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Done right, it should be over and above the premium for synergy but doing it right requires that you value control and synergy from scratch (and not with arbitrary rules of thumb - say 20% of value)
The control premium should not include synergy. However, depending on how you are estimate the control premium, you could have elements of synergism reflected in the premium data. For example, if you are estimating the control premium by analyzing acquisition premium data (i.e. companies acquiring100% controlling interests in publicly traded, minority, stocks), then the control premium could contain synergistic premiums to the extent the deal was synergistic. More importantly, if you operate under the assumption that publicly traded stocks trade at or near their controlling values, then acquisition premium data largely reflects synergy. On the other hand, if you are estimating the control premium using a discounted cash flow analysis, then whether the premium reflects synergy is solely dependent upon the cash flows used in the model. If done correctly, then then the premium should only reflect control. For example, if the company is currently overcompensating the CEO relative to fair market rates, then normalizing the salary would be a control adjustment. The present value of the after-tax differential in the salaries would reflect a control premium. However, if you incorporated another element in the cash flow stream, say, a lower tax rate because of favorable tax-loss carry forwards that the buyer could bring to the table, then that is synergistic. So, it just depends on how you formulate your equations.