Funding startups using contingent option of value appreciation: theory and formula

Wang，Shaun Shuxun

2023

10.1108/CFRI-04-2023-0088

China Finance Review International   Impact Factor & Quartile

2044-1398

2044-1401

Purpose: This paper provides a structural model to value startup companies and determine the optimal level of research and development (R&D) spending by these companies. Design/methodology/approach: This paper describes a new variant of float-the-money options, which can act as a financial instrument for financing R&D expenses for a specific time horizon or development stage, allowing the investor to share in the startup's value appreciation over that duration. Another innovation of this paper is that it develops a structural model for evaluating optimal level of R&D spending over a given time horizon. The paper deploys the Gompertz-Cox model for the R&D project outcomes, which facilitates investigation of how increased level of R&D input can enhance the company's value growth. Findings: The author first introduces a time-varying drift term into standard Black-Scholes model to account for the varying growth rates of the startup at different stages, and the author interprets venture capital's investment in the startup as a “float-the-money” option. The author then incorporates the probabilities of startup failures at multiple stages into their financial valuation. The author gets a closed-form pricing formula for the contingent option of value appreciation. Finally, the author utilizes Cox proportional hazards model to analyze the optimal level of R&D input that maximizes the return on investment. Research limitations/implications: The integrated contingent claims model links the change in the financial valuation of startups with the incremental R&D spending. The Gompertz-Cox contingency model for R&D success rate is used to quantify the optimal level of R&D input. This model assumption may be simplistic, but nevertheless illustrative. Practical implications: Once supplemented with actual transaction data, the model can serve as a reference benchmark valuation of new project deals and previously invested projects seeking exit. Social implications: The integrated structural model can potentially have much wider applications beyond valuation of startup companies. For instance, in valuing a company's risk management, the level of R&D spending in the model can be replaced by the company's budget for risk management. As another promising application, in evaluating a country's economic growth rate in the face of rising climate risks, the level of R&D spending in this paper can be replaced by a country's investment in addressing climate risks. Originality/value: This paper is the first to develop an integrated valuation model for startups by combining the real-world R&D project contingencies with risk-neutral valuation of the potential payoffs.

Float-the-money option Time-varying growth rate Venture capital

English

First ; Corresponding

2-s2.0-85169830392

Scopus

Southern University of Science and Technology,Shenzhen,China

Wang，Shaun Shuxun. Funding startups using contingent option of value appreciation: theory and formula[J]. China Finance Review International,2023.

Wang，Shaun Shuxun.(2023).Funding startups using contingent option of value appreciation: theory and formula.China Finance Review International.

Wang，Shaun Shuxun."Funding startups using contingent option of value appreciation: theory and formula".China Finance Review International (2023).