I'm not sure why there needs to be any factor for purchased ships. My joke about privateers buying ships aside, I know some people do buy ships - once you have high enough rank to get them and enough money to afford them, it may be quicker than hunting around for an enemy group and hoping it has the type of ship you want. Regardless if you're a merchant or a privateer, if you bought the ship then it's yours honestly and you should be able to sell it for full price, plus or minus commerce skills and perks.
Prize ships, by contrast, would normally be disposed of by an admiralty court which is why your commerce skill doesn't work, you're not the one selling them. Then you get a fixed percentage of the proceeds, i.e. the 25%.
Merchants should at most get the same 25% for captured ships as privateers. According to what I read on the Wikipedia article on LoM's, they should not get anything as they shouldn't be taking prizes anyway - it was only legal to take a prize if you had a LoM, which is why the East India Company got them for its East Indiaman ships.
Prize ships, by contrast, would normally be disposed of by an admiralty court which is why your commerce skill doesn't work, you're not the one selling them. Then you get a fixed percentage of the proceeds, i.e. the 25%.
Merchants should at most get the same 25% for captured ships as privateers. According to what I read on the Wikipedia article on LoM's, they should not get anything as they shouldn't be taking prizes anyway - it was only legal to take a prize if you had a LoM, which is why the East India Company got them for its East Indiaman ships.