Private Equity puzzles, solved step by step

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

Showing 11–20 of 30 · filtered from 100Clear filters

034Roughly how many cinema tickets are sold in India in a year? Build it from the demand side, then check it from the supply side.Market sizing and estimationHardAdvent InternationalBoston · 2022
Try it first
Before building anything: which order of magnitude feels right?
Show the worked solution
Roughly 0.8 to 0.9 billion tickets a year, on round assumptions. Demand: 1,400 million people, a quarter of whom go in a year, about 2.5 times each, gives about 875 million. Supply: about 9,000 screens, 4 shows a day, 200 seats, 30% full, gives about 788 million. Two routes agreeing within about 11% is the check; every input should be tested against an industry report.
Why build it twice?
If you want to know how many people eat at a canteen each day, you can count students and guess how often they eat there, or count tables, sittings and how full they look at lunch. Either guess on its own could be badly off; if both land near the same number you can trust it. A sizing built from demand and checked from supply catches the assumption that is wildly off, which a single chain never reveals. Interviewers care more about the check than about the final digit.
Demand of 1,400 million people times 25% who go times 2.5 visits gives 875 million tickets, and supply of 9,000 screens times 1,460 shows times 200 seats times 30% occupancy gives 788 million, so two independent routes agree on roughly 0.8 to 0.9 billion.
How do you defend each assumption out loud?
Segment before you guess. A quarter of the population going at least once a year is an average of very different groups: urban young adults may go many times, while much of rural India has no screen nearby. Say which segment drives the answer and why your share and frequency are reasonable for it, then give one number. On supply, the interviewer will push on occupancy: 30% is plausible because weekday afternoon shows run thin while weekend evenings fill. The screen count is an assumption to confirm, not a fact to recite.
Input Assumption If you halve it
People who go in a year 25% 438m demand
Visits per goer 2.5 438m demand
Occupancy 30% 394m supply
Screens 9,000 394m supply
Every input moves the answer one for one, so the honest range is wide and worth saying out loud.
A growth investor would go one step further: tickets times an average price gives box office revenue, and food and drink add a second stream on the same visits. Say the limitation: streaming changes how often people go, so a figure built on old habits may overstate tomorrow's market.
Where candidates lose it
The common loss is a single long chain with one unrealistic link, usually that most Indians go to the cinema several times a year, giving a number in the billions with no check. The interviewer then asks how many screens that implies, and the answer falls apart.
The second loss is reciting a screen count or a ticket figure from memory as fact. Present every input as an assumption, explain why it is reasonable, and offer the second route as the check.
What the interviewer asks next
What average ticket price would you assume, and what does that make the box office?
How would you split the answer between multiplex and single-screen cinemas?
Which single assumption would you research first, and where?
Asked at Advent International, Private Equity, Boston, 2022 (Wall Street Oasis): Market sizing questions, e.g.: how many books were sold this year in the US?
038A fund draws 1,000 at once and returns 1,500 in a single distribution after 5 years. The waterfall has an 8% compounding preferred return, a full GP catch-up and 20% carry. How much does the GP receive, and what share of the fund's profit is that?Fund economics numeracyHardSecondaries and fund of funds
Try it first
Profit is 500. How much carry does the GP get?
Show the worked solution
The GP receives about 30.7, all of it from the catch-up, which is 6.1% of the profit. LPs first get their 1,000 back, then the 8% compounding preferred return: 1,000 x (1.08^5 - 1) = 469.3. That leaves 30.7. A full catch-up sends 100% of the next distributions to the GP until it holds 20% of profit, which would take 117.3, so the money runs out inside that tier.
