Alex's business is experiencing diminishing market shares and no longer needs any external finance. In fact, it is trying to buy back its stock and pay off its debts. At which stage is Alex's business in?

Alex's business is in the Maturity Phase of the business life cycle.

In the 4-Stage model (Introduction, Growth, Maturity, Decline), the maturity phase includes an excess of cash which can be paid out as dividends or reinvested in the company, and also features a more competitive environment, often due to copycats, which take away market share.