Minority discount
Valuation & CompsA reduction applied when moving from a control basis value to the value of a stake that cannot direct the business.
Also written: discount for lack of control, DLOC, lack of control discount
A minority discount and a control premium describe the same gap from opposite ends. The premium grosses a minority value up to a control value; the discount brings a control value down to a minority one. They are not the same number, which is where people trip.
The arithmetic: gross 100 up by a 25% premium and you get 125. Coming back down from 125 to 100 is 25 over 125, so 20%. In general the discount equals the premium divided by one plus the premium, so a 30% premium corresponds to a 23% discount.
Whether it applies at all depends on the basis you started from. A value built from listed peer multiples is already a minority value, because it came from the prices of small parcels of shares, so applying a minority discount to it charges twice for the same lack of control. It belongs against a value derived from precedent transactions, or one already grossed up by a control premium.
It is distinct from the illiquidity discount, which compensates for not being able to sell rather than for not being able to direct. Both can apply to the same stake, in which case they multiply rather than add, and each has to be justified separately or the whole calculation looks like a series of haircuts chosen to reach an answer.
Worked example
A business is worth 750 of equity on a control basis. A 10% stake pro rata is 75.
A 20% minority discount takes it to 60. If the company is also private, a further 25% illiquidity discount takes it to 45, a combined 40% rather than the 45% that adding the two would suggest.