Private Equity puzzles, solved step by step

Puzzles: 100
Traced to a firm: 22
Topics: 12
Hard: 30

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024A company has a 500 toggle note that pays either 10% in cash or 11% in kind. It toggles to PIK for three years. What is the note worth at the end, and what is total leverage if there is 300 of other debt and EBITDA stays flat at 100?Credit and PIK mathsCoreAres ManagementLos Angeles · 2026
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After three years of PIK at 11%, the note is
Show the worked solution
About 684, and leverage of about 9.8x. Each year 11% is added to the balance rather than paid: 500 grows to 555, then 616, then 683.8. Add the 300 of other debt and total debt is 984 against EBITDA of 100, so 9.8x, up from 8.0x today. The company has kept 150 of cash over the three years and taken on 184 of extra debt to do it.
What does toggling to PIK actually do?
Think of a credit card where you can skip the monthly payment and let the interest be added to the balance. Nothing leaves your account this month, but next month's interest is charged on a bigger number. A toggle noteA bond or loan whose issuer can choose each period to pay interest in cash or to add it to the principal, usually at a higher rate for the in-kind option. lets the borrower choose that every period, and the price of choosing it is a higher rate charged on a balance that compounds. Here the cash option costs 50 a year. The PIK option costs 55 in year one, and because that 55 is added to the note, 61.05 in year two and 67.77 in year three.
With 300 of other debt and EBITDA flat at 100, three years of 11% PIK on the 500 note take total debt from 800 to 984 and leverage from 8.0x to 8.55x, 9.16x and 9.84x, while the 150 of cash interest avoided is less than the 184 of debt added.
How does the leverage climb, year by year?
Start at 800 of debt on 100 of EBITDA, 8.0x. After year one the note is 555 and total debt 855, so 8.55x. After year two the note is 616.05 and leverage 9.16x. After year three it is 683.82 and leverage 9.84x. Because EBITDA is flat, every unit the note accretes is a unit of leverage with no new earnings to carry it, and the ratio rises by almost two turns in three years without the business doing anything. That is the whole point of the question: PIK is deferred cash, not free cash, and it is deferred at a compounding rate.
The relationship
$N_3 = 500 \times 1.11^3 \approx 683.8 \qquad \text{Leverage} = \frac{683.8 + 300}{100} \approx 9.8x$
N_3 the note balance after three years of in-kind interest
1.11 one plus the PIK rate, applied to the growing balance each year
300 the other debt, which does not accrete
What it says in wordsThe note grows at the in-kind rate compounded, and leverage is all the debt divided by an EBITDA that has not moved.
When is toggling sensible, and what should you add?
When the cash has a better use than paying interest: a short period of heavy investment, or a downturn the company expects to come out of. The toggle buys time at a known price, and the question for the lender and the sponsor is whether the EBITDA that eventually has to carry 984 of debt will be there when the time runs out. Say the things the simple version leaves out: the 1-point premium over the cash coupon is what the lender charges for the option, PIK interest is often still a tax deduction even though no cash moves, and a 9.8x company usually needs an equity cure, a sale or growth, because refinancing at that level is hard.
Where candidates lose it
The common error is simple interest, three years of 55, which gives 665. PIK compounds on the accreted balance, so the answer is about 684, and the gap is the interest on interest.
The second loss is to say 684 and stop. The interviewer asked about leverage because that is what the toggle changes: convert to total debt over EBITDA, show the climb from 8.0x to 9.8x, and say that flat EBITDA is what makes the climb dangerous.
What the interviewer asks next
If EBITDA instead grows 10% a year, what is leverage after three years?
What would the lender want in exchange for the toggle option, beyond the extra 1%?
How does three years of PIK change the recovery for the 300 of other debt if the company is worth 7x EBITDA at the end?
Asked at Ares Management, Credit, Los Angeles, 2026 (Wall Street Oasis): First 1v1 they said was mainly behavioral had PIK question
025At a fork in the road stand two guides. One always lies and one always tells the truth, and you cannot tell which is which. You may ask one guide a single question. What do you ask to find the road to the deal site?Logic and brainteasersCoreMid-market buyout fund
Try it first
Which single question works?
Show the worked solution
Ask either guide: which road would the other guide say leads to the site? Then take the other road. If you asked the truth-teller, he truthfully reports the liar's wrong answer. If you asked the liar, he lies about the truth-teller's right answer, which is also the wrong road. Either way the answer is the wrong road, so the right road is the one not named. The question works because it passes through both guides, so exactly one lie is applied.