What order does the money flow in?
Think of a restaurant partnership where the investor gets her money back first, then an 8% a year return on it, and only then does the chef share in the profit. A waterfall pays in tiers: capital back, then the preferred returnThe minimum return LPs receive before the GP shares in profit, often 8% a year, here compounding., then the GP's catch-up, then the 80/20 split, and each tier must fill before the next one starts. Here capital takes 1,000, the preferred return takes 469.3, and only 30.7 is left to flow further.
The relationship
$\text{Pref} = 1000\,(1.08^5 - 1) = 469.3 \qquad \text{Full catch-up} = \frac{0.2}{0.8}\times 469.3 = 117.3$
1.08^5 - 1 five years of 8% compounding, 46.9%
0.2 / 0.8 the catch-up needed for the GP to hold 20% of the profit paid so far
What it says in wordsThe catch-up tier is a quarter of the preferred return, because the GP must end with one part to the LPs' four.
Of 1,500 returned, 1,000 repays capital and 469.3 pays the preferred return, so only 30.7 reaches the GP catch-up, which needs 117.3 to fill; the GP's share of profit is 6.1% here and reaches the full 20% only at 1,587.
Why does the GP's share jump so fast just above the hurdle?
Because inside the catch-up tier every extra unit goes to the GP. Between 1,469 and 1,587 of proceeds, each additional 1 of exit value adds 1 to carry, so the GP's share climbs from zero to 20% across a band of only 117. Above 1,587 the split settles at 80/20 and stays there.
This is why secondaries buyers and LPs model carry near the hurdle so carefully. A fund sitting just above its hurdle has a GP with a strong incentive to push value up through that band, and a buyer of the LP interest must remember that much of the next gain goes to the GP. The limitation: real waterfalls run on dated cash flows, often deal by deal, with clawbacks; a single drawdown and exit is the clean case.
Where candidates lose it
The common loss is answering 100, 20% of the 500 profit, as if carry were a flat share. Near the hurdle the catch-up tier decides the answer, and here it is barely filled.
The second loss is using a simple 8% a year, 400 over five years, instead of compounding. That leaves 100 for the catch-up, and the GP's share comes out at 20%, not 6.1%. Ask whether the hurdle compounds before you start.
What the interviewer asks next
What would the GP receive with a 50% catch-up instead of a full one?
At what total proceeds does the GP first receive anything?
How does a deal-by-deal waterfall change the GP's carry on the same fund?
041Estimate the annual power bill of a data centre with 20 MW of IT capacity, running at 70% utilisation, with a power usage effectiveness (PUE) of 1.4 and a tariff of Rs 7 per kWh.Market sizing and estimationHardInfrastructure fund
Try it first
Which is closest to the yearly bill?
Show the worked solution
About Rs 120 crore a year. 20 MW at 70% use is 14 MW of IT load. A PUE of 1.4 means the site draws 1.4 times that for cooling and losses, 19.6 MW. Running all year, 19.6 MW times 8,760 hours is about 171.7 million kWh. At Rs 7 a kWh that is about Rs 1,202 million, or Rs 120 crore. The tariff is an assumption to check.
What does PUE add to the bill?
A home air conditioner does not just cool the room; it also uses power to run its own compressor and fan. Power usage effectivenessTotal power drawn by the whole facility divided by the power used by the IT equipment alone. 1.0 would mean no overhead at all. is total site power divided by IT power, so a PUE of 1.4 means every 1 MW of servers needs another 0.4 MW for cooling, power conversion and lighting. Here that is 5.6 MW on top of 14 MW of IT load, and the bill pays for all 19.6.
20 MW of IT capacity at 70% use draws 19.6 MW once a PUE of 1.4 adds cooling and losses, which over 8,760 hours is 171.7 million kWh and about Rs 120 crore a year at an assumed Rs 7 per kWh.
How do you keep the units straight out loud?
Convert once, early, and say it. One megawatt running for one hour is 1,000 kWh, so 19.6 MW for a year is 19.6 x 8,760 x 1,000, about 171.7 million kWh. Then price it: Rs 7 times 171.7 million is about Rs 1,202 million. A crore is ten million, so divide by ten: Rs 120 crore. Most wrong answers to this question are right in method and a factor of ten off in units.
