Division Carveout in LBO

Struggling with this and would be much appreciated if someone can walk me through. Namely, I am building an LBO where the fund would carveout a division from a target company. Assuming you can sell the division for X after 1 year of holding the full group, how do you build the LBO to account for the lack of cash flows coming from the sold division, as well as the need to adjust cost items?

Also, is it correct to cut out the cash flows from the sold business, as theoretically I would expect the target would want to be paid for the full group and doesn't necessarily care we don't get a benefit from the cash flows of that division, so technically should it be valued as a group?

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