Transaction EV with min. cash balance

In an LBO, how do you think about EV and deal value when you are incorporating a minimum cash balance.

Let's say you have EqV 1,000m, Gross debt 500m, and cash on balance sheet of 300m. EV should be 1,200m.

Sources:

• Sponsor equity: [600]m
• Acquisition debt: [600]m

Uses:

• Acquisition of equity: 1,000m
• Paydown of net debt: 200m

How would the EV, deal value and S&U change if you need to maintain a min. cash balance of 200m and you are using the existing cash on balance sheet to do this? This is what I am thinking:

The EV of the company doesn't change, but I am not sure about the deal size and the S&U. This is what I think is most accurate, but I'm not sure.

Sources:

• Sponsor equity: 800m
• Acquisition debt: 600m
• Cash on balance sheet: 200m

Uses:

• Acquisition of equity: 1,000m
• Paydown of net debt: 400m
• Funding min. cash balance: 200m

The way I'm thinking about it is that in order to maintain a min. cash balance of 200m, somehow, the sponsor needs to get an additional 200m, either from their own funds (in which case they can use balance sheet cash to fully repay debt, or by using balance sheet cash in which case the sponsor needs an additional 200m to repay debt). So while the EV is always constant (1,200m), the deal size (at least how it looks in S&U) is now inflated by 200m. Is this correct? Is there a better way to illustrate this in the S&U? I was thinking to put two rows, so total sources for the txn and then below, transaction-implied company EV.