Without condemning nor condoning the cost of IPOs in general: it's because it's very expensive to "make a market" for public consumption of a previously (ostensibly) unknown security. The modern model of IPOs may not be as applicable these days due to the rise of private equity, but the essence of the problem is that you're herding a lot of very expensive cats to do due diligence on a thing involving a lot of money.
When you're deploying a small army of lawyers, investment bankers and accountants, the costs tend to add up really quickly. To respond to your specific question about the cost of the IPO in proportion to its size: there is a floor on how expensive a traditional IPO will be when all IPOs have a certain minimum amount of due diligence required. Even if the IPO itself is not remarkably large, there is something of an "activation level" that you'll pay just to initiate the process and get everything moving.
What kind of due diligence is required? Isn't the concern here mostly how the stock should be priced?
And why then are private funding rounds so much cheaper to get done? Diligence still has to be done for private funding. Why is more diligence required for an IPO?
It's hard to give a comprehensive answer to your first question since it would require so much background knowledge of valuation. But in short:
> Isn't the concern here mostly how the stock should be priced?
Yes, and this is extremely nontrivial :) There are many competing incentives and metrics to evaluate. Public investors want to buy at a discount relative to future growth. The company wants to get as much money as possible. Investment banks don't want to be associated with fraudulent or poor performing IPOs. They also want to ensure there is sufficient liquidity to make the market move on the new security when it's listed while making everyone happy. And aside from these logistical obstacles, you have the standard financial problem of price discovery and valuation for a security which is fundamentally new.
As for these questions:
> And why then are private funding rounds so much cheaper to get done? Diligence still has to be done for private funding. Why is more diligence required for an IPO?
Private funding involves proportionately greater amounts of money from fewer overall investors. It does not as a rule involve the general investing public. By law public investments must be secure against a number of risks that can be accepted in private investments. You're offering a novel security to a large population of amateur investors who cannot tolerate as much risk as professional investors who either represent institutions or are independently wealthy. Insulating IPOs from that kind of risk requires a lot of due diligence.
Depends on the capital structure of the corporation, the financing deals it has, and the nature of the business it runs.
To simplify quite a bit: You're going to need to make sure the earnings it has aren't juiced, that it owns what it says it does, that it isn't going to violate any agreements it has, and that the people running it aren't questionable.
When we zoom in, recognize that you need actual evidence to move forward - and that's way more expensive than you'd imagine at first glance.
It isn't enough to write "Jim said we own a plot of land with nice trees", either. To unpack that one element of due diligence, you'll need the deed to the land, the land registry document confirming ownership, a report from an arborist attesting to the fact that the trees are of the right quality and type, an accountant's quality of earnings determining the value of the tree-fruit, etc.
When you're deploying a small army of lawyers, investment bankers and accountants, the costs tend to add up really quickly. To respond to your specific question about the cost of the IPO in proportion to its size: there is a floor on how expensive a traditional IPO will be when all IPOs have a certain minimum amount of due diligence required. Even if the IPO itself is not remarkably large, there is something of an "activation level" that you'll pay just to initiate the process and get everything moving.