The relationship
$\text{Bill} = C \times u \times PUE \times 8760 \times 1000 \times p = 20 \times 0.7 \times 1.4 \times 8760 \times 1000 \times 7$
C IT capacity, 20 MW
u utilisation, 70%
PUE total power over IT power, 1.4
p tariff, Rs 7 per kWh, an assumption
What it says in wordsMultiply the power actually drawn by the hours in a year, convert to kWh, and price it.
Now the investor's view. Power is usually the largest running cost of a data centre, so PUE is an economic number, not a technical one: improving it from 1.4 to 1.3 saves about Rs 8.6 crore a year here. Many colocation contracts pass power through to tenants, which shifts who bears the tariff risk. Ask how the contracts treat power before you treat the bill as the owner's cost.
Where candidates lose it
The common loss is a factor of ten in the units: candidates convert MW to kWh correctly and then slip between million and crore, landing at Rs 12 crore or Rs 1,200 crore. Say each conversion out loud.
The second loss is pricing only the IT load and forgetting the PUE, which understates the bill by 40% and misses the point of the question.
What the interviewer asks next
What tariff would make the bill Rs 150 crore?
If utilisation rises to 90%, what happens to the bill and to the PUE?
In a colocation contract, who usually pays for power, and why does that matter to the investor?
043An asset earns 9% a year unlevered and debt costs 12%. What is the return on equity at 0%, 40% and 70% debt funding? When does adding leverage lower the equity return?Leverage and capital structureHardLarge-cap buyout fundPrivate credit
Try it first
At 70% debt, roughly what does equity earn?
Show the worked solution
9%, 7% and 2%: here every turn of debt lowers the equity return, because debt costs more than the asset earns. On 100 of assets earning 9, debt of 40 costs 4.8 and leaves 4.2 on equity of 60, which is 7%. Debt of 70 costs 8.4 and leaves 0.6 on equity of 30, which is 2%. Leverage helps only when the asset earns more than the debt costs; when it earns less, leverage works in reverse.
How does leverage change the equity return?
Borrow at 12% to buy a flat that earns 9% in rent and you lose 3% a year on every borrowed rupee, and the more you borrow, the bigger the loss as a share of your own money. Equity keeps whatever the asset earns after the debt is paid, so each unit of debt adds the gap between the asset return and the debt cost, times the debt-to-equity ratio. With a 9% asset and 12% debt that gap is minus 3 points.
The relationship
$r_E = r_A + (r_A - r_D)\frac{D}{E} = 9\% + (9\% - 12\%) \times \frac{70}{30} = 2\%$
r_A the unlevered asset return, 9%
r_D the cost of debt, 12%
D/E debt over equity, 70/30 at 70% debt
What it says in wordsEquity earns the asset return plus the asset-debt gap, scaled up by how much debt sits on each unit of equity.
With an asset earning 9%, debt at 12% drags the equity return down to 7% at 40% debt and 2% at 70%, while debt at 6% lifts it to 11% and 16%, because leverage magnifies whatever the gap between the two rates is.
Why does a buyout investor worry about this?
A business bought at a high multiple has a low unlevered return: at 12x EBITDA, pre-tax cash yield on the purchase price is in single digits. If borrowing costs rise above that yield, the leverage that used to lift returns now pulls them down, and the deal depends entirely on growth and multiple expansion. This is called negative leverage, and it is why higher rates squeeze what sponsors can pay.
Debt share Equity return, debt at 12% Equity return, debt at 6%
0% 9% 9%
40% 7% 11%
70% 2% 16%
The same three capital structures give falling returns when debt costs more than the asset earns and rising returns when it costs less.
Say the limitations. The sums ignore tax: interest is usually deductible, which lowers the after-tax cost of debt and moves the break-even. And they treat the asset return as fixed. A growing business can out-earn expensive debt later even if it does not today, which is the bet some sponsors knowingly make.
Where candidates lose it
The common loss is the reflex that leverage always increases equity returns. It magnifies the spread, and when the spread is negative it magnifies losses of return. Interviewers ask this exactly to catch that reflex.