Why does a direct question fail?
Imagine asking two shopkeepers whether a price is fair, knowing one of them always exaggerates, but not which. One answer is honest and one is not, and with no way to tell them apart you have learned nothing you can act on. A direct question about the road gives the truth from one guide and a lie from the other, and since you do not know which guide you asked, the answer carries no usable information. Asking a guide whether he is the truth-teller is worse: both say yes, the honest one because it is true and the liar because it is false. The trick has to work the same way whichever guide you happen to be facing.
Whichever guide you ask and whichever road is correct, the answer to the question of what the other guide would say is always the wrong road, so taking the road not named is right in all four cases.
How does routing the question through the other guide fix it?
By making sure the answer passes through exactly one liar. Ask the truth-teller what the liar would say and you get an honest report of a lie; ask the liar what the truth-teller would say and you get a lie about the truth; both contain one lie, so both point to the wrong road. The table in the figure checks all four cases: truth-teller or liar, left road or right road correct, and in every cell the named road is the wrong one. Because the answer is wrong by construction, you do not need to know which guide you asked. You simply take the other road.
You ask What he does Road he names What you do
The truth-teller Reports the liar's answer honestly The wrong road Take the other
The liar Lies about the truth-teller's answer The wrong road Take the other
Both guides name the wrong road when asked what the other would say, so the rule is the same whichever one you met.
Why does a deal desk ask a puzzle with no numbers in it?
Because it tests whether you can design a question whose answer is useful regardless of what you do not know. The puzzle is a small model of diligence: a management team, a seller's banker and a reference customer each have a reason to shade the truth, and the skill is to ask questions whose answers you can act on without first knowing who is being straight with you. Asking a supplier how the target compares with its other customers, rather than asking management how the supplier feels about them, is the same move: route the question so the bias cancels. The limit is that the puzzle assumes a guide who lies perfectly and consistently; a real counterparty who is merely selective needs several questions, not one.
Where candidates lose it
The common loss is panicking and asking the direct question, or asking a guide about himself, which both guides answer identically. Candidates also sometimes find the right question but then take the road it names, forgetting the final flip.
The second loss is giving the answer as a memorised line without showing it works in every case. Walk the four cases out loud, or draw the table, so the interviewer sees that you checked rather than recalled.
What the interviewer asks next
What question works if there are three roads instead of two?
Suppose the guides answer only yes or no. Rephrase the question so it still works.
What question would tell you which guide is the liar, and why is that less useful than finding the road?
028A sponsor invests 100. In year 2 it takes a dividend recap of 60, and in year 5 it exits for 180. What is the money multiple, and is the IRR higher or lower than a deal that simply turns 100 into 240 at year 5?Returns mathsCoreMid-market buyout fund
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Both deals return 2.4x. Which has the higher IRR, and by roughly how much?
Show the worked solution
The multiple is 2.4x in both cases, but the recap deal's IRR is about 24.1% against 19.1%. Money back is 60 plus 180, which is 240 on 100. The single exit's IRR is 2.4 to the power one fifth, less one. The recap returns part of the money in year 2, and cash that comes back sooner lifts the IRR even though the total is unchanged.
Why does the same multiple give a different IRR?
Lend a friend Rs 100 and get Rs 240 back. If Rs 60 of it comes back after two years, you have that money in hand for three years while waiting for the rest. The multiple counts how much money comes back; the IRR counts how fast it comes back, so pulling cash forward raises the IRR without touching the multiple. The two deals below differ only in timing.
Both deals turn 100 into 240 over five years, but the deal that returns 60 in year 2 earns an IRR of 24.1% while the single exit at year 5 earns 19.1%, because early cash shortens the average time the money is out.
How do you get the recap IRR without a spreadsheet?
The single exit is a one-line calculation: 2.4 to the power 0.2 is about 1.191, so 19.1%. The recap needs a guess and a check, because there are two inflows. Try 24%: 60 divided by 1.24 squared is about 39.0, and 180 divided by 1.24 to the fifth is about 61.4. Together that is 100.4, just above the 100 invested, so the true rate is a touch higher. Guess, discount each cash flow, and nudge the rate until the present values add back to the cheque. The answer is 24.1%.
