The entry price sensitivity worked on a five-year buyout, with the debt held constant so that the table measures price and nothing else.
On this illustrative five-year buyout, six points. Buying 50.0 million of EBITDA at 10.0 times instead of 9.0 times, with the same 275.0 million of debt and the same exit, raises the equity cheque from 175.0 to 225.0 and takes the IRR from 22.1 to 16.1 per cent: 6.0 points for one turn. A sensitivity table that resizes the debt with the price shows only 4.1 points, because it quietly adds leverage.
Worked in full in The Buyout Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Entry price is the one input the sponsor fixes on day one and can never improve afterwards. Every other driver, EBITDA growth, debt paydown, the exit multiple, has years to move. That is why investment committees spend so long on the last half turn, and why the sensitivity that frames the argument should measure price and nothing else.
| Input | Value |
|---|---|
| Entry EBITDA | 50.0 |
| Entry multiple, base case | 9.0x |
| Debt at closing, 5.5x EBITDA | 275.0 |
| EBITDA in year 5 (7.0% a year) | 70.0 |
| Exit multiple | 9.0x |
| Debt repaid over five years from cash flow | 120.0 |
Equity in = entry EBITDA × entry multiple − debt. Equity out = exit EBITDA × exit multiple − (debt − paydown). IRR = (equity out ÷ equity in)1/5 − 1.
In Excel, with one cash flow out and one in: =(EquityOut/EquityIn)^(1/5)-1, or =IRR() on the dated series once there are interim flows.
| Line | Bought at 9.0x | Bought at 10.0x |
|---|---|---|
| Enterprise value paid | 450.0 | 500.0 |
| Less debt | −275.0 | −275.0 |
| Equity invested | 175.0 | 225.0 |
| Exit enterprise value, 70.0 × 9.0x | 630.0 | 630.0 |
| Less net debt at exit | −155.0 | −155.0 |
| Equity at exit | 475.0 | 475.0 |
| Multiple of money | 2.71x | 2.11x |
| IRR over five years | 22.1% | 16.1% |
The exit is identical, so the whole difference is in the denominator. One turn on 50.0 of EBITDA is 50.0 of extra price, and because the lenders' 275.0 does not move, every euro of it is equity: the cheque grows by 28.6 per cent for the same 475.0 back. The multiple drops from 2.71x to 2.11x and the IRR by 6.0 points.
Many models build the entry sensitivity by keeping loan-to-value constant: at 9.0x the debt is 61.1 per cent of the price, so at 10.0x the model lends 61.1 per cent of 500.0, which is 305.6, or 6.11 times EBITDA. The equity cheque rises only to 194.4, net debt at exit is 185.6, exit equity 444.4, and the IRR comes out at 18.0 per cent. The cost of the turn appears to be 4.1 points.
That table answers a different question. It assumes lenders will advance more because the sponsor agreed to pay more, which they will not: debt is sized on the company's EBITDA and cash flow, not on the purchase price. It also keeps the 120.0 of paydown unchanged, although 30.6 more debt carries more interest and leaves less cash to repay it, so even the 18.0 per cent is flattering. The resized table mixes a price effect with a leverage effect and attributes both to price.
| Entry multiple | Equity in, debt 275.0 | MOIC | IRR | IRR if debt resized |
|---|---|---|---|---|
| 8.0x | 125.0 | 3.80x | 30.6% | 26.6% |
| 8.5x | 150.0 | 3.17x | 25.9% | 24.3% |
| 9.0x | 175.0 | 2.71x | 22.1% | 22.1% |
| 9.5x | 200.0 | 2.38x | 18.9% | 20.0% |
| 10.0x | 225.0 | 2.11x | 16.1% | 18.0% |
| 10.5x | 250.0 | 1.90x | 13.7% | 16.0% |
The cost of each half turn is not constant. It is largest at the cheap end, 4.7 points between 8.0x and 8.5x, and smaller at the expensive end, 2.4 points between 10.0x and 10.5x, because each extra 25.0 of price is a smaller share of a larger cheque. That asymmetry is why a sponsor who has already stretched finds the next half turn easier to concede than the first one.
At 10.0x, getting back to the 2.71x the 9.0x deal earned needs 610.7 of exit equity, which is 765.7 of enterprise value. At a 9.0x exit that is EBITDA of 85.1 instead of 70.0, growth of 11.2 per cent a year instead of 7.0. Alternatively, with the plan's 70.0 of EBITDA, the exit multiple has to reach 10.94x. Simply exiting at the 10.0x paid, with no expansion, gives 2.42x and 19.4 per cent: better than 16.1, still 2.7 points short.
With the debt held where lenders put it, one more turn of entry multiple on this deal costs 6.0 points of IRR and needs 15.1 more of exit EBITDA to repay. Any table that says 4.1 has borrowed the difference. The free LBO model and sensitivity workbook for this book run the entry price with the debt held constant beside the table that resizes it, and the paper LBO walk-through shows the same arithmetic solved by hand.
Because the extra price is paid entirely in equity when the debt is fixed by lenders, while the exit value does not change. One turn on 50.0 of EBITDA is 50.0 more equity on a 175.0 cheque, 28.6 per cent more, for the same 475.0 at exit. The multiple falls from 2.71x to 2.11x and the five-year IRR from 22.1 to 16.1 per cent.
Not if the question is what the price costs. Resizing debt at a constant loan-to-value lends 305.6 at 10.0x instead of 275.0, adding 0.61 of a turn of leverage, so the table mixes a price effect with a leverage effect and shows 18.0 per cent instead of 16.1. Hold the debt at what lenders will actually provide and show leverage as a separate sensitivity.
In the illustrative case, buying at 10.0x and wanting the same 2.71x as at 9.0x needs an exit multiple of 10.94x on 70.0 of EBITDA, or EBITDA of 85.1 at a 9.0x exit, an 11.2 per cent growth rate instead of 7.0. Exiting at the 10.0x paid, with no expansion, gives 2.42x and 19.4 per cent.
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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