The second loss is working in percentages of the asset instead of the equity. Compute earnings, subtract interest, and divide by the equity cheque: 0.6 on 30 is 2%, not 0.6%.
What the interviewer asks next
At what cost of debt does leverage stop mattering for this asset?
How does the interest tax shield change the 70% debt answer at a 25% tax rate?
If the asset return grows 1 point a year, how long before 70% debt at 12% starts to help?
044Work backwards: EBITDA grows from 100 to 140 over 5 years and the business exits at 9x. Entry debt is 5x EBITDA and 200 of it is repaid by exit. What is the highest entry multiple that still returns 3x the equity?Mental paper LBOsHardNeuberger BermanNew York · 2022
Try it first
Where does the maximum entry multiple land?
Show the worked solution
About 8.2x. Exit EV is 140 x 9 = 1,260. Debt falls from 500 to 300, so exit equity is 960. A 3x return allows entry equity of 960 / 3 = 320. Add the 500 of entry debt and the most you can pay is an EV of 820, which is 8.2x entry EBITDA. Pay more and the 3x target is missed; fees and costs would lower the ceiling further.
Why work backwards instead of guessing an entry price?
If you want to arrive at a wedding by 7 and the drive takes two hours with half an hour of traffic, you leave at 4:30. You fix the end point and walk back. A target multiple fixes the exit equity you need relative to the cheque, so the maximum price is found by running the LBO in reverse: exit value, less exit debt, divided by the target, plus entry debt. Every number you need is in the question.
Exit EV of 1,260 less 300 of remaining debt leaves exit equity of 960, which supports entry equity of 320 at a 3x target; adding 500 of entry debt sets the maximum entry EV at 820, or 8.2x EBITDA of 100.
The relationship
$EV_{0}^{max} = \frac{E_5 \times m_{exit} - D_5}{\text{target}} + D_0 = \frac{1260 - 300}{3} + 500 = 820$
E_5 x m_exit exit EV, 140 x 9
D_5 debt left at exit, 300
target the money multiple required, 3x
D_0 entry debt, 5 x 100 = 500
What it says in wordsThe most you can pay is the exit equity divided by the target multiple, plus the debt you borrow at entry.
What does 8.2x tell the investment committee?
It is a ceiling, not an offer. Entering at 8.2x and exiting at 9x means the plan relies on a little multiple expansion as well as 40% EBITDA growth and 200 of debt paydown, so the committee will test each of those three. 3x over five years is an IRR of about 25%: 3 to the power one fifth is about 1.246.
Say the limitations. Transaction fees and financing costs come out of the equity at entry, so the true ceiling on the headline price is lower. A real model would also hold some cash at exit and might pay interest in kind. And if the lenders will not provide 5x at an 8.2x price, the equity cheque grows and the ceiling falls.
Where candidates lose it
The common loss is forgetting to add the entry debt back: candidates divide exit equity by 3, get 320, and say 3.2x. That is the equity cheque over EBITDA, not the enterprise multiple.
The second loss is using entry debt instead of exit debt when computing exit equity, which ignores the 200 repaid and makes the ceiling look lower than it is. Track debt at both ends.
What the interviewer asks next
If the exit multiple is 8x instead of 9x, what is the new ceiling?
How much does the ceiling fall if 20 of fees are paid out of the equity at entry?
What IRR does 3x in five years imply, and what multiple would 25% need?
Asked at Neuberger Berman, Private Equity, New York, 2022 (Wall Street Oasis): Interviews 4-5 were very technical again and also included multiple paperback LBOs and other, more advanced technicals.
045A seller wants 100 upfront plus an earnout of 50 if year-2 EBITDA hits a target. You think the chance of hitting it is 40%. At a 12% discount rate, what is the earnout worth to you today, and what is the total price in value terms?Probability and expected value in dealsHardMid-market buyout fund
Try it first
What is the earnout worth to you today?
Show the worked solution
The earnout is worth about 15.9 to you, so the price in value terms is about 115.9. A 40% chance of 50 is 20 on average, payable in two years, and 20 / 1.12^2 is 15.9. The headline price is 150, but you are paying about 116 in value. A seller who thinks the chance is 80% values the same earnout at 31.9, which is why earnouts close price gaps.
