The institute is of course named after the notable economist and novelist. The purpose of the Ayn Rand Institute is to promote the ideas and works of Ayn Rand. The essentials of these ideas are reason, egoism, individual rights and capitalism. Business ethics is just a category of ethics that applies in the world of business. Objectivism upholds the idea that rational self-interest is the ethical basis for human behavior in general and therefore for business behavior in particularly.
Businesses are ethical to the extent that they act in their own self-interest.
For a public corporation this would mean that it is ethical if it works to maximize shareholder wealth. Thus there is no contradiction between ethical behavior and business. Under capitalism, every productive individual can make a living and do well. On the contrary, the mixed economy and socialism deny individuals the ability to make a living and work for themselves. According to Ayn Rand productivity is an essential virtue, and under capitalism productivity is always rewarded.