The relationship
$100 = \frac{60}{(1+r)^2} + \frac{180}{(1+r)^5} \quad\Rightarrow\quad r \approx 24.1\%$
r the IRR, the rate that makes the discounted inflows equal the investment
60 the recap dividend in year 2
180 the exit proceeds in year 5
What it says in wordsThe IRR is the single rate at which the discounted cash coming back exactly repays the cash put in.
Say what the recap costs, because an interviewer will push. The dividend was paid with new debt, which is why the exit cheque is 180 and not 240. The company carried more leverage for three years, so the higher IRR came with higher risk of a covenant problem. That is the honest trade: an LP sees a better IRR and early cash back, and the business sees a thinner cushion.
Where candidates lose it
The fast wrong answer is that the IRRs are equal because the multiples are equal. Candidates who think of IRR as a multiple spread over years miss that IRR weights early cash more heavily.
The second loss is getting stuck on a two-cash-flow IRR. You do not need the exact figure in your head; bracket it with one trial rate, say it is a little above 24%, and explain why.
What the interviewer asks next
Why might a GP favour a dividend recap late in a fund's life?
If the recap had been 100 in year 2 and exit 140 in year 5, what happens to the IRR and to the multiple?
What does an LP look at besides IRR to judge whether the recap added value?
029A sponsor buys a platform at 11x EBITDA of 100, then adds three bolt-ons with EBITDA of 10, 15 and 25, bought at 6x, 7x and 5x. What is the blended entry multiple for the whole group?Valuation riddlesCoreMid-market buyout fundIndian mid-market PE
Try it first
Which is closest to the blended multiple?
Show the worked solution
About 9.27x: total price of 1,390 over total EBITDA of 150. The platform costs 1,100. The bolt-ons cost 60, 105 and 125, which is 290 for 50 of EBITDA, a 5.8x average of their own. Add prices, add EBITDA, divide. The simple average of the four multiples, 7.25x, is wrong because it weights a 10 of EBITDA deal the same as a 100.
Why can you not average the multiples?
Buy 10 kg of rice at Rs 60 a kg and 1 kg of saffron rice at Rs 600 a kg. The average price per kg is not Rs 330; it is Rs 1,200 over 11 kg, about Rs 109. A multiple is a price per unit of EBITDA, so blending multiples means total price over total EBITDA, which weights each deal by its size. The platform holds two thirds of the group's EBITDA, so it pulls the blend towards 11x.
Drawn with width equal to EBITDA and height equal to the multiple, each deal's area is its price; the four blocks hold 1,390 of price over 150 of EBITDA, a blended multiple of 9.27x, well above the 7.25x simple average.
What does the blend tell you about the buy-and-build story?
The sponsor has bought 150 of EBITDA for 9.27x. If the larger group is worth the platform's 11x at exit, the same EBITDA is worth 1,650, against 1,390 paid. That gap of 260 is the multiple arbitrage that buy-and-build plans are built on, and it exists only if the market values the combined group at the platform's multiple.
Block EBITDA Multiple Price
Platform 100 11x 1,100
Bolt-on 1 10 6x 60
Bolt-on 2 15 7x 105
Bolt-on 3 25 5x 125
Group 150 9.27x 1,390
Adding prices and EBITDA separately gives 1,390 over 150, a blended 9.27x for the group.
Say the limitation. Bolt-on EBITDA is often bought on the seller's figures, before integration costs, lost customers and the management time each deal eats. Small businesses sell for lower multiples partly because they are riskier. The blend is a fair measure of what was paid; whether the group deserves 11x at exit is a separate judgement.
Where candidates lose it
The average of the four multiples, 7.25x, is the trap, and it is tempting because the question lists four multiples side by side. The interviewer is checking whether you treat a multiple as a price per unit and weight it by size.
The second loss is stopping at the number. A buyout interviewer wants the next sentence: the blend is below the platform multiple, and that gap is the paper value the strategy is counting on.
What the interviewer asks next
What exit multiple on the group would leave the sponsor no better off than the entry blend?
Why do smaller businesses trade at lower multiples, and is that gap sure to close once they are inside a platform?
How would integration costs change the blended multiple you report to the investment committee?
031On a 5-year hold, how much more exit equity do you need to lift the IRR from 20% to 25%?Returns mathsCoreLarge-cap buyout fund
Try it first
Pick the closest answer.
Show the worked solution
About 22.6% more exit equity: from 2.49x the cheque to 3.05x. 1.2 to the fifth is 2.49 and 1.25 to the fifth is 3.05. Their ratio is (1.25 / 1.2) to the fifth, about 1.226. Five points of IRR compound every year, so over five years they add up to almost a quarter more money at exit, and more again over longer holds.