How do you value a payment that may not happen?
A shopkeeper who offers a Rs 500 voucher to anyone who spends Rs 5,000 next month books its cost by how many customers she expects to claim it, not by the face value. An earnout is a contingent payment, so you value it as chance times amount, discounted for the wait: 0.4 x 50 / 1.12^2 is about 15.9. That number, not 50, is what the earnout adds to your price.
The relationship
$V = \frac{p \times EO}{(1+r)^t} = \frac{0.4 \times 50}{1.12^2} \approx 15.9$
p your estimate of the chance the target is hit, 40%
EO the earnout payment, 50
r the discount rate, 12%
t years until payment, 2
What it says in wordsAn earnout is worth the chance of paying it, times the amount, discounted to today.
The same 50 earnout is worth 15.9 today to a buyer who puts the chance at 40% and 31.9 to a seller who puts it at 80%, so the buyer feels it is paying 115.9 while the seller feels it is receiving 131.9.
Why does an earnout make a deal possible?
Because both sides can be right in their own terms. The seller, confident in the plan, values the package at about 132; the buyer, more cautious, values it at about 116; and the contract lets each side bet on its own view. If the target is hit, the buyer pays more but has a business that performed. If not, the buyer has paid 100 for a business that did not.
Say the risks. Earnouts are a common source of disputes: how EBITDA is defined, which costs the buyer loads onto the business after closing, and whether the seller's management stays to run it. A buyer controls the business that decides the payout, so the contract needs a tight EBITDA definition and agreed accounting policies.
Where candidates lose it
The common loss is counting the earnout at its face value of 50, which makes the price look like 150 and either overpays or kills the deal. The other is applying the probability but forgetting two years of waiting.
The second loss is treating the 40% as a fact. It is your estimate; the seller's is higher. Say that the gap between the two estimates is exactly what the earnout is for.
What the interviewer asks next
What chance of hitting the target makes the earnout worth 25 to you?
Would you rather the earnout be all-or-nothing or paid in proportion to EBITDA achieved, and why?
How would you protect the seller from the buyer managing EBITDA down after closing?
051A sponsor buys a business at 12x EBITDA, funded 50% with debt, and repays none of the debt. It expects to sell at 9x. By how much must EBITDA grow before the sponsor simply gets its money back?Mental paper LBOsHardLarge-cap buyout fund
Try it first
Before you work it: how much EBITDA growth returns the equity, and no more?
Show the worked solution
EBITDA must grow by 33.3% just to hand the sponsor its money back. Take EBITDA of 100: the business costs 1,200, funded by 600 of debt and 600 of equity. With no paydown the debt is still 600 at exit, so equity is 600 only if the business is again worth 1,200. At 9x that needs EBITDA of 133.3, which is 12 over 9 minus 1.
Why is the answer not 25%?
Picture a flat bought for 12 years of rent and sold later when buyers will pay only 9 years of rent. To get your price back, the rent has to rise until 9 years of it equals the old 12. That is a rise of 12 over 9, a third, not a quarter. A 25% cut in the multiple needs a 33.3% rise in earnings to undo it, because the recovery is measured on the smaller multiple. It is the same base effect that makes a 10% fall need an 11.1% rise.
Entry and exit both show an enterprise value of 1,200: twelve turns of EBITDA 100 going in, nine turns of EBITDA 133.3 coming out, so EBITDA has to grow 33.3% before the 600 of equity is returned.
Why does the 50% debt not change the answer?
Write the equity at exit as exit value less debt. The debt was 600 going in and, with no repayment, is 600 coming out. Equity is returned in full only when the exit value equals the entry value, so the break-even growth is the same at 30% debt, 50% debt or no debt at all. Leverage changes how fast equity grows once you pass break-even, and how fast it is wiped out below it. It does not move the break-even itself when nothing is repaid.
The relationship
$g = \frac{M_{\text{entry}}}{M_{\text{exit}}} - 1 = \frac{12}{9} - 1 = 33.3\%$
