Downstream firm's equity financing for capacity expansion in a supply chain

In this research, we investigate a supply chain consisting of a downstream firm who purchases a component from an upstream firm and then transforms it into a final product. The downstream firm has a production capacity constraint and considers to raise capital from an investor through equity financing. The raised capital not only enables the downstream firm to expand the capacity but also allows the investor to hold equity shares in the downstream firm. We derive the optimal pricing and production decisions of the two firms and discuss the optimal equity financing strategy of the downstream firm. We consider two distinct models: the external equity financing model, where the capital is raised from an outside institution, and the internal equity financing model, where the capital is raised from the upstream firm. We show that because the cooperative relationship between the two firms can be improved in the internal equity financing model, the production quantity in this model may be even higher than that in a benchmark model with no capacity constraint and no equity holding by the investor in the downstream firm. In addition, the original shareholder of the downstream firm gets more benefit from the internal equity financing activity than from the external equity financing activity. We also analyze the impacts of the key model parameters on the equity financing strategy and find that the dependence of the financing strategy on the initial asset of the downstream firm is quite different in the two models. Moreover, when the production cost of the downstream firm is changed, less capital raised for expanding capacity may create more value for the original shareholder of the downstream firm in each model. Finally, we show that the key finding remains unchanged when deterministic demand is changed to stochastic demand.