Having trouble understanding how PE shops make money off of an LBO...

To simplify (a lot): think of a company's value (total enterprise value, or TEV) as total equity + total debt.  Mechanically, when KKR buys a company from the public markets, the company has some TEV, which is its its value in the public markets + its total debt outstanding.  Let's use a concrete e.g.  Say KKR is buying Company A, with TEV 10 bn today.  KKR will pick a certain amount of equity to put down on the detail--often around 30%, so lets say $3 bn of equity value.  KKR approaches banks to get $7 bn worth of debt financing, using the company as collateral (let's ignore looking at how the debt is structured for now).  That's what makes PE "risky" then--if the company goes bankrupt, the debt-holders will be paid back first, but if it grows in value, then the growth goes to the equity holders.  That's essentially what leveraging is.  So, for example, let's say that the debtholders on average are being paid 10% interest (~L+450, which is reasonable for a company that would be highly levered after a PE deal, but is still worth $10 bn.  The actual debt payment for a given slice if debt depends on its seniority--i.e. different liens are paid different amounts--and the leverage through those notes--total debt that is senior to the notes in question/EBITDA).  So every year, KKR needs to pay $700 MM worth of debt off.  Everything beyond that $700 MM in debt payments, and beyond that $7 bn in debt outstanding in the cap structure, accrues to the equity holder.  So now let's say that KKR thinks it can grow this company at 10% per year...I'll calculate value accretion for KKR in one years (I'm making it real simple, assuming no refi of debt):

Year 0: total debt = 7bn; total equity = 3 bn; TEV = 10 bn

Year 1: total debt = 7 bn; TEV = 11 bn (10% growth), total equity = TEV - total debt = 4 bn; gains to KKR = 4 bn - 700 mm in debt payments = 3.3 bn = 10% YOY growth (3.3 / 3).

OK, that's not great for KKR--they'd be getting the same IRR on their equity as debtholders would be getting on (much safer) debt.  But now let's say KKR thinks it can get 15% returns:

Year 0: total debt = 7bn; total equity = 3 bn; TEV = 10 bn

Year 1: total debt = 7 bn; TEV = 11.5 bn (15% growth), total equity = TEV - total debt = 4.5 bn; gains to KKR = 4.5 bn - 700 mm in debt payments = 3.8 bn = 27% YOY growth.

So by increasing growth by 5 percentage points, KKR increases IRRS 2.7x, or 17 percentage points.  That's because KKR is essentially being compensated for holding the riskiest part of company A's cap structure (unless there were holdco debt or a holdco PIK) by being able to take advantage of upside in returns.  If the company's growth can exceed the total debt payments, then KKR is rewarded at a leveraged level.

This is the most basic way to drive IRRs--buy a company, leverage it, grow it at a rate faster than debt payments accrete, and make money on that.  There are obviously lots of other ways for PE firms to make money:

1) Pay down the debt over time so that your controlling portion of the company becomes a larger portion of TEV.  i.e. KKR could pay down pieces of debt in the first case on the 300 MM that it earns, making 10% returns the next year generate more than a 10% return on the initial 3 bn equity investment

2) Add debt.  As a company grows, even without paying down debt, a PE firm can add debt to the balance sheet because leverage would be going down with growth.  This is a way of "cashing out" of a deal by "re-levering" a company's balance sheet and taking the proceeds, as the equity holder.

3) Charge management fees, give dividends to equity holders: go into a firm and charge them many millions in fees for the PE firms strategic guidance and help.  Bain had a deal a few years ago when it paid itself a dividend on an acquisition that was about the size of their initial equity chunk...meaning that they'd made all of their money back essentially as soon as the deal was closed.  The company could have gone bankrupt the next day and Bain would've been right back where they started.

4) Sell off parts of the company.  Eddie Lampert, for eg., (not LBO guy) realized that the real estate value of K-Mart's stores alone was about equal to its stock price when ESL bought a huge part of the company, so he could make ROI without improving the company, but rather, by selling off lots of stores.

5) Lots of other ways I won't go into here

The basic idea is that, by becoming the equity holder at the top of a firm's cap structure, and heavily levering a firm, denominator for an LBO firm's returns is low relative to TEV.  At the same time, the numerator for returns has high variance because of levering--debtholders are first in line for their defined chunk, so downside and upside for the numerator are particularly large.  So long as the company grows fast enough that total growth on TEV exceeds total % of debt payments, the LBO shop makes higher returns than debtholders.  By unwinding debt over time, growing the company, selling assets, etc., the LBO shop can drive its IRRs based on the "risky bet" that the company has more "value growth potential" than the debt payments that it guarantees to make.

Does that all make sense?  Feel free to PM with any questions...