Discount for Lack of Control

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archived_user

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DLOC = 1/ (1-Control premium)
Easy formula to remember. However, I’m just curious at why not DLOC = 1 - Control premium? (Discount + Premium = 1)???
Can someone explain in easy way please?
Thank you.
 
Well, formula is not correct. It should be like this:
DLOC = 1 - 1 / (1+Control Premium).
Premium is added. Say 25% premium means A*(1+25%). If we have A=100, then we will get 125.
So let’s imagine that stock value is 100, but if we have control of it, the value of the stock for us will be higher - 125.
Now, the opposite. Stock price is 125 assuming if we have control. For an investor, which does not have control, stock price should be equal to 100. Let’s calculate the discount on 125 that is needed to arrive on 100.
Intuitively, DLOC = (125 - 100) / 125 = 20%.
Using the curriculum formula: DLOC = 1 - 1 / (1+Control premium) = 1 - 1 / 1.25 = 20%.
You see? Absolute value of DLOC and absolute value of control premium are not equal. Their sum cannot amount to 1.
 
In math at school, there were such problems showing that if we want to add X percentage to number A to get number B, and then deduct Y percentage from number B to get number A, percentages X and Y will be different from each other.
 
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