During buyouts, why don’t companies buy at the current share price?

Broadcom is buying VMWare and the stock is currently up $20/share, or 21%.
Why doesn't BRCM just spend billions buying VMW at the lower share price, then announce they'll pay $120/share (or whatever the buyout price is).
The market cap Friday was ~ $38 billion, and now it's $49 billion. Isn't this strategy costing BRCM billions more?