I believe the market will determine the new price - buyer and seller agreeing on some value/per share. This is the difference between this distribution being a dividend vs being a forward split. A forward split would automatically reduce the pps by holding the market cap constant and then calculating the pps from the new number of outstanding shares. A dividend will not automatically change the price; the market demand/supply will create a new price. Theoretically, if there is great news released prior to market opening, the pps could jump to $50 (or any other number) if that is what the demand/supply dictates for the first trade.
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