Final answer:
Both mature and declining companies may be involved in purchasing treasury stock, as it is a way to manage their capital structure without committing to recurring payments or diluting ownership further.
Step-by-step explanation:
When investigating the financial statements of two companies, one in the maturity phase and another in the decline phase, a common financial activity that both may be involved in is purchasing treasury stock (C). Both mature and declining companies might buy back shares to consolidate ownership, send positive signals to the market, or simply because they have excess cash and no profitable new investments.
Taking out new loans (A) and issuing bonds (B) involves committing to scheduled interest payments, which might not be ideal for a company in decline as it may not have sufficient income to meet these obligations. Issuing common stock (D) would not typically be an activity for companies in either of these stages, as mature companies might already have substantial equity and do not need to dilute ownership further, whereas declining companies may not attract new equity investors easily.