads to an increased (raw) cash multiple and a decreased adjusted cash multiple.