I study a model of bank capital regulation where, in order to meet regulatory capital requirements on new investments, the bank must issue equity to a market that is less informed about the value of its existing assets (Myers and Majluf (1984)). In such a situation, banks with good news will optimally forgo positive net present value projects whenever the capital requirements are too high, providing a micro-foundation for the cost of capital to society. I characterize the optimal regulatory mechanism in this context and show that while the regulator can always choose a mechanism that reveals the private information of the bank to the market (thereby resolving the underinvestment problem) it is not always optimal to do so. Namely, when the probability that the bank receives bad news about its existing assets is low, the optimal mechanism involves a pooling regulation whereby the bank's capital requirement does not vary with its private information. If instead the probability of receiving bad news is high, a separating mechanism that reveals the bank's private information to the market is preferred, but only when there is a large difference in the value of the bank's assets with respect to its private information. This sheds light on how the optimal regulation should be adjusted throughout the business cycle and with respect to the opacity of the bank's assets. Finally, I study how the optimal mechanism should be adjusted to account for moral hazard with respect to the risk and opacity of the bank's assets.