Building an LBO model

Key takeaways

• Sources must equal uses: the purchase enterprise value, transaction and financing fees and cash left on the balance sheet are funded by debt tranches and sponsor equity.
• Free cash flow available for debt repayment equals net income plus D&A, less capex, less the increase in net working capital; mandatory amortization is paid first and a cash sweep applies the rest to prepayable debt.
• Computing interest on beginning-of-year balances avoids a circular reference; interest on average balances is more accurate but makes interest depend on the repayment it helps determine.
• Equity value at exit equals exit enterprise value less net debt at exit, and MOIC equals exit equity divided by entry equity.
• IRR is the discount rate that sets the net present value of the sponsor's cash flows to zero, found by iteration; with one investment and one exit it equals MOIC to the power of one over the holding period, less one.
• In the Linwood example, $495.0m of equity grows to $1,114.9m in five years: a 2.25x MOIC and a 17.6 percent IRR.

What an LBO model answers

A DCF values a business from its cash flows at a blended cost of capital. An LBO model looks at the same cash flows from one investor's seat: the sponsor's equity. It lays out a specific financing structure, runs the business forward year by year, sends the cash to lenders in a defined order, and measures what is left for the equity at exit. The output is not a value but a return, compared with the return the sponsor requires.

Three levers create the return. The operating business grows its EBITDA. The company repays debt from its cash flow, so a larger share of enterprise value belongs to equity at exit. And the exit multiple may be higher or lower than the entry multiple. Leverage does not create value by itself, but because the equity check is small relative to enterprise value, each dollar of value gained is a larger percentage gain on equity.

The model is built in a fixed order, because each schedule feeds the next: entry valuation and sources and uses; operating projections down to EBIT; the debt schedule, which supplies interest; net income and free cash flow, which supply the cash available for repayment; and finally exit value and returns.

The deal: Linwood Specialty Coatings

Linwood Specialty Coatings is a hypothetical producer of industrial coatings with LTM revenue of $500.0m and LTM EBITDA of $100.0m, a 20.0 percent margin. Fund A agrees to acquire 100 percent of the company at 10.0x LTM EBITDA on a cash-free, debt-free basis. That phrase means the headline price is an enterprise value: the sellers deliver the business with no debt and no surplus cash, and any existing debt is repaid out of the price at closing.

Debt is sized as a multiple of LTM EBITDA, because lenders think in those terms and set limits on them. Here the lenders offer a senior secured term loan of 4.0x EBITDA and senior subordinated notes of 1.5x, total leverage of 5.5x. The sponsor funds the rest with equity.

Sources and uses of funds

The sources and uses table is the deal on one page. Uses list everything the money is spent on at closing: the purchase enterprise value (which pays the sellers and retires any existing debt), transaction fees, financing fees paid to lenders and arrangers, and cash put on the balance sheet so the company can operate from day one. Sources list where the money comes from: each debt tranche, sponsor equity and, where relevant, equity rolled over by management or sellers.

Sponsor equity is the plug. Once uses are fixed and the debt is sized, equity is whatever makes the two columns equal. That makes the check mechanical: if sources do not equal uses, something is missing.

Accounting treatment differs by fee type. Under both US GAAP and IFRS, debt issuance costs are generally deducted from the carrying amount of the debt and amortized into interest expense over the life of the loan, while acquisition-related transaction costs are expensed. For clarity, this model treats both fees as cash paid at closing and ignores the later non-cash amortization and its small tax effect. A full model would include it.

Operating projections and the income statement

The operating case runs from revenue to EBIT without reference to financing. Linwood's plan assumes revenue growth of 6 percent in years 1 and 2 and 5 percent in years 3 to 5, with the EBITDA margin rising from 20.0 to 21.0 percent by year 3 through procurement savings and pricing. D&A is 3.0 percent of revenue, capex 3.5 percent and net working capital 10 percent of revenue, so each year's working capital investment is 10 percent of the revenue increase. The tax rate is 25 percent.

Below EBIT the income statement depends on the debt schedule: interest comes from it, and in turn the debt schedule needs net income to compute cash flow. This is the loop the next two sections resolve.

To keep every table adding exactly, this model rounds each line to $0.1m as it is calculated. The rounding changes the returns by less than a hundredth of a percentage point compared with carrying full precision.