g EBITDA growth needed to get the equity back
M_entry the purchase multiple, 12x
M_exit the exit multiple, 9x
What it says in wordsWith no debt repaid, the break-even EBITDA growth is the entry multiple divided by the exit multiple, less one.
What does this do to a real growth plan?
Say the plan grows EBITDA 50% to 150. Sold at 12x, the business would be worth 1,800 and the equity 1,200, double the cheque. Sold at 9x it is worth 1,350 and the equity 750, only 1.25x. The first third of the growth plan is spent refilling the hole left by the lower multiple. This is why sponsors who pay high multiples underwrite their exit at the entry multiple or lower, and why the interviewer asks the question.
Where candidates lose it
The fast wrong answer is 25%, read straight off the drop from 12x to 9x. It measures the cut on the old multiple, when the earnings have to climb back on the new one: 12 over 9 is 1.333, not 1.25.
The second trap is letting the 50% debt pull you into a leverage calculation. With no paydown the debt cancels out of the break-even, and saying so in one sentence shows the interviewer you saw it.
What the interviewer asks next
The company repays 200 of debt over the hold. What EBITDA growth now returns the equity?
EBITDA grows 50% and the exit is at 9x after five years. What is the IRR? (equity 750 on 600)
Why might a buyer at 9x in five years pay less than you did, even for a better business?
058A deal is worth 2.0x the equity after four years, an IRR of about 18.9%. Holding one more year would add 10% to the exit equity, taking it to 2.2x. Does the IRR rise or fall, and what growth in the extra year would keep the IRR flat?Returns mathsHardLarge-cap buyout fundMid-market buyout fund
Try it first
Hold a fifth year for 10% more equity. What happens to the IRR?
Show the worked solution
The IRR falls, from 18.9% to about 17.1%, even though the money multiple rises from 2.0x to 2.2x. IRR is an average yearly growth rate, and a year that adds 10% is below the 18.9% the deal has been earning. To keep the IRR flat, the fifth year must grow equity by 18.9% itself, to about 2.38x. The hurdle for holding on is the IRR already achieved.
Why can a bigger multiple mean a lower IRR?
Think of a batsman averaging 19 runs a match over four matches. If he scores 10 in the fifth, his total rises but his average falls. IRR is the average yearly growth of the equity, so any year that grows it by less than the current IRR lowers the average, even while the total keeps rising. The money multiple is the total; the IRR is the average. Here the deal has averaged 18.9% a year and the fifth year offers 10%.
At 2.0x after four years the IRR is 18.9%; a fifth year that adds 10% lifts the multiple to 2.2x but drops the IRR to 17.1%, and only 2.38x at year 5 would hold the IRR flat.
The relationship
$2.0^{1/4} = 1.189 \qquad 2.2^{1/5} = 1.171 \qquad 2.0 \times 1.189 = 2.378$
2.0^(1/4) one plus the IRR of 2.0x over four years
2.2^(1/5) one plus the IRR of 2.2x over five years
2.378 the multiple at year 5 that keeps the IRR at 18.9%
What it says in wordsTake the root of the multiple by the number of years to get one plus the IRR; to hold it, the extra year must grow by the same factor.
How would a fund actually weigh the choice?
Both numbers matter to an investor, and they point opposite ways. The extra year adds 0.2x of money but costs about 1.8 points of IRR, so the right call depends on what the cash would earn if it were returned now. If the investors could put it to work at more than 10% elsewhere, selling at year 4 is better; if not, the extra 0.2x is real money. Say this trade-off out loud, then say the limit: the 10% is a forecast, while the 2.0x offer may be on the table today.
Where candidates lose it
Candidates hear that equity grows and say the IRR rises. They are describing the money multiple. IRR is a rate per year, and a below-average year pulls a rate down.
The second miss is on the flat-IRR part: answering 10%, or the old IRR divided over five years. The extra year has to match the rate already earned, about 18.9%, which takes the multiple to roughly 2.38x.
What the interviewer asks next
What if the extra year adds 25%? What IRR then?
Why do investors track both IRR and the money multiple rather than one of them?
How does a dividend recap at year 4 change this decision?

