Actually adventured is right on non-operating cash being usually discounted. In general the second company will not be valued at $10bn more than the first.
Would you rather have a $1 in cash and a $9 share in the first company, or a $10 share in the second company where $1 is the cash per share? The second case is more risky so you wouldn't pay the full extra $1 for the second share.
Of course it could also be the case that the spread is larger than $1, if the first company is too short on cash and there is a liquidity risk depressing the valuation.
Would you rather have a $1 in cash and a $9 share in the first company, or a $10 share in the second company where $1 is the cash per share? The second case is more risky so you wouldn't pay the full extra $1 for the second share.
Of course it could also be the case that the spread is larger than $1, if the first company is too short on cash and there is a liquidity risk depressing the valuation.