Rocket Lab USA (RKLB, Nasdaq) had a market value on April 18^th 2022 of $3.92 billion.  Rocket Lab is a non-governmental space launch company, offering customers access to the Electron small orbital launch vehicle, which it boasts is the second-most frequently launched US rocket. The Electron, which boosts payloads up to 300kg into low Earth orbit, is on the only reusable small launch vehicle in service. Rocket Lab has completed 25 Electron launches to date, successfully deploying 112 satellites into orbit. (This is true; what follows is made up.)  The CFO knows the true value of the company; however, all that outsiders know is that there is a probability of 0.27 that its  value is $1b. and a probability of 0.0.73 that its true value is $5b. 

Rocket Lab is developing the Neutron rocket, a large-scale reusable launch system, which will be able to deploy a 13,000kg payload into low Earth orbit, or a 1,500kg payload into an orbital trajectory to Mars or Venus.  However, it will need an additional investment of $1.2b. which it is planning to raise through an equity issue.  It can only make the investment through an equity issue and if it does make the investment, it will be able to obtain the NPV of the new project, which is $0.05b.

Answer the following questions:

1. 1) Will the managers of Rocket Lab issue equity to raise the funds for the new investment if they know that the true value of the firm is $1b.
2. 2) Will the managers of Rocket Lab issue equity to raise the funds for the new investment if they know that the true value of the firm is $5b.?
3. 3) If the managers announce that they are planning to issue new equity worth $1.2b what will happen to the stock price upon this announcement (but before the actual equity issuance)?