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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.

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.

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.

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.

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.

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.

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.

This study examines the appropriate measures that need to be intensified among African countries to achieve sustainable environment to mitigate climate change.

The study employs panel data covering the period 2000 to 2020 among 54 African countries and Cox proportional hazard model for the analysis.

Estimates indicate that the practice of carbon farming, the development of rooftop gardens, renewable energy production and consumption contribute positively toward achieving sustainable environment, while governance adversely affects this objective of achieving sustainable environment.

The study recommends that governments should enforce the constant practice of carbon farming among these countries through passing laws to enforce its application among farmers and allocate 2% of ministry of agriculture's budget toward financing carbon farming for poor farmers.

Empirical studies have been carried out exploring measures to deal with climate change. Nonetheless, the appropriate measures of achieving sustainable environment to mitigate climate change have less been explored in literature on Africa. Hence, this study fills the gap in existing empirical studies.

The peer review history for this article is available at: https://publons.com/publon/10.1108/IJSE-04-2023-0290.

Pre-construction of a project comprises stages that are pivotal for the procurement performance. It is defined as the duration from the project's initiation to construction. However, Private Public Partnerships (PPPs) have been subjected to a long pre-construction, thereby leading to an inefficient development process. Therefore, the purpose of this paper is to pay attention to the influencing factors elongating the pre-construction duration.

Based on data of 5,677 PPP projects between 2009 and 2021 in China, the authors adopt the Accelerated Failure Time (AFT) model in duration analysis to empirically analyze the following underlying dynamics determining the duration of PPP pre-construction stages: (1) policy uncertainty; (2) corruption; and (3) procurement method selection. To observe the influencing paths more specifically, the authors divided the pre-construction duration into the pre-tendering period and tendering period and regressed them separately.

The results indicate that the pre-construction duration is significantly prolonged with increased policy uncertainty and corruption degree as well as the use of tendering methods. Meanwhile, the above factors have a greater impact on the pre-tendering period than the tendering period.

The contribution of this study is twofold: (1) theoretically, this paper provides new evidence on the impact of PPP policy uncertainty, corruption and procurement method selection on the pre-construction duration. It complements empirical studies on the factors elongating the time efficiency of PPPs projects. (2) In practice, it provides a specific path for the government to improve the time efficiency of PPPs.

The purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.

The paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.

The study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.

The research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.

The study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

The damping accumulated discrete MGM(1, m) power model is proposed for the problem of forecasting the share of agricultural output value and the share of employment in China.

In this study, the damping accumulated discrete MGM(1, m) power model was developed based on the idea of discrete modelling by introducing a damping accumulated generating operator and power index. The new model can better identify the non-linear characteristics existing between different factors in the multivariate system and can accurately describe and forecast the trend of changes between data series and each of them.

The validity and rationality of the new model are verified through numerical experiment. It is forecasted that in 2023, the share of agricultural output value in China will be 7.14% and the share of agricultural employment will be 21.98%, with an overall decreasing trend.

The simultaneous decline in the share of agricultural output value and the share of employment is a common feature of countries that have achieved agricultural modernisation. Accurate forecasts of the share of agricultural output value and the share of employment can provide an important scientific basis for formulating appropriate agricultural development targets and policies in China.

The new model proposed in this study fully considers the importance of new information and has higher stability. The differential evolutionary algorithm was used to optimise the model parameters.