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Assuming we are talking about a cash dividend:
Suppose Enterprise Value is 100.
A 10 dollar cash dividend is paid out.
Therefore, retained earnings will decrease by 10 - equity value decreases by 10
So, now we have enterprise value of 90.
However, 10 dollars must be paid - so cash (which is subtracted from EQV as it is already implied, and EV only includes operating assets) decreases by 10, which "increases" the EV back to 100.
So you are correct: EQV should decrease and EV will stay the same.
A more intuitive way is to realize that paying a dividend only influences capital structure, and not operating assets. This means that EV will not change.

 

I will say I am just a prospect, so take this with a grain of salt. I am going off intuition here.

EV is the value of net operating assets to all stakeholders, yes. A sale and leaseback, from my understanding, is the sale of a fixed/operating asset (which would decrease EV, since you have sold an operating asset) and then leasing it back from the firm that you sold it to. Now, what is interesting is that I am not sure if it would be considered a capital lease in this case. Leases are generally included in enterprise value, as they are treated as "debtors. So I guess, no change as you said.

Would be great if someone more experienced could chime in.

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