Increasing enterprise value. Increase share price or pay out dividends. I ain't got no MBA, but I sure as heck can't figure out what else a shareholder would actually want. If you've started a high tech entrepreneurial VC funded business, don't try to pay out a dividend. Good way to lose your job. So, that pretty much leaves share price. Now, there are lots of externalities here, but the idea is to govern towards positive trends: higher revenue, lower expenses, a few key ratios that exhibit a healthy company
Minimizing risks. The shareholders trust management to be close enough to the business to objectively perceive and report risks. I suppose there are lots of ways to minimize risk, but the most effective one I can identify is staying focused on a clear strategic direction. Another key way to manage risk is to understand the absolutely essential expenses in the business and manage them to be lower than the overall revenue. If things get tight, management shouldn't be cutting into bone.
Aligning interests. I've said several times in this series that representing the interests of shareholders, customers and employees should never be mutually exclusive. This doesn't happen by accident, but by setting intentional direction for the company. The mission of the business should clearly benefit all of these groups.
Transparency. Accurate reporting and auditing, accountability, and non tolerance of dishonesty. These are absolutely critical in today's business environment. Hire only people you trust, and then setup controls that don't depend on that trust.