If company shares are cheaper than other source of money, then company can buy back them, or other potential owner can buy them. It also sends strong signal to owners and investors about future of the company.
If company shares are costing more than other sources of money, then company can sell more of them to return costly money back or to expand business.
For example, bank rent rate is 10% per year. Company worth is $1 million. Company created 1 million of shares. 1 share is $1 of company worth. Company pure profit is 10% per year. Company needs $1 million in circulation to operate.
If company will rent money from bank, it will have 10%-10%=0% of profit. If company will sell 100% of shares, it will have 10%-0%=10% of profit, but this profit will go to someone else. If company will sell 50% of shares and will rent $0.5 million from bank, it will have 10%-5%=5% of profit, 2.5% will go to company, 2.5% will go to other owners. By reinvesting this profit, company can reduce bank money or expand company to worth more, increasing company profit share.