Why would a private company have a higher multiple ?

Well it comes down to why and what you value a company on. Private markets are less liquid but traditionally valued things could be high potential for growth in the future. The word ‘premium’ is odd though, because maybe there’s a premium on the COE for being illiquid and not necessarily positively for being private if that makes sense. But usually squestions like this is something like growth potential

Faster growth rate, proprietary technology, a better brand, more loyal customers. Example: Beyond Meat and Impossible Foods... Impossible has a GMO heme which enables them to create better products than BM.

Apart from what others said above, my first answer to this question would be: "Priced at a premium based on what? P/B, P/S, P/E, EV/EBITDA". If this is the way the question was asked, with no other info, it's confusing.

Also, smaller companies (private or public), tend to command lower multiples than listed ones, as they are seen as higher risk. The illiquidity matters less if you are looking at the entire company vs a share: a share can be illiquid if private and liquid if listed. However, if you have 50% of a listed firm and want to sell, it is almost as illiquid as 50% of a private company.

This is a medium to advanced level IB technical that usually tech boutiques will ask. The main answer is illiquidity premium and higher risk. The fuller explanation can be derived from the above users' explanations.

EDIT: The above answer is incorrect. I was thinking about why the cost of equity for private companies might be higher than that of public companies. An increased cost of equity leads to a higher WACC, which then leads to a discounted valuation. Hominem is correct as usual. Thank you for noticing!