Why is the answer not five per cent?
Two runners leave together, one about 4% faster. After one lap the gap is small. After five laps it is five small gaps stacked, each measured on a longer distance. An extra five points of IRR is an extra growth factor of 1.25 / 1.20, about 1.042, applied every year, so over five years the exit has to be 1.042 to the fifth, about 1.226 times larger. That is a 22.6% increase in exit equity.
The relationship
$\frac{(1.25)^5}{(1.20)^5} = \left(\frac{1.25}{1.20}\right)^5 = 1.0417^5 \approx 1.226$
1.25^5 the exit multiple at 25% a year for five years, 3.05x
1.20^5 the exit multiple at 20% a year, 2.49x
What it says in wordsThe extra exit value needed is the ratio of the two yearly growth factors, raised to the number of years.
Lifting the IRR from 20% to 25% over five years needs exit equity of 3.05x the cheque instead of 2.49x, 22.6% more, and the same five points need 33.1% more over a seven-year hold.
How much more enterprise value does that take?
Less than 22.6%, if the deal carries debt at exit. Say exit EV is 1,000 with 400 of debt, so equity of 600 earns 20%. Equity needs to rise to about 736, and with debt unchanged that needs EV of about 1136. Leverage works in your favour here: a 13.6% rise in enterprise value delivers the 22.6% rise in equity. That is also why sponsors stress-test exit multiples so carefully, since small EV moves swing equity hard either way.
Say the limitation: the sums assume a single cheque in and a single exit. With interim dividends or staged investments, the required change in exit value differs, and the IRR needs a full cash flow schedule.
Where candidates lose it
The common loss is thinking linearly: five more points sounds like a small tweak, so candidates say exit value needs to rise by 5% or so. Compounding turns five points a year into about 23% over five years.
The second loss is dividing 25 by 20 and answering 25%. That compares the rates, not the money multiples. Raise the ratio of the growth factors, 1.25 over 1.20, to the number of years.
What the interviewer asks next
What exit multiple of the cheque does 30% over five years need?
Over a three-year hold, how much more exit equity does the same move need?
If exit equity can only rise 10%, how much shorter must the hold be to reach 25%?
032A portfolio company has a loan of 300 at 9% with three years left. It can repay early at a 2% call premium and refinance at 7.5%. How much does refinancing save, net of the premium?Credit and PIK mathsCorePrivate creditMid-market buyout fund
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Ignoring discounting, what is the net saving?
Show the worked solution
About 7.5 before discounting, about 5.7 after. The rate falls 1.5 points on 300, saving 4.5 a year, or 13.5 over three years. The call premium is 2% of 300, which is 6, paid up front. Net, 13.5 less 6 is 7.5. Discount the savings at 7.5% and they are worth 11.7 today, so the net gain is about 5.7.
How should you think about a call premium?
Switching to a cheaper phone plan midway through a contract usually costs an exit fee. You switch only if the monthly saving, times the months left, beats the fee. A call premium is the lender's exit fee: it compensates the lender for losing a loan that pays above today's rate, so the borrower refinances only when the saving over the remaining term beats it. Here the fee is 6 and each year saves 4.5, so the fee is earned back in 1.33 years.
The borrower pays a premium of 6 at the refinancing date and saves 4.5 a year for three years, so the cumulative saving turns positive during year two and ends at 7.5, or about 5.7 discounted at 7.5%.
When would refinancing not be worth it?
Work out the breakeven rate gap. Spread the premium over the years left: 6 over 3 years is 2 a year, which is 0.67% of 300. Refinancing pays only if the rate falls by more than the premium divided by the years remaining, about 67 basis points here. With one year left the breakeven gap would be the full 2 points, and refinancing at 7.5% would lose money.
The relationship
$\text{Net} = L\,(r_{old}-r_{new})\,n - pL = 300 \times 1.5\% \times 3 - 2\% \times 300 = 7.5$
L the loan, 300
r_old - r_new the rate cut, 1.5 points
n years remaining, 3
p the call premium, 2%
What it says in wordsThe saving is the rate cut times the loan times the years left, less the premium paid to get out.
Say what the sums leave out. A new loan carries its own arrangement fee and legal costs, often a point or more, which would eat most of the 7.5. Lenders also build call protection to step down over time, so waiting a year can cut the premium. And if the business improves, a lender may simply reprice the existing loan, which avoids the premium altogether.