Input	Assumption	If you halve it
People who go in a year	25%	438m demand
Visits per goer	2.5	438m demand
Occupancy	30%	394m supply
Screens	9,000	394m supply

Debt share	Equity return, debt at 12%	Equity return, debt at 6%
0%	9%	9%
40%	7%	11%
70%	2%	16%

065Size the annual revenue pool of private dental clinics in an Indian metro of 1.2 crore people. Then say what share of it a rollup of 60 clinics could hold.Market sizing and estimationHardIndian mid-market PEMid-market buyout fund

Try it first

On these assumptions, roughly what share of private visits could 60 clinics handle?

Show the worked solution

About Rs 720 crore a year, of which 60 clinics could hold roughly 7.5%. Take 25% of 1.2 crore people seeing a dentist, 2 visits each and 80% of visits at private clinics: 48 lakh visits. At Rs 1,500 a visit that is Rs 720 crore. Sixty clinics at 20 visits a day for 300 days handle 3.6 lakh visits, about Rs 54 crore of revenue. Every input is an assumption to be tested.

Why build the market from visits rather than from spend per person?

Think of sizing the market for haircuts. Average spend per person hides the fact that some people go monthly and others never; counting the people who go, how often, and what one cut costs is easier to defend line by line. A visit-based tree gives you inputs you can each test separately, and it produces the same unit, visits, that a clinic's capacity is measured in. That second point is why it suits a rollup question: the market and the business are counted in the same currency.

A metro of 1.2 crore people produces about 48 lakh private dental visits a year on these assumptions, worth about Rs 720 crore at Rs 1,500 a visit, and 60 clinics doing 6,000 visits each would handle 7.5% of them, about Rs 54 crore of revenue.

How do you test the demand side against supply?

Turn the visits into clinics and see if the number feels right. Forty eight lakh visits over 300 working days is 16,000 visits a day; at 15 a day for a small single-dentist clinic, that is about 1,067 clinic-equivalents. If a local count found far more or far fewer clinics than that, one of the demand assumptions is wrong, most likely the share who visit or the fee. Say that you would check it with a street count in two or three neighbourhoods before trusting the total.

Input	Assumption	Result
Population	1.2 crore
Share who visit a dentist in a year	25%	30 lakh patients
Visits per patient	2	60 lakh visits
Share at private clinics	80%	48 lakh visits
Average revenue per visit	Rs 1,500	Rs 720 crore
60-clinic rollup capacity	6,000 visits each	7.5% share

Each line is an assumption to be tested; together they give about Rs 720 crore of private clinic revenue and a 7.5% capacity share for a 60-clinic rollup.

What does the share tell a buyout investor?

It frames the thesis. At about 7.5%, the rollup would be the largest single brand in a fragmented market without needing to win most patients, which is the shape a rollup thesis wants. The limits matter as much: the fee per visit blends cheap check-ups with expensive implants, so a chain that skews to higher-value treatment could earn more from the same visits, and capacity is not demand. Sixty clinics only reach 3.6 lakh visits if patients actually come.

Where candidates lose it

Candidates often multiply the whole population by an annual spend and get a number they cannot defend, or forget that many visits happen at government hospitals and charitable clinics, which a private chain cannot capture.

The second miss is stopping at the market size. The question asks for the rollup's share, which needs one clinic's capacity stated in the same unit as the market.

What the interviewer asks next

Implants are 10% of visits but half of revenue. How does that change the sizing?
How would you test the 25% visit rate without any published data?
What would make you worry that 60 clinics cannot fill their chairs?

