The cost of capital is a critical concept in corporate finance, representing the return required by investors for providing capital. When comparing the cost of retained earnings to the cost of equity, it's important to understand their relationship. Retained earnings are profits that a company keeps to reinvest in its business rather than distributing as dividends. The cost of retained earnings is essentially an opportunity cost: the return shareholders could have earned if the earnings had been distributed as dividends and reinvested elsewhere.
The cost of retained earnings is generally equal to the cost of new equity, but without flotation costs. Flotation costs are the expenses incurred when a company issues new securities, such as underwriting fees, legal fees, and administrative costs. These costs are absent when a company uses its internally generated retained earnings. Therefore, while the underlying opportunity cost for shareholders is the same (the return they expect on their equity investment), the cost of retained earnings is slightly lower than the cost of *new* equity due to the absence of these issuance expenses. It is certainly not zero, as there's a clear opportunity cost, nor is it always higher or always lower without qualification.