Articles

How do you solve a paper LBO by hand?

The interview test in four steps, sources and uses to IRR, with the shortcuts that keep you within a few hundredths of the full model.

Julian R. Sterling · from The Buyout Investor

A paper LBO is four steps done by hand: size the equity from sources and uses, grow EBITDA to the exit year, pay down debt with the cash left after interest, and turn the exit equity into a multiple and an IRR. On a company bought for 9.0× EBITDA of 50.0 with 5.0× of debt, 6 per cent growth and a flat exit multiple, the 210.0 of equity becomes 426.0 in five years: 2.03× and a 15.2 per cent IRR.

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 paper LBO is the standard buyout interview test because it shows whether a candidate knows where the return comes from, not whether they can drive a spreadsheet. Everything below can be done with a pencil in about ten minutes, and every figure is checked against a full year-by-year calculation.

The assumptions

An illustrative mid-market buyout, in millions. All free cash goes to repay debt.

Input	Value
Entry EBITDA	50.0
Entry and exit multiple	9.0×
Debt at closing	5.0× EBITDA
Transaction fees	10.0
EBITDA growth a year	6%
Interest on opening debt	8%
Capex, cash tax and working capital, share of EBITDA	45%
Holding period	5 years

Step 1: sources and uses

The purchase price is 9.0 × 50.0 = 450.0 of enterprise value. Add 10.0 of fees and the uses are 460.0. Debt at 5.0× is 250.0. Equity is the balancing item, not an input:

Step 2: grow EBITDA to the exit

Six per cent a year for five years: 50.0 × 1.06⁵ = 66.9. At a flat 9.0× the exit enterprise value is 602.2. If the multiple is the same at both ends, the growth in value is simply the growth in EBITDA at the entry multiple: (66.9 − 50.0) × 9.0 = 152.2.

Step 3: pay down the debt

This is the step candidates rush. Free cash flow is EBITDA less the 45 per cent that goes to capex, tax and working capital, less interest on the debt still outstanding. Because the debt falls, interest falls and paydown accelerates:

Interest at 8 per cent on the opening balance of each year.

Year	EBITDA	Cash before interest	Interest	Debt repaid	Closing debt
1	53.0	29.2	20.0	9.2	240.8
2	56.2	30.9	19.3	11.6	229.2
3	59.6	32.8	18.3	14.4	214.8
4	63.1	34.7	17.2	17.5	197.3
5	66.9	36.8	15.8	21.0	176.3
Total				73.7	176.3

Under time pressure you do not need five rows. Add up five years of EBITDA (298.8), take 55 per cent of it as cash before interest (164.3), and deduct five years of interest on an average debt of roughly 213.1, which is 85.3. That gives 79.1 of paydown against 73.7 in the table: the shortcut overstates by 5.3, because it ignores that interest is front-loaded while the cash is back-loaded. Good enough: it gives 2.05× instead of 2.03×.

Step 4: exit equity, MOIC and IRR

Without a calculator, the fifth root is the hard part. Memorise four anchors for a five-year hold: 1.5× is 8.4 per cent, 2.0× is 14.9, 2.5× is 20.1, 3.0× is 24.6. A 2.03× sits 6 per cent of the way from 2.0× to 2.5×, so interpolate to about 15.2 per cent. The same anchors are tabulated for every holding period in how to convert MOIC to IRR.

What if: growth, exit multiple and leverage

Interviewers almost always follow with "and if the multiple contracts?". Have the grid ready.

MOIC and IRR, five-year hold, 5.0× debt at entry.

EBITDA growth	Exit 8.0×	Exit 9.0×	Exit 10.0×
3% a year	1.30× / 5.3%	1.57× / 9.5%	1.85× / 13.1%
6% a year	1.71× / 11.3%	2.03× / 15.2%	2.35× / 18.6%
9% a year	2.17× / 16.8%	2.54× / 20.5%	2.90× / 23.8%

One turn of exit multiple moves the outcome by about 0.32× in either direction; three points of growth move it by roughly 0.5×. A one-turn contraction at 6 per cent growth takes the deal from 15.2 to 11.3 per cent, which is why a flat multiple is a base case and not a conservative one.

