The exit multiple moves equity by exactly one year of exit EBITDA per turn, and how many IRR points that buys depends on leverage and the holding period.
One turn of exit multiple changes the exit equity by exactly one year of exit EBITDA, because the debt does not move with the multiple. On an illustrative buyout of 50.0 of EBITDA at 9.0x with 5.0x of debt, EBITDA reaches 66.9 in year five, so each turn is worth 66.9 of equity: 10.0x lifts the IRR from 15.2 to 18.6 per cent and 8.0x cuts it to 11.3. How many points a turn buys depends on how much equity it lands on and over how many years.
Worked in full in The Buyout Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The exit multiple is the assumption every investment committee argues about and every sensitivity table shows first. It is also the one the sponsor controls least. The arithmetic below separates what a turn is worth in dollars, which is simple and fixed, from what it is worth in IRR, which is not.
| Input | Value |
|---|---|
| Entry EBITDA | 50.0 |
| Entry multiple | 9.0x |
| Debt at closing | 5.0x EBITDA, 250.0 |
| Transaction fees | 10.0 |
| Equity, the balancing item | 210.0 |
| EBITDA growth a year | 6.0% |
| Interest on opening debt | 8.0% |
| Capex, cash tax and working capital, share of EBITDA | 45.0% |
| Holding period | 5 years |
All free cash repays debt. After five years EBITDA is 66.9 and debt has fallen from 250.0 to 176.3. The year-by-year build is the one in how to solve a paper LBO.
Exit equity = exit EBITDA × exit multiple − net debt at exit
Δ exit equity per turn = exit EBITDA
IRR = (exit equity ÷ entry equity)1/years − 1
In Excel, with exit EBITDA in B1, the multiple in B2, exit debt in B3 and entry equity in B4: =((B1*B2-B3)/B4)^(1/5)-1.
Step 1: the base case. 66.9 × 9.0 = 602.2 of enterprise value, less 176.3 of debt, leaves 426.0 of equity. On 210.0 invested that is 2.03x and a 15.2 per cent IRR.
Step 2: one turn up. At 10.0x the enterprise value is 669.1 and the equity 492.9. The debt is the same 176.3, so the whole 66.9 of extra value goes to the equity: 2.35x and 18.6 per cent, 3.4 points more.
Step 3: one turn down. At 8.0x the equity is 359.0, 1.71x and 11.3 per cent: 3.9 points less. The same 66.9, in the other direction, costs more IRR than it adds on the way up, because the IRR is the fifth root of the multiple of money and that curve is concave.
| Exit multiple | Enterprise value | Exit equity | MOIC | IRR |
|---|---|---|---|---|
| 7.0x | 468.4 | 292.1 | 1.39x | 6.8% |
| 8.0x | 535.3 | 359.0 | 1.71x | 11.3% |
| 9.0x | 602.2 | 426.0 | 2.03x | 15.2% |
| 10.0x | 669.1 | 492.9 | 2.35x | 18.6% |
| 11.0x | 736.0 | 559.8 | 2.67x | 21.7% |
The equity column moves in equal steps of 66.9 and the MOIC in equal steps of 0.32x. The IRR column does not: 4.5 points between 7.0x and 8.0x, 3.1 between 10.0x and 11.0x. One turn is 31.9 per cent of the entry cheque and 15.7 per cent of the base-case exit equity, which is why the exit multiple is the line that decides whether a deal clears its hurdle.
Turned round, the table gives the exit multiple a target needs. Compound 210.0 at the target rate for five years, add the 176.3 of debt and divide by 66.9: a 20 per cent IRR needs 10.44x, a 15 per cent IRR needs 8.95x, and the equity is returned with no gain at 5.77x. Buying at 9.0x and planning on 15 per cent leaves almost no room for a lower exit.
A turn is always worth exit EBITDA in dollars. What it is worth in IRR depends on the size of the cheque it lands on and how long it takes to arrive.
| Case | Equity | Exit debt | 8.0x | 9.0x | 10.0x |
|---|---|---|---|---|---|
| 4.0x debt, five years | 260.0 | 102.8 | 10.7% | 13.9% | 16.8% |
| 5.0x debt, five years | 210.0 | 176.3 | 11.3% | 15.2% | 18.6% |
| 6.0x debt, five years | 160.0 | 249.7 | 12.3% | 17.1% | 21.3% |
| 5.0x debt, three years | 210.0 | 214.8 | 7.6% | 15.2% | 21.9% |
| 5.0x debt, seven years | 210.0 | 122.1 | 12.5% | 14.9% | 17.0% |
Valuing a turn at entry EBITDA. A turn of exit multiple applies to the EBITDA at exit, 66.9 here, not the 50.0 the company earned when it was bought. Using 50.0 understates the swing by 16.9 and puts the 10.0x case at 476.0 of equity and a 17.8 per cent IRR instead of 492.9 and 18.6. The error grows with the growth assumption: the more EBITDA the plan delivers, the more each turn is worth, and the more the exit multiple and the operating plan become one bet rather than two.
The second mistake runs the other way. A model that assumes multiple expansion credits the sponsor with value it did not create: at 10.0x, 66.9 of the 282.9 gain, 23.7 per cent, comes from the multiple alone. A committee should see the 9.0x case as the base and the turn as a separate line, which is how a returns bridge treats it. The entry side of the same question, where one turn of price costs more because the debt is held fixed, is in how much IRR one more turn of entry multiple costs.
Every figure here is illustrative. Exit multiples depend on market conditions at the time of sale that no model can forecast, which is the reason to show the turn as a sensitivity, not to assume it.
The book's own case, with the sensitivity from the lowest to the highest exit multiple and the two-way grid, is in the free workbooks for this case; a blank version of the model is the LBO model template.
Compound the equity at the target rate and add back the debt left at exit, then divide by exit EBITDA. On 210.0 of equity over five years, 20 per cent needs 522.5 of exit equity; with 176.3 of debt and 66.9 of EBITDA that is a 10.44x exit, against 9.0x paid. The deal breaks even, an IRR of zero, at 5.77x.
Because IRR is a root of the multiple of money. Each turn adds or removes the same 66.9 of equity, but the IRR is concave in it: 9.0x to 10.0x adds 3.4 points, 9.0x to 8.0x removes 3.9. The further the multiple falls, the steeper each further turn bites: 8.0x to 7.0x costs another 4.5 points.
Yes, in IRR terms. The turn is the same 66.9 of value, but it lands on a smaller equity cheque. At 4.0x debt a turn up is worth 2.9 points of IRR; at 6.0x it is worth 4.1, and a turn down costs 4.8 instead of 3.2.
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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