Free cash flow available for debt repayment

The cash that can repay debt is levered free cash flow: net income, plus non-cash charges, less the investment the business needs. Unlike the unlevered free cash flow in a DCF, it is after interest, because interest is paid before any principal. It is before debt repayment, because repayment is what it funds.

Linwood's minimum cash balance of $10.0m was funded at closing and stays constant, so all free cash flow is available for debt service. If the plan had required cash to build up (for a seasonal peak or an acquisition), the model would hold it back before the sweep.

The debt schedule: amortization and the cash sweep

The debt schedule applies cash in the order the loan documents require. First, interest, already deducted in net income. Second, mandatory amortization on the term loan, $4.0m a year. Third, the cash sweep: the credit agreement requires excess cash flow to prepay the term loan. This model sweeps 100 percent of it, the maximum pace of deleveraging. In practice, term loan agreements usually set an excess cash flow sweep at a stated percentage that steps down as leverage falls, and the definition of excess cash flow is negotiated; model the actual terms when they are known.

The notes are not touched. Subordinated notes typically carry call protection that makes early repayment expensive, and they rank behind the term loan, so they stay outstanding until the exit, when they are repaid from the sale proceeds.

Interest here is computed on each tranche's beginning-of-year balance. That is a deliberate convention. Debt is actually repaid through the year, so interest on the average of beginning and ending balances is more accurate. But the ending balance depends on the sweep, the sweep depends on free cash flow, free cash flow depends on net income, and net income depends on interest. Using average balances therefore makes interest a function of itself, a circular reference that a spreadsheet can only solve by iterative calculation. Iteration works, but a circular model can fail to converge or hide errors, so many practitioners use beginning balances (slightly overstating interest while debt is falling) or break the loop with a switch.

Credit statistics through the hold

Lenders and the investment committee read the same schedule through credit ratios. Total leverage (total debt divided by EBITDA) shows how many years of EBITDA the debt represents; senior leverage does the same for the term loan alone; interest coverage (EBITDA divided by interest) shows how comfortably operating earnings meet interest. Loan agreements often contain maintenance covenants set on such ratios, though many sponsor-backed term loans are covenant-lite, with tests only on the revolving credit facility.

Linwood deleverages from 5.5x at closing to 2.4x by year 5, through a combination of EBITDA growth (the denominator rises 36.6 percent) and repayment (the term loan falls 55.15 percent, from $400.0m to $179.4m). Coverage nearly doubles, from 2.3x to 4.3x.

Exit, equity value and MOIC

The model assumes Fund A sells Linwood at the end of year 5 at 10.5x year 5 EBITDA. Exit enterprise value is paid to all capital providers: the buyer, in effect, repays the remaining term loan and notes, and the sellers keep the balance sheet cash. What remains is equity value at exit.

The base case assumes a modest rise in the multiple, from 10.0x to 10.5x. Many investment committees insist on a base case exit at or below the entry multiple, so that the return does not depend on the market paying more for the same earnings. The next topic shows returns across a range of exit multiples and holding periods and how much of this deal's gain the extra half turn provides.

The multiple of invested capital (MOIC), also called the money multiple, divides the value returned to the equity by the equity invested. It ignores time: 2.25x in three years and 2.25x in seven years look identical, which is why it is always shown with IRR. The model also ignores exit costs and management incentive equity, both of which reduce the sponsor's proceeds in practice.

IRR, solved numerically

The internal rate of return is the annual discount rate at which the present value of the sponsor's cash inflows equals the present value of its outflows, so that net present value is zero. It accounts for timing: returning the same cash sooner gives a higher IRR.

IRR has no general algebraic solution. It is found by iteration: guess a rate, compute NPV, and adjust. If NPV is positive, the rate is too low; if negative, too high. Spreadsheet IRR functions use a refinement of this search. The secant method below converges quickly: from two guesses, draw a straight line through their NPVs and take the rate where the line crosses zero as the next guess.

When the sponsor makes one investment and receives one payment n years later, the IRR also has a closed form: MOIC to the power of 1 / n, less one. The numerical search should agree with it, which is a useful check. Once there are interim cash flows (dividends, add-on equity, fees), only the numerical method works.