Control Premiums and Minority Discounts Using Multiples

Hi there,

I'm currently writing a paper about how to apply control premiums and minority discounts in terms of multiple valuation. My focus is to valuate a private company with publicly traded comparable companies. So during my research I came across some questions:

Given the following value basis:

control value -> free marketable minority value and in between lays the control premium/minority disocunt.

I'm struggling hard to connect these two value types to the enterprise value and the equity value based on trading multiples. And I also find it hard to decide wheter to use enterprise value multiples and equity value multiples, especially in relation to the premiums and discounts.

Is the EV considered as the control value? Can the free marketable minority value be considered as the market cap?

For example:

If I have a company that wants to buy a 90% share of a private company. How would the valuation with multiples look like for the 90% share and also for the 10% one?

I hope this isnt to confusing - but I am confused ;-)

Thanks :) Dave