Where candidates lose it
The common loss is quoting the gross saving of 13.5 and forgetting the premium, or quoting one year's saving of 4.5. The interviewer wants the full trade: saving over the remaining term against the one-off cost.
The second loss is ignoring the fees on the new loan. Mentioning them, even without a number, shows you know refinancing has a cost on both sides.
What the interviewer asks next
With one year left, does refinancing at 7.5% still make sense?
The new lender charges a 1% arrangement fee. What is the net saving now?
Why do lenders insist on call protection in leveraged loans, and why does it usually step down?
033A business has revenue of 800 and a 12% EBITDA margin. The new owner cuts the cost base by 3% with revenue unchanged. What are the new EBITDA, the new margin and the EBITDA growth?Operating levers and margin mathsCorePortfolio operations teamIndian mid-market PE
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By how much does EBITDA grow?
Show the worked solution
EBITDA rises from 96 to 117.1, a 22% increase, and the margin from 12% to 14.6%. Costs are 800 less 96, which is 704. A 3% cut saves 21.1, and with revenue fixed every rupee of it reaches EBITDA. Because costs are about 7.3 times EBITDA, a small cost change is a large profit change: 3% times 7.33 is 22%.
Why does a 3% cost cut grow EBITDA by 22%?
A family earning Rs 1 lakh a month and spending Rs 88,000 saves Rs 12,000. Trim spending by 3%, about Rs 2,640, and savings jump to about Rs 14,640, up 22%. Profit is the thin slice left after costs, so any change to the large cost base is magnified when measured against the small profit. The magnifier is the ratio of costs to EBITDA, here 704 over 96, about 7.3.
Cutting a cost base of 704 by 3% saves 21.1, which lifts EBITDA from 96 to 117.1 and the margin from 12% to 14.6%, a 22% rise in profit from a small change in costs.
How does an operating partner use this, and where does it break?
Multiply by the exit multiple to see what it is worth. At 8x EBITDA, 21.1 of lasting savings adds about 169 of enterprise value, which is why cost programmes sit at the centre of so many buyout plans. The thinner the margin, the bigger the magnifier: at a 5% margin costs are 19 times EBITDA and a 3% cut lifts EBITDA by 57%.
The relationship
$g_{EBITDA} = c \times \frac{\text{Costs}}{\text{EBITDA}} = 3\% \times \frac{704}{96} = 22\%$
c the percentage cut to the cost base
Costs / EBITDA how many times larger the cost base is than profit
What it says in wordsEBITDA growth from a cost cut equals the cut times the ratio of costs to EBITDA.
Say the limitations. Not all of 704 can be cut: raw materials may be fixed by contract and wages by law, so the 3% often has to come from a much smaller part of the base. Cuts that hurt service can cost revenue later. And the same magnifier works in reverse: a 3% cost overrun would take 22% off EBITDA.
Where candidates lose it
The common loss is answering 3%, applying the cut to EBITDA instead of to costs. The interviewer is testing whether you see that costs are many times larger than profit.
The second loss is computing a 15% margin by adding 3 points to 12%. The new margin is 117.1 over 800, which is 14.6%; it rises by 2.6 points, not 3.
What the interviewer asks next
What revenue growth, with costs growing at the same rate, would deliver the same EBITDA as the 3% cut?
Which costs in a manufacturing business are hardest to cut, and why?
If half of the cost base is fixed, what does a 10% revenue fall do to EBITDA?
035Without a calculator, estimate the square root of 2.5. Then use it: an investment returns 2.5x in 2 years. What is the annual return?Mental mathsCoreGrowth equity
Try it first
What annual return turns 1 into 2.5 over two years?
Show the worked solution
The square root of 2.5 is about 1.58, so 2.5x over two years is about 58% a year. 1.5 squared is 2.25 and 1.6 squared is 2.56, so the root lies between them and much nearer 1.6: 2.5 is 25 of the 31 hundredths along, giving about 1.581. One Newton step from 1.6 gives 1.5813, against a true 1.5811.
How do you find a square root you have not memorised?
A train leaves one station at 6:00 and reaches the next at 9:00. A signal four fifths of the way along is passed at about 8:24: you slide between the two times you know. Find the two squares you know that bracket the number, then slide between them in proportion: the root sits about as far along as the number sits between the squares. 1.5 squared is 2.25 and 1.6 squared is 2.56. The target 2.5 is 0.25 above the lower square out of a gap of 0.31, about 0.81 of the way, so the root is about 1.5 plus 0.081, or 1.581.
