The break-even EBITDA of a leveraged co-investment, with debt paydown that shrinks as the business does, and why the exit multiple matters more than the downside case.
Solve for the exit EBITDA at which exit multiple × EBITDA, less the net debt still outstanding, equals the equity invested. On an illustrative buyout of 50.0 of EBITDA at 10.0x with 5.0x of debt, the co-investor's 265 of equity comes back intact as long as EBITDA falls no more than 11.0 per cent, to 44.5, and the exit multiple holds. Lose one turn of multiple and the cushion shrinks to 2.0 per cent; lose two and EBITDA has to grow 9.0 per cent just to return the capital.
Worked in full in The Co-Investment Practitioner by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A co-investor usually sees a sponsor's base case, an upside and a downside, and has a few weeks to form its own view. The quickest independent test is not another scenario. It is the break-even: how much the business can deteriorate before the co-investor loses money. It turns a set of plans into one number that can be set against the company's history, and it shows how much of the protection comes from the exit multiple rather than from the business.
| Input | Value |
|---|---|
| EBITDA at entry | 50.0 |
| Entry multiple | 10.0x |
| Enterprise value | 500 |
| Transaction costs, funded with equity | 15.0 |
| Debt at 5.0x EBITDA | 250 |
| Equity invested | 265 |
| Holding period | 5 years |
| Debt repaid each year, share of that year's EBITDA | 30% |
| Sponsor's plan: EBITDA growth a year | 6% |
Equity is 51.5 per cent of the 515 of total cost. In the sponsor's plan EBITDA reaches 66.9 in year 5, 90.2 of debt is repaid (on the straight-line EBITDA path used in Step 1), and at a 10.0x exit the equity is worth 509.3: 1.92x and a 14.0 per cent IRR. The question is what happens when the plan is not met.
Step 1: write exit equity as a function of exit EBITDA. Assume EBITDA moves in a straight line from 50.0 to its exit level E5. Debt paydown is 30 per cent of each year's EBITDA, so a weaker business repays less.
Paydown = 0.30 × Σ EBITDA1..5 = 0.30 × [250 + 3 × (E5 − 50)]
Exit equity = M × E5 − (250 − paydown)
Step 2: set exit equity equal to the equity invested and solve. At a 10.0x exit multiple:
10.0 × E5 − 250 + 0.30 × [250 + 3 × (E5 − 50)] = 265
E5 = 44.5, a fall of 11.0%
Check: paydown 70.0, exit net debt 180.0, exit EV 445.0, exit equity 265
Excel: put the exit-equity formula in one cell and use Goal Seek to set it to 265 by changing E5
Step 3: repeat for lower exit multiples. The same equation with M = 9.0 gives 49.0, a fall of 2.0 per cent. With M = 8.0 it gives 54.5: EBITDA must rise 9.0 per cent. At 7.0x it must rise 22.8 per cent.
| Exit multiple | Break-even EBITDA | Change from entry | Debt repaid | Exit net debt |
|---|---|---|---|---|
| 10.0x (flat) | 44.5 | -11.0% | 70.0 | 180.0 |
| 9.0x | 49.0 | -2.0% | 74.1 | 175.9 |
| 8.0x | 54.5 | +9.0% | 79.0 | 171.0 |
| 7.0x | 61.4 | +22.8% | 85.3 | 164.7 |
The business-only cushion is 11.0 per cent of EBITDA over five years. That is not much for a company bought at 10.0x, and all of it depends on someone paying 10.0x again. One turn of multiple on 50.0 of EBITDA is worth 50.0 of exit equity, 0.19x of the co-investor's money, which is why the multiple line of the table moves the break-even so much more than any operating assumption.
| Exit multiple | -30% | -20% | -10% | 0% | +10% | +20% | +30% |
|---|---|---|---|---|---|---|---|
| 8.0x | 0.35x | 0.51x | 0.68x | 0.85x | 1.02x | 1.18x | 1.35x |
| 9.0x | 0.48x | 0.66x | 0.85x | 1.04x | 1.22x | 1.41x | 1.60x |
| 10.0x | 0.61x | 0.82x | 1.02x | 1.23x | 1.43x | 1.64x | 1.84x |
Flat EBITDA at a flat multiple returns 1.23x: debt paydown of 15.0 a year is the only source of gain, and it first has to earn back the 15.0 of costs. The sponsor's 2.0x target needs EBITDA up 37.6 per cent at 10.0x, 51.5 per cent at 9.0x and 68.5 per cent at 8.0x. Laid out this way, the deal is a bet on growth with a modest cushion, not a protected investment with upside.
Compare the break-even with the company's own record. If EBITDA has fallen more than 11 per cent in any past downturn, the base case is not the risk to underwrite; the cycle is.
The book covers how a co-investor underwrites a sponsor's deal in the time it is given; the free workbook for this case prices the follow-on decision that comes after a miss. The full LBO mechanics behind the paydown line are in how to solve a paper LBO, and weighting scenarios into one expected multiple is in probability-weighted MOIC for a co-investment.
The exit EBITDA at which exit enterprise value, less the net debt left at exit, equals the equity put in. On the illustrative deal, 265 of equity and 180.0 of exit net debt need an exit EV of 445.0, so at a 10.0x multiple exit EBITDA must be at least 44.5: an 11.0 per cent fall from the 50.0 at entry.
Because the equity is a thin slice on top of the debt and loses value long before it is worthless. At 10.0x the equity of the illustrative deal is only wiped out if EBITDA falls 59.6 per cent, to 20.2. But break-even, the point where the co-investor gets its money back and no more, is reached after a fall of only 11.0 per cent.
On the illustrative deal, one turn of exit multiple on flat EBITDA of 50.0 is worth 50.0 of exit equity, 0.19x of MOIC. It moves the break-even from an 11.0 per cent EBITDA fall at 10.0x to a 2.0 per cent fall at 9.0x, and at 8.0x the company must grow EBITDA 9.0 per cent just to return the capital.
This article is one calculation from The Co-Investment Practitioner. 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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