New issue of common shrares to investor

Hi, If a company wanted to get an equity infusion from a new investor, could it issue new shares to the investor and price these shares lower than what the other outstanding shares are trading at? If possible, are there any other key criteria to take into consideration?

Example: Company X has 1,000 shares out standing at $10. Can it issue 100 news shares to company Y @$5?

Thanks!

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