Shaun Shuxun Wang, Jing Rong Goh, Didier Sornette, He Wang and Esther Ying Yang
Many governments are taking measures in support of small and medium-sized enterprises (SMEs) to mitigate the economic impact of the COVID-19 outbreak. This paper presents a…
Abstract
Purpose
Many governments are taking measures in support of small and medium-sized enterprises (SMEs) to mitigate the economic impact of the COVID-19 outbreak. This paper presents a theoretical model for evaluating various government measures, including insurance for bank loans, interest rate subsidy, bridge loans and relief of tax burdens.
Design/methodology/approach
This paper distinguishes a firm's intrinsic value and book value, where a firm can lose its intrinsic value when it encounters cash-flow crunch. Wang transform is applied to (1) calculating the appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs, (2) describing the frailty distribution for SMEs and (3) defining banks' underwriting capability and overlap index in risk selection.
Findings
Government support for SMEs can be in the form of an appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs.
Research limitations/implications
More available data on bank loans would have helped strengthen the empirical studies.
Practical implications
This paper makes policy recommendations of establishing policy-oriented banks or investment funds dedicated to supporting SMEs, developing risk indices for SMEs to facilitate refined risk underwriting, providing SMEs with long-term tax relief and early-stage equity-type investments.
Social implications
The model highlights the importance of providing bridge loans to SMEs during the COVID-19 disruption to prevent massive business closures.
Originality/value
This paper provides an analytical framework using Wang transform for analyzing the most effective form of government support for SMEs.
Details
Keywords
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.
Abstract
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.