A Framework for Valuation and Portfolio Optimization of Venture Capital Deals with Contractual Terms

Mohammadreza Valaei, Vahid Khodakarami and Hakim Bendjenna

Mathematical Problems in Engineering, 2024, vol. 2024, 1-21

Abstract: Venture capitalists invest not only in the business aspect of a deal but also in its contractual terms. Therefore, the selection of deals and the combination of contractual terms pose challenging decisions for them. This paper consists of two main sections. The first section introduces a novel framework for the valuation of venture capital (VC) deals, including startups and their contractual terms. By taking into account risk situations, this section presents the valuation of combined contractual terms, including call options, liquidity preference, and participant rights. In the second section, a new multiobjective mathematical model for VC deals and contractual terms portfolio selection is developed using right-tail probability, strategy alignment, and a utility function. To solve the proposed model, three metaheuristic algorithms—Non-Dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Binary Harmony Search Algorithm, and Dynamic Tuning Parameter Binary Harmony Search Algorithm (DTPBHS)—are applied. Based on numerical examples, DTPBHS outperforms other algorithms in the “Mean Ideal Distance†index, but NSGA-II demonstrates the best performance in the “Rate of Achievement of two objectives simultaneously†index. Furthermore, we demonstrate that the proposed utility function is more robust than the right-tail probability function under default deals conditions.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3427721

DOI: 10.1155/2024/3427721

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