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

• Published in: China finance review international Vol. 14; no. 1; pp. 173 - 190
• Main Author: Wang, Shaun Shuxun
• Format: Journal Article
• Language: English
• Published: Beijing Emerald Publishing Limited 06.03.2024; Emerald Group Publishing Limited
• Subjects: Angel investors; Brownian motion; Business models; Economic growth; Entrepreneurial finance; Failure; Funding; Growth rate; Investments; Mortality; Performance evaluation; Private equity; R&D; Research & development; Research & development expenditures; Startups; Stochastic models; Valuation; Venture capital; Time-varying growth rate; Venture capital; Float-the-money option
• ISSN: 2044-1398; 2044-1401
• DOI: 10.1108/CFRI-04-2023-0088

PurposeThis 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/approachThis 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.FindingsThe 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/implicationsThe 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 implicationsOnce 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 implicationsThe 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/valueThis 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.