Private Equity puzzles, solved step by step
- Puzzles
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- Topics
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- Hard
- 30
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.Advent 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?
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.Infrastructure 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 relationshipC 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?
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.Indian 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?
