Minimum Cash Balance / Effect on Equity and EV - LBOs

Hi all, 

I'm having trouble understanding what happens with the min cash balance during a LBO. 

Example Scenario

EBITDA = 10m, EV = 10x / £100m, existing debt = £20m, existing cash = £30m (£25m is excess, remainder min cash).

Assume the buyer takes on existing debt and cash on balance sheet and no new debt raise.

My Indicative S&U

Uses = Equity value / offer : 110m (100-20+30), Existing Debt: 130m === TOTAL 130m

Sources = Excess Cash: 25m, Sponsor Equity = 105m === TOTAL 130m

Is this this correct? My key issue is I don't understand what happens with the minimum cash - why are we paying the seller more for the minimum cash if it's considered part of the core operations and should already be reflected in the EV? Should the offer value be £5m less?

Thanks for any guidance!