The value of the operational side of the business is termed the "Enterprise Value" [although the EV does take into account financing effects as the debt/equity/other mix affects the Weighted Average Cost of Capital (WACC) i.e. the discount rate]. This is the total value of the business.
That value is divided amongst the firm's debt, equity, and hybrids. The value of the equity is the Enterprise Value minus all the more senior claims to the cash flows of the business (like the debt, preference shares etc.).
An example, to respond to the previous question:
Let's say AAA is worth $100mm, with $20mm of debt and $80mm of equity. AAA acquires a project at no cost which increases the value of the company to $200mm. The value of the debt once issued essentially depends on the risk free rates + the default risk of the company. Assuming that AAA had low default risk when it was worth $100mm, the default risk will be slightly but not significantly (as it is already quite low) lower (assuming the new project is not highly risky..long story). So the debt should still be worth about $20mm. The value of the equity will make up the remainder, being $180mm - so each share will have gone up 125%.
EDIT: This is the 100% theoretical side, of course in reality with fluctuating market prices the actual picture of what's going on is confusng..