066Two companies each have EBITDA of 100 and trade at 8x. One carries debt of 2x EBITDA, the other 6x. EBITDA falls 25% and the multiple stays at 8x. By how much does the equity value fall in each?Leverage and capital structureHardLarge-cap buyout fundMid-market buyout fund
Try it first
The business value falls 25% in both. What happens to the equity?
Show the worked solution
Company A's equity falls 33%; Company B's is wiped out. Both businesses fall from 800 to 600 of enterprise value, a loss of 200. The debt does not fall with them, so the loss lands entirely on the equity. A had 600 of equity and keeps 400. B had only 200 and keeps nothing: its lenders are now owed exactly what the business is worth.
Why does the equity take the whole fall?
Picture two people who each own a Rs 80 lakh flat. One owes Rs 20 lakh on it, the other Rs 60 lakh. If flat prices drop by Rs 20 lakh, both still owe the bank the same amount, so the first owner's stake falls from 60 to 40 and the second's from 20 to nothing. Debt is a fixed claim, so any change in the value of the business falls first and entirely on the equity. The more debt, the thinner the equity cushion that absorbs it.
Both companies lose 200 of enterprise value when EBITDA falls 25% at 8x; with debt of 200, Company A's equity drops from 600 to 400, 33%, while with debt of 600, Company B's equity drops from 200 to zero.
The relationship
$\%\Delta E = \%\Delta EV \times \frac{EV}{E} \qquad 25\% \times \tfrac{800}{600} = 33\% \qquad 25\% \times \tfrac{800}{200} = 100\%$
%Delta EV the fall in enterprise value, 25%
EV/E enterprise value over equity, the leverage multiplier
E equity value before the fall
What it says in wordsThe equity's percentage fall is the business's percentage fall multiplied by how many times larger the business is than the equity.
What does a buyout investor take from this?
Leverage works in both directions with the same multiplier. At 6x debt on 8x value, the equity is a quarter of the business, so every 1% move in enterprise value is a 4% move in the equity. That is what makes high leverage attractive on the way up and fatal on the way down. The limit worth saying: in practice B's equity rarely goes straight to zero on paper. It may keep some option value while the debt has years to run, and the lenders would usually step in through a restructuring before the equity holders lost control.
Where candidates lose it
The fast wrong answer is 25% for both, carrying the business's fall straight across to the equity. It ignores that the debt holds its value while the business shrinks.
The second slip is on Company B: saying 75% by scaling the 25% by three. Work in money, not percentages: 200 lost against 200 of equity is everything.
What the interviewer asks next
How far can EBITDA fall before Company A's equity is wiped out?
If EBITDA rises 25% instead, what are the two equity gains?
Why might B's equity still trade above zero after the fall?

1.08^5 - 1	five years of 8% compounding, 46.9%
0.2 / 0.8	the catch-up needed for the GP to hold 20% of the profit paid so far

C	IT capacity, 20 MW
u	utilisation, 70%
PUE	total power over IT power, 1.4
p	tariff, Rs 7 per kWh, an assumption

r_A	the unlevered asset return, 9%
r_D	the cost of debt, 12%
D/E	debt over equity, 70/30 at 70% debt

E_5 x m_exit	exit EV, 140 x 9
D_5	debt left at exit, 300
target	the money multiple required, 3x
D_0	entry debt, 5 x 100 = 500

Try it first

Why build it twice?

How do you defend each assumption out loud?

Where candidates lose it

What the interviewer asks next

Try it first

What order does the money flow in?

Why does the GP's share jump so fast just above the hurdle?

Where candidates lose it

What the interviewer asks next

Try it first

What does PUE add to the bill?

How do you keep the units straight out loud?

Where candidates lose it

What the interviewer asks next

Try it first

How does leverage change the equity return?

Why does a buyout investor worry about this?

Where candidates lose it

What the interviewer asks next

Try it first

Why work backwards instead of guessing an entry price?

What does 8.2x tell the investment committee?

Where candidates lose it

What the interviewer asks next

Try it first

How do you value a payment that may not happen?

Why does an earnout make a deal possible?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the answer not 25%?

Why does the 50% debt not change the answer?

What does this do to a real growth plan?

Where candidates lose it

What the interviewer asks next

Try it first

Why can a bigger multiple mean a lower IRR?

How would a fund actually weigh the choice?

Where candidates lose it

What the interviewer asks next

Try it first

Why build the market from visits rather than from spend per person?

How do you test the demand side against supply?

What does the share tell a buyout investor?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the equity take the whole fall?

What does a buyout investor take from this?

Where candidates lose it

What the interviewer asks next