1- IRR for the project is calculated by using the IRR function in excel after lining up the initial equity purchase price, any dividends paid, and the equity sales price at the end of the holding period. Yes, IRR is where the discount rate will cause all cash inflows and outflows to sum to NPV = 0, but the 0 is not important so much as what the IRR number is. You see, when I'm an investor who demands a 20% rate of return to make an investment, I look at IRR's of investments/projects put before me. If I'm given three investments that have IRR's of 15%, 20%, and 25%, I will accept either of the last two, with preference toward 25% (higher is better). In an LBO, the process is incredibly risky, therefore PE firms have very high demands as to what return they earn on an investment (generally north of 20%). So IRR is important in an LBO context because it's a quick way for a PE firm to look at a model and say yes or no. Just because NPV = 0 doesn't mean the sponsor isn't earning any returns. It means that the sponsor is earning returns equal to IRR, and an excess return equal to IRR - Required Rate of Return (RRR). The cash flow numbers used to calculate IRR are taken AFTER debt obligations have been satisfied (note how I said IRR was calculated based on EQUITY purchase price, EQUITY dividends, and EQUITY sales price). Equity is determined after debt has been satisfied, so the IRR reflects only the returns attributable to the equity holders (the PE firm).

2- A dividend recapitalization is when the target company issues more debt to increase its cash balance. It then takes this cash balance and pays a dividend to the sponsor company (the PE firm). This is important because in order for the PE firm to make any money, it has to receive cash. The target company could use free cash flows to pay a dividend to the PE firm, but a dividend recapitalization accelerates the amount of money the PE firm receives, meaning it earns back its initial investment faster. This payment of a dividend does NOT affect the sponsor's equity stake in the business. It merely removes cash from the target's balance sheet and puts it on the sponsor's, while making the target more levered.

For an example, let's lay out a few numbers. PeCo paid 1B in equity and 4B in debt for Target Co in 2010. Each year TargetCo generates 500M in FCF, 400M of which is required to pay the debt. In 2011, there is 100M free for TargetCo to either pay down more debt, or pay PeCo a dividend. Let's say PeCo thinks it's not worth paying down the debt (or isn't allowed to based on terms of the debt) and wants TargetCo to pay it a dividend. PeCo can extract all $100M in the form of a dividend. But maybe $100M isn't enough because PeCo is looking at some other attractive investments out there and needs another $400M to make a new investment. So PeCo "forces" Target Co to raise $400M in debt and pay it a dividend equal to $400M + $100M (from the FCF). Now PeCo has all the funds it needs (and has already achieved a 50% return ([400 + 100] / 1000). Target Co is more levered, but lives on. Now it's important to note that this dividend is NOT buying out PeCo. When PeCo sell TargetCo down the line, it will still be able to sell its 100% equity stake.

3- Sort of. When an investment bank raises money for the deal, it will commonly underwrite the bank debt and senior debt, then syndicate the debt to institutional investors or commercial banks. I don't think they charge a higher interest rate, rather, they make their money on the volume of deal they generate. When issuing High-Yield debt, the bank that may not be able to be sourced and sold to investors in time for the closing of the deal, the iBank will offer a "bridge loan", or a loan that guarantees the amount of high-yield debt that the PE firm needs to use to buy the target company until it can finish raising it. Generally the bridge loan is crazy expensive for the PE firm and too risky for the bank to keep on its books, so bridge loans rarely get used, or if they do, get syndicated immediately (so I've read).

4- Because an LBO doesn't care about the NPV of a project (where as in a DCF, the NPV is critical to calculating an implied share price/ EV). A PE firm undertaking an LBO cares more about the IRR versus its required rate of return . If the IRR of the project is greater than its RRR, then it will invest (all other things held equal). There's no use calculating a WACC or discount rate for the investment because the PE firm already knows it's required rate of return/discount rate it must use. Technically you can discount the LBO's dividends and sale by the 20% RRR of the PE firm, but why not calculate IRR and just look at it versus the RRR?

5- Debt investors don't like prepayment/ having their bonds called because generally, when a bond is called or prepaid, that means it can be refinanced at a lower rate. If a bond can be refinanced at a lower rate, then by nature, the bond investors are holding a bond that is paying higher interest than the market rate, so the value of their bonds has gone up. As a bond investor, you would get mad if you had a superb investment returning above average rates called back because then you have to redeploy your capital into "worse" investments and have to start up your research/investment processes. This is why bondholders will request a period where bonds are non-callable and after that period, callable at a significant premium.

6- You mean when will a banker use an LBO model in something other than advising a PE firm on what to pay or the seller of a company if it's a good deal to sell? I suppose in a sell-side M&A context, LBO's can be used to justify a client as a potential investment and use the analysis to source a deal.

7- Day one, you would have a cash outflow equal to the total deferred financing fees paid. Subsequently, every year you would have a cash inflow of the amortization of part of the financing fees paid. This transaction doesn't touch CFF, only CFO.