What should the equity split be between partners where one provides all the capital and the other runs the business?
I think my one suggestion here is to split them apart. Split the shares one of you gets for investing capital apart from the shares you get for being co-founders for the next 10 years.
First, decide what the right equity split is for the go-forward co-founding team. 50/50? 80-20? 90-10?
Then, decide on a valuation for the capital coming in. It may be a very low valuation, but decide on one.
For example, what you’ll often see is say a 50-50 split in founder stock, but then, one founder’s $100,000 contribution valued at a say $300,000 post-money valuation. In other works, this co-founder also buys 1/3 of the company for that $100,000.
As a result, Founder A now owns 66% and Founder B 33%, but their “founders stock” is equal prior to the investment:
Sometimes, some of this investment can also be “in kind”, i.e. for sweat equity and other work before the second co-founder joins. It doesn’t have to be cash. But if you value it, it makes things fairer here. Or at least, easier to grok.