The skeleton of a man with a severe dislocated fracture of the knee, found in a cemetery in Lund, southern Sweden, is helping to unravel the complexities of social attitudes towards individuals with disabilities in the late medieval period. The research combines traditional osteological methods and 3D modelling - a cutting-edge technique for viewing and studying traumatic injury and related skeletal changes - with contextual information from historical texts and digitized excavation records to build a more nuanced understanding of disability and care in the past.

New research shows that cyberbullying should be classified as an adverse childhood experience due to its strong link to trauma. Even subtle forms—like exclusion from group chats—can trigger PTSD-level distress. Nearly 90% of teens experienced some form of cyberbullying, accounting for 32% of the variation in trauma symptoms. Indirect harassment was most common, with more than half reporting hurtful comments, rumors or deliberate exclusion. What mattered most was the overall amount of cyberbullying: the more often a student was targeted, the more trauma symptoms they showed.

Together, or not together, that is the question. Hamlet is not the only one facing life-changing questions – wild animals have to make decisions pivotal to their survival on a daily basis. In a modelling case study, scientists of the GAIA Initiative investigated whether exchange of information among African white-backed vultures (Gyps africanus) bring more advantages than disadvantages to the individual vulture in its search for food. They found that social foraging strategies are overall more beneficial than non-social strategies, but that environmental conditions such as vulture and carcass densities greatly influence which strategy yields the best results.

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.