The maximum price is not a guess at the multiple. It is the exit equity discounted at the return the fund needs, plus whatever the lenders will put in.
Work backwards from the exit. With the debt sized by the lenders, the equity at exit does not depend on what the sponsor pays, so the maximum price is that exit equity discounted at the target IRR, plus the debt, less fees. On an illustrative company with 50.0 of EBITDA, 275.0 of debt and 433.0 of equity at the end of year five, a 20 per cent IRR supports 435.9 of enterprise value, 8.72x EBITDA. Paying the 9.0x the seller wants returns 18.1 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 →
This is the inverse of the usual entry sensitivity. How much IRR one more turn of entry multiple costs starts from a price and reads off the return; here the return is fixed and the price is the unknown, the number a deal team takes into the final bid.
A fictional mid-market buyout, figures in millions. The lenders will advance 5.5x entry EBITDA whatever the price, which is how leveraged loans are sized in practice: on the company's earnings and cash flow, not on the cheque the sponsor writes.
| Input | Value |
|---|---|
| Entry EBITDA | 50.0 |
| EBITDA growth a year | 6.0% |
| Debt at closing, 5.5x EBITDA | 275.0 |
| Interest on opening debt | 8.0% |
| Tax rate | 25% |
| Capex, equal to depreciation, % of EBITDA | 20% |
| Working capital, % of the EBITDA increase | 10% |
| Transaction fees, % of enterprise value, funded with equity | 3.0% |
| Exit multiple, year 5 | 9.0x |
| Target IRR | 20% |
All free cash flow after interest and tax sweeps the debt. Because the debt is fixed at 275.0, the interest bill, the paydown and the exit net debt are the same at any purchase price.
| Year | EBITDA | Interest | Tax | Capex | Free cash flow | Closing debt |
|---|---|---|---|---|---|---|
| 1 | 53.0 | 22.0 | 5.1 | 10.6 | 15.0 | 260.0 |
| 2 | 56.2 | 20.8 | 6.0 | 11.2 | 17.8 | 242.2 |
| 3 | 59.6 | 19.4 | 7.1 | 11.9 | 20.9 | 221.3 |
| 4 | 63.1 | 17.7 | 8.2 | 12.6 | 24.2 | 197.1 |
| 5 | 66.9 | 15.8 | 9.4 | 13.4 | 27.9 | 169.2 |
Working capital absorbs between 0.3 and 0.4 a year and is in the free cash flow column. Over five years 105.8 of debt is repaid. At 9.0x the year 5 EBITDA of 66.9, the exit enterprise value is 602.2, and the equity is 602.2 less 169.2 of net debt: 433.0.
Maximum equity today = exit equity / (1 + IRR)5 = 433.0 / 1.2^5 = 433.0 / 2.4883 = 174.0
Maximum enterprise value = (equity + debt) / (1 + fees) = (174.0 + 275.0) / 1.03 = 435.9
Maximum entry multiple = 435.9 / 50.0 = 8.72x
Excel: =((ExitEV-ExitNetDebt)/(1+IRR)^5+Debt)/(1+Fee)/EBITDA
The sources and uses close: 435.9 of price and 13.1 of fees make 449.0 of uses, funded by 275.0 of debt and 174.0 of equity, 38.8 per cent of the total. The equity turns into 433.0, a multiple of 2.49x, which over five years is exactly 20 per cent.
Now price the seller's ask. At 9.0x the enterprise value is 450.0, fees are 13.5, and the equity cheque is 188.5 for the same 433.0 back: 2.30x and 18.1 per cent. The gap between the ask and the fund's walk-away price is 14.1 of enterprise value. That number, not the IRR shortfall, is what the negotiation is about.
With interim distributions, such as a recap, a single discount factor no longer works: discount each flow at the target rate and add them, or Goal Seek the entry multiple on an =IRR() of the dated equity flows. The single-exit shortcut is the same identity that converts MOIC to IRR by holding period.
| Target IRR | Exit 8.0x | Exit 9.0x | Exit 10.0x |
|---|---|---|---|
| 15% | 8.87x | 9.52x | 10.17x |
| 20% | 8.20x | 8.72x | 9.24x |
| 25% | 7.67x | 8.10x | 8.52x |
One turn of exit multiple is worth about half a turn of entry multiple at a 20 per cent target, because the extra 66.9 of exit value is discounted over five years before it can be paid away today. Growth matters more than either: at 9.0x and 20 per cent, flat EBITDA supports only 7.30x, 3 per cent growth 7.97x and 9 per cent growth 9.55x. A price that only works at 9 per cent growth is a bet on the plan, and the investment committee should see it written that way.
If the model instead assumes the exit multiple equals whatever is paid, the solve becomes circular: a lower price also lowers the assumed exit. Goal Seek then returns 8.41x, an enterprise value of 420.6. That price, if the company really does sell at 9.0x, makes 22.3 per cent. Neither answer is wrong; they rest on different exit views, which is why the exit multiple must be a separate, evidenced input, with its own justification in the memo.
Forgetting the fees. Transaction costs are paid at closing and funded with equity, so they sit in the denominator of the return just like the price. Leaving them out of the solve gives a maximum of 8.98x, an enterprise value of 449.0; pay that and the fund's IRR is 18.2 per cent, not 20. On this deal the fees are worth a quarter of a turn of price.
The second mistake is letting the debt scale with the price in the solve, as if lenders advanced a fixed share of whatever the sponsor agrees to pay. They do not, so the solve shows a higher walk-away price than the lenders will fund; the same error in the forward sensitivity is worked in the entry multiple article linked above.
The book's own deal, with sources and uses balancing on the equity, the sweep and the dated IRR, is in the free workbook for this case, and the blank one-page version is the LBO model template.
Project the exit equity first, because with debt sized by lenders it does not depend on the price. Discount it at the target IRR over the hold, add the debt raised, and divide by one plus transaction fees. In the illustrative case, 433.0 of exit equity at 20 per cent over five years is worth 174.0 today; with 275.0 of debt and 3.0 per cent fees that is 435.9 of enterprise value, or 8.72x EBITDA.
Because it compounds over the whole hold. At a 9.0x exit, moving the target from 15 to 20 per cent cuts the maximum entry multiple from 9.52x to 8.72x, and 25 per cent takes it to 8.10x. Each five points of hurdle costs between six and eight tenths of a turn on this company, because the debt is fixed and the whole reduction lands on the equity cheque.
Only if there is a reason. Setting them equal makes the solve circular: the lower the price, the lower the assumed exit. In the illustrative case Goal Seek then returns 8.41x instead of 8.72x. The exit multiple should be an independent, evidenced view of what a buyer will pay in year five, and the entry price solved from it.
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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