Since 1.5 squared is 2.25 and 1.6 squared is 2.56, the root of 2.5 sits about 25/31 of the way from 1.5 to 1.6, close to 1.581, which makes 2.5x over two years about 58.1% a year rather than 75%.
How do you sharpen the estimate and check it?
Use one Newton step: take a guess, divide the number by it, and average the two. From 1.6, 2.5 divided by 1.6 is 1.5625, and the average of 1.6 and 1.5625 is 1.58125. One averaging step from a good guess gets you to three decimals, close enough for any interview. Check by squaring: 1.58 squared is 2.4964, just under 2.5, so the root is a hair above 1.58.
The relationship
$x_{1} = \tfrac{1}{2}\left(x_0 + \frac{N}{x_0}\right) = \tfrac{1}{2}\left(1.6 + \frac{2.5}{1.6}\right) = 1.58125$
x_0 the starting guess, 1.6
N the number whose root you want, 2.5
x_1 the improved guess
What it says in wordsAverage your guess with the number divided by your guess, and you land much closer to the root.
Now the investing use. A growth deal returning 2.5x in two years earns the square root of 2.5, less one, each year: about 58%. The fast answer, 150% over two years so 75% a year, ignores compounding: 1.75 squared is 3.06, not 2.5. Say the limitation: short holds produce eye-catching IRRs on modest money, so investors read the multiple alongside it.
Where candidates lose it
The common loss is splitting the gain evenly: 150% over two years, 75% a year. That treats the return as simple interest. Over two years the factor is squared, so you need a square root, about 1.581.
The second loss is freezing on the root itself. Interviewers are not testing whether you have 1.5811 memorised. They want to see you bracket it with 1.5 and 1.6 and slide.
What the interviewer asks next
Estimate the cube root of 3, and use it for 3x over three years.
What annual return turns 1 into 2 over two years?
A deal returns 2.5x in two years and another 3x in four. Which would an LP prefer, and why might they disagree?
036A target company faces a lawsuit: a 30% chance it must pay Rs 200 crore in damages in 2 years, otherwise nothing. At a 10% discount rate, how much should the price come down? What would you negotiate instead of a price cut?Probability and expected value in dealsCoreAres ManagementLondon · 2025
Try it first
What is the lawsuit worth in today's money?
Show the worked solution
About Rs 49.6 crore off the price, but a cut is the weaker fix. Expected damages are 30% x 200 = Rs 60 crore, payable in two years, so 60 / 1.1^2 is Rs 49.6 crore today. A price cut is fair on average yet leaves you Rs 200 crore exposed if the case is lost. A specific indemnity from the seller backed by an escrow moves the bad branch to the seller instead.
How do you put a number on something that may never happen?
A shopkeeper who knows that 3 in 10 customers return a gadget within the warranty sets aside money for returns before counting profit. A contingent liability is priced as chance times cost, then discounted for time: here 0.3 x 200 = Rs 60 crore, and two years at 10% brings it to Rs 49.6 crore. That is the average cost across all the ways the case could end, in today's money.
A 30% chance of paying Rs 200 crore in two years is worth Rs 60 crore on average and Rs 49.6 crore today at 10%, which is the fair price cut, yet on the losing branch the buyer still owes Rs 165.3 crore in today's money.
The relationship
$PV = \frac{p \times D}{(1+r)^t} = \frac{0.3 \times 200}{1.1^2} \approx 49.6$
p the chance of losing, 30%
D damages if lost, Rs 200 crore
r the discount rate, 10%
t years until payment, 2
What it says in wordsThe value of a possible future payment is its chance times its size, discounted back to today.
Why is a price cut not the best answer?
Because a buyer does not live the average; it lives one branch. Cut the price by 49.6 and lose the case, and you have paid for a Rs 200 crore liability with a Rs 49.6 crore discount. A specific indemnityA promise by the seller to reimburse the buyer for one named liability, here the lawsuit, if it costs money after completion. puts the bad branch back with the seller, who knows the case best. Backing it with an escrow, part of the price held back until the case ends, makes sure the money is there to collect.
