Final answer:
In Modigliani and Miller's world without taxes, altering debt-to-equity ratios does not impact firm value due to perfect capital markets. However, the firm's private benefits from investment affect its borrowing decisions, potentially leading to less borrowing than the social optimum.
Step-by-step explanation:
The question pertains to the Modigliani and Miller theorem which theorizes about the debt-to-equity ratio in firms and its effect on firm value in a world without taxes. In the Modigliani and Miller framework without taxes, changes in a firm's debt-to-equity ratio do not affect the firm's value. This is because, according to the theorem, in a perfect market without taxes, bankruptcy costs, or asymmetric information, the total value of a firm is determined by its operating income and investment decisions, not by how that income is split between debt and equity.
However, the scenario provided implies that the firm can fully monopolize the total benefits of its investments, which would adjust its private demand curve. If the firm can only accrue private benefits from its investments or innovations, under an 8% borrowing rate, it would opt for $30 million of finance. Still, from a societal perspective, the optimal borrowing level would be $52 million to maximize benefits for society as a whole. The firm's choice to borrow less than the socially optimal level indicates a disparity between the firm's incentives and society's interests.
Positive externalities of a firm's investment, such as advancements in technology, can benefit society and warrant a higher level of investment. However, if a firm cannot internalize these social benefits, it might invest less than is socially optimal. This demonstrates the interplay between private and social considerations in financial decisions made by firms.