Same operating case, 6 per cent growth, exit at 9.0×.

Debt at entry	Equity in	Equity out	MOIC	IRR
4.0×	260.0	499.4	1.92×	13.9%
5.0×	210.0	426.0	2.03×	15.2%
6.0×	160.0	352.5	2.20×	17.1%

Leverage adds less than candidates expect: two extra turns of debt add 3.2 points of IRR, because more debt also means more interest and less paydown. The operating case does most of the work.

The common mistake

Forgetting the fees, or putting them on the wrong side. Fees are a use of funds paid with equity, and they are gone at exit. Leave them out and the equity cheque is 200.0, the multiple 2.13× and the IRR 16.3 per cent: more than a point too high from a line that is 2 per cent of the price. The second common error is applying the exit multiple to the entry EBITDA, or treating the exit enterprise value as the equity. At exit the debt is still 176.3, which is 2.6× the exit EBITDA, and the equity is 71 per cent of the exit value, not all of it.

Takeaway

• Equity is the plug: EV plus fees minus debt.
• Value growth at a flat multiple is EBITDA growth times the entry multiple.
• Paydown is cash after capex, tax, working capital and interest; interest falls as debt falls.
• Convert MOIC to IRR from memorised anchors, then interpolate.
• Close with a bridge: growth plus paydown minus fees must equal the equity gain.

The full version of this exercise, with a revolver, a second lien, a cash sweep, an interest cap and a covenant test, is in the free workbook for this case on the companion page of The Buyout Investor, which also holds a timed 60-minute test with an answer key. For a blank model to rebuild your own deal, use the LBO model template.

Questions readers ask

What IRR does a 2.0x MOIC equal over five years?

About 14.9 per cent, because 2.0 raised to the power one fifth is 1.149. The other anchors worth memorising for a five-year hold are 1.5x at 8.4 per cent, 2.5x at 20.1 per cent and 3.0x at 24.6 per cent. Interpolating between them gets a paper LBO answer within a few tenths of a point without a calculator.

Do transaction fees go into the equity cheque in an LBO?

Yes. Fees are a use of funds, and since debt is sized as a multiple of EBITDA, the equity pays for them. In an illustrative deal, 10.0 of fees lifts the equity from 200.0 to 210.0 and cuts the IRR from 16.3 to 15.2 per cent, because the fees earn nothing at exit.

How much does leverage add to a paper LBO return?

Less than most candidates expect. In an illustrative case growing EBITDA 6 per cent a year with a flat 9.0x exit, moving from 4.0x to 6.0x of debt lifts the IRR from 13.9 to 17.1 per cent, 3.2 points. Extra debt cuts the equity cheque but also adds interest, so it repays less.

Also on this site

• How do you convert MOIC to IRR?IRR = MOIC^(1/years) minus 1 for a single exit: 2.0x is 14.9 per cent over five years and 26.0 over three. Interim distributions break the formula.
• Is exiting below the entry multiple a conservative assumption?A buyout priced at 10.0x and sold at 9.0x looks prudent. On the same model's DCF, 9.0x assumes 4.10 per cent growth for ever; at the DCF's own 6.97x the return is 1.75x, not 2.35x.
• Why is net IRR lower than gross IRR in private equity?A buyout returning 17.05 per cent gross leaves the investor 12.70 per cent net: 1.90 points go to the management fee and 2.44 points to carry.
• How does the 30 per cent EBITDA interest cap affect LBO returns?The cap binds above 0.30 / rate turns of debt, 3.33x at 9 per cent. At 5.5x it adds 5.0 of tax and cuts exit equity by 6.6, IRR 17.93 to 17.56.
• At what exit does a 1x non-participating preference convert?The senior last round converts exactly at its own post-money: 80 for 20 per cent at 400 converts above 400 and gets 1.00x at any exit from 80 to 400.
• Why a secondaries bid-ask gap often has no zone at allThe seller's floor and the buyer's ceiling are the same present value at two rates, so at equal required returns the zone is exactly zero — and here it is 11.02 points apart.

Reading guide: private equity and private markets → · All 324 articles →

If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.