Say the trade-offs. Sellers dislike escrows because cash is locked up, so expect to give something back, perhaps a smaller cut or a cap on the indemnity. Warranty and indemnity insurance usually excludes known issues like this one, so check the policy before relying on it. And the 30% is itself an estimate: ask the legal team how they reached it, because the answer moves one for one with it.
Where candidates lose it
The common loss is taking the full Rs 200 crore off the price, which overpays for caution and usually kills the deal, or taking Rs 60 crore off and forgetting the two years of time value.
The second loss is stopping at the number. The question asks what you would negotiate, and a buyout interviewer wants structure: an indemnity, an escrow or a holdback, so the risk sits with the party that knows it best.
What the interviewer asks next
The seller refuses an escrow. What else could you ask for?
How would you treat the lawsuit in the enterprise value to equity value bridge?
If your lawyers say the chance of losing is between 20% and 50%, how does that change your approach?
Asked at Ares Management, Infrastructure, London, 2025 (Wall Street Oasis): How would you itemise a potential lawsuit?
037You buy 30% of a company from its existing shareholders for 300. The company has net debt of 500 and EBITDA of 160. What EV/EBITDA multiple did you pay?Valuation riddlesCoreGrowth equityMid-market buyout fund
Try it first
Which multiple did you pay?
Show the worked solution
About 9.4x EV/EBITDA. Paying 300 for 30% values all the equity at 300 / 0.3 = 1,000. Enterprise value is equity plus net debt, 1,000 + 500 = 1,500. Divided by EBITDA of 160, that is 9.38x. Two steps turn a minority cheque into a whole-company multiple: gross up to 100%, then add back the debt.
Why can you not divide the cheque by EBITDA?
Buying a 30% share of a flat for Rs 30 lakh tells you the owners think the whole flat's equity is worth Rs 1 crore. If the flat also carries a Rs 50 lakh home loan, the flat itself is worth Rs 1.5 crore. EBITDA is earned by the whole company for all its funders, so it has to be compared with the whole company's value, which is all the equity plus the net debt. The cheque is a fraction of only one of those two pieces.
Paying 300 for 30% implies equity of 1,000, and adding net debt of 500 gives an enterprise value of 1,500, which is 9.38x EBITDA of 160; had the 300 gone into the company as new money, the multiple would have been 7.5x.
The relationship
$\frac{EV}{EBITDA} = \frac{\text{Cheque}/\text{stake} + \text{Net debt}}{EBITDA} = \frac{300/0.3 + 500}{160} = 9.375$
Cheque / stake the value of 100% of the equity implied by the price paid
Net debt borrowings less cash, 500
EBITDA 160
What it says in wordsGross the cheque up to the whole equity, add net debt, and divide by EBITDA.
Does it matter whether the money goes to the sellers or into the company?
Yes, and growth investors are asked this often. If the 300 is new money paid into the company, the company's cash rises by 300, net debt falls to 200, and the same price buys a business valued at only 1,200, or 7.5x. Buying existing shares sends the cash to the sellers, so the company's debt is unchanged and the multiple is 9.38x. Ask which it is before you answer.
Say the limitation. A minority price can carry a discount for lack of control, or a premium if the investor gets preference shares with downside protection. So the implied multiple is a starting point, not a clean comparison with what a buyer of 100% would pay.
Where candidates lose it
The common loss is forgetting the debt: grossing the cheque up to 1,000 and reporting 6.25x. That mixes an equity value with an enterprise-level profit.
The second loss is not asking whether the investment is primary or secondary. New money changes net debt, and the multiple moves from 9.4x to 7.5x on the same cheque.
What the interviewer asks next
What P/E did you pay if net income is 80?
The 300 is new money. What is the post-money equity value and your stake?
Why might a minority investor accept a higher implied multiple than a buyer of the whole company?

N_3	the note balance after three years of in-kind interest
1.11	one plus the PIK rate, applied to the growing balance each year
300	the other debt, which does not accrete

You ask	What he does	Road he names	What you do
The truth-teller	Reports the liar's answer honestly	The wrong road	Take the other
The liar	Lies about the truth-teller's answer	The wrong road	Take the other

r	the IRR, the rate that makes the discounted inflows equal the investment
60	the recap dividend in year 2
180	the exit proceeds in year 5

Block	EBITDA	Multiple	Price
Platform	100	11x	1,100
Bolt-on 1	10	6x	60
Bolt-on 2	15	7x	105
Bolt-on 3	25	5x	125
Group	150	9.27x	1,390

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