Work the LBO backwards from the return: the equity the target demands, the debt still owed, and the EBITDA that has to sit under them at exit.
Work backwards: compound the equity cheque at the target IRR, add the debt still outstanding at exit, divide by the exit multiple, and solve for the growth rate that produces that EBITDA. An illustrative buyout of 50.0 of EBITDA at 9.0x, with 190.0 of equity and 275.0 of debt, needs EBITDA growth of 8.57 per cent a year, 50.9 per cent over five years, for a 20 per cent IRR at a 9.0x exit. With no growth at all it returns 1.9 per cent.
Worked in full in The Buyout Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An LBO model is usually run forwards: management's plan goes in, an IRR comes out. That hides what the return depends on. The investment committee question is the reverse: how good does the plan have to be for this deal to earn the fund's target? Once the required growth is on the page it can be compared with the company's history, with the market and with the plan, and the gap between them is the real risk in the deal.
| Item | Value |
|---|---|
| Entry EBITDA | 50.0 |
| Entry multiple, enterprise value | 9.0x, 450.0 |
| Fees and expenses | 15.0 |
| Debt at closing, 5.5x | 275.0 |
| Equity cheque | 190.0 |
| Interest on opening debt | 8.0% |
| Tax rate | 25% |
| Unlevered cash flow after tax, capex and working capital | 45% of EBITDA |
| Hold, exit multiple | 5 years, 9.0x |
All free cash flow repays debt: each year the debt falls by 45 per cent of EBITDA less interest after tax. The sources and uses follow the sources and uses table for an LBO.
Exit equity needed = 190.0 × (1 + 20%)5 = 190.0 × 2.4883 = 472.8
A 2.49x multiple of money over five years
If debt were fixed, the arithmetic would be one line: exit EV = 472.8 + debt, exit EBITDA = EV / 9.0. But the debt at exit depends on the cash the company generates, which depends on the EBITDA path you are solving for. The clean way is to put the growth rate in one cell, build the five-year debt schedule from it, and let Goal Seek or a bisection find the rate that makes exit equity equal 472.8.
EBITDAt = 50.0 × (1 + g)t
Debtt = Debtt−1 − (45% × EBITDAt − 8.0% × Debtt−1 × (1 − 25%))
Exit equity = 9.0 × EBITDA5 − Debt5 = 472.8
Excel: Data, What-If Analysis, Goal Seek: set ExitEquity to 472.8 by changing g
| Year | EBITDA | Interest | Debt repaid | Closing debt |
|---|---|---|---|---|
| 1 | 54.3 | 22.0 | 7.9 | 267.1 |
| 2 | 58.9 | 21.4 | 10.5 | 256.6 |
| 3 | 64.0 | 20.5 | 13.4 | 243.2 |
| 4 | 69.5 | 19.5 | 16.7 | 226.5 |
| 5 | 75.4 | 18.1 | 20.4 | 206.1 |
Exit EBITDA of 75.4 at 9.0x is 678.9 of enterprise value; less 206.1 of debt, 472.8 of equity. The gain of 282.8 splits into 228.9 from EBITDA growth at a constant multiple and 68.9 from debt paydown, less the 15.0 of fees spent at entry. Growth does almost all of the work; paydown is itself a product of that growth.
| Target IRR | Exit at 8.0x | Exit at 9.0x | Exit at 10.0x |
|---|---|---|---|
| 15% | 8.1% | 5.9% | 4.0% |
| 20% | 10.8% | 8.6% | 6.6% |
| 25% | 13.7% | 11.4% | 9.4% |
One turn of multiple contraction costs about as much as five points of target return: a 20 per cent IRR with an exit at 8.0x asks for 10.8 per cent a year, close to what a 25 per cent IRR asks at 9.0x. That is why a prudent committee runs the required growth at an exit below entry as well, the test discussed in what entry multiple an LBO can pay for a 20% IRR.
With no growth the deal barely returns its money. Flat EBITDA of 50.0 repays 33.8 of debt in five years, leaving 241.2; at 9.0x the equity is 208.8, 1.10x and 1.9 per cent a year. At 5.5x leverage and 8.0 per cent interest, interest absorbs most of the free cash flow, so leverage alone cannot carry the return.
Holding the debt at its closing amount when solving backwards. That gives exit EBITDA of (472.8 + 275.0) / 9.0 = 83.1, and a required growth of 10.69 per cent a year, two points too high. The opposite error is worse: taking the debt paydown from management's plan while testing a lower growth rate, which credits the downside case with the cash of the upside one. The growth, the cash flow and the debt must move together, which is why the rate has to be solved rather than read off.
The book takes one mid-market buyout from entry price to exit and shows where the return really came from; the free workbooks for this case carry the LBO model, the returns bridge and every sensitivity.
Whatever the target return requires at the leverage and exit multiple chosen, which is why the backwards calculation is worth doing. In the illustrative buyout a 15 per cent IRR needs 5.9 per cent a year at a 9.0x exit, 20 per cent needs 8.6 per cent, and 25 per cent needs 11.4 per cent. Any market level for growth should be checked against the company's own history.
A lot. For a 20 per cent IRR the illustrative deal needs 6.6 per cent a year if it exits at 10.0x, 8.6 per cent at 9.0x and 10.8 per cent at 8.0x. One turn of multiple contraction, from 9.0x to 8.0x, adds 2.2 points of required growth every year for five years.
Very little at 5.5x leverage and 8 per cent interest. In the worked case, flat EBITDA of 50.0 lets the company repay only 33.8 of its 275.0 of debt in five years; exiting at the 9.0x entry multiple returns 208.8 on 190.0 of equity, 1.10x and 1.9 per cent a year, once the 15.0 of fees is lost.
This article is one calculation from The Buyout Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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