Exit decision of venture capital based on linear contract in continuous time: IPO or M&A

Abstract

Based on the assumption that the long-term value of a venture capital satisfies the algebraic Brownian motion, we develop a continuous-time exit model of venture capital under different exit modes, namely, initial public offering (IPO) and mergers and acquisitions (M&A). The employee incentive problem is analyzed jointly with the exit decision of the firm in terms of the exit timing and the exit mode. Further, the problem of capital exit is considered from two perspectives, namely, optimal venture capital and social welfare maximization, and the differences between these exit decisions are compared. Our model predicts that the timing of an IPO, the purpose of which is to maximize the utility of the capitalists, lags behind the exit timing, whose purpose is to maximize social welfare. Using a numerical analysis, this paper also proves that increasing the production efficiency, lowering the interest rates, and improving risk management can make the exit decision of venture capitalists converge with that of maximizing social welfare.