Private Equity puzzles, solved step by step

About 360 halls, and the wedding calendar sets that figure, not annual demand. Fifty lakh people marrying once in about 70 years gives roughly 36,000 weddings a year. If half use a hall for 1.5 events each, that is 27,000 hall bookings. Spread evenly that needs only 74 halls, but if 40% fall on 30 peak dates, those dates alone need 360.

How do you get from a population to a number of weddings?

Start with something every listener can check: most people marry once, and a city's population turns over roughly once a lifetime. Take a lifetime of about 70 years. Then 50 lakh people divided by 70 gives about 71,000 people marrying each year, and two people make one wedding, so about 36,000 weddings. A rate built from one human fact, how often a person marries, is easier to defend than a recalled statistic, because the interviewer can follow every step. You can refine it later for a young city or for weddings held in hometowns elsewhere.

Not every wedding uses a banquet hall; some are at home, at temples, on open lawns or in hotels. Assume half use a hall, so 18,000. Many families book a hall for more than one function, a reception or a sangeet as well as the main day, so assume 1.5 hall events each: 27,000 bookings a year. Every one of these is an illustrative assumption to be tested, not a sourced figure.

Why is 27,000 divided by 365 the wrong answer?

Think of an umbrella shop. Averaged over the year, it sells a few a day, but it must hold stock for the first heavy rain, when everyone wants one at once. A banquet hall cannot store an empty Tuesday and sell it on an auspicious Saturday, so capacity has to match the peak, not the average. Weddings bunch into a season, and within the season onto a small number of favoured dates. If 40% of bookings land on 30 dates, those dates carry about 360 events each, and with one main event a hall per evening, the city needs about 360 halls.

What does this tell an investor about the business?

Utilisation is the economics. A city sized for its peak runs most halls far below capacity most of the year, so a hall's earnings depend on how it fills off-peak dates with corporate events, smaller parties and exhibitions. The ratio here, 360 halls against 74 if demand were even, says average utilisation is around 20% on wedding business alone. Say the weak assumptions out loud: the peak share and the hall share move the answer most, so they are what you would test with local operators.

About 25 lakh litres a day. One crore people at four per household is 25 lakh households. A household uses about 0.8 litres a day: 0.25 for tea, 0.35 for drinking and 0.2 for curd and cooking. That is 20 lakh litres at home. Tea stalls, restaurants and sweet shops add perhaps a quarter more, about 5 lakh litres, for roughly 25 lakh in total, or 250 ml a person.

Why build the estimate around a household?

Think about how milk actually enters a home: one or two packets delivered each morning, bought for the whole family. A household is the unit that buys milk and the unit whose uses you can picture, so an assumption made at household level is one the interviewer can check against their own kitchen. One crore people at four per household gives 25 lakh households. The household size is an assumption to state, not a statistic to recite; a city with more single migrants would have smaller households.

Then list the uses. Tea for four people, two cups each, takes about a quarter of a litre. A child's glass or two of drinking milk adds about 0.35. Curd, cooking and the odd sweet take another 0.2. That is 0.8 litres per household per day, and 25 lakh households make 20 lakh litres.

What does the household count miss?

Milk drunk outside the home. Tea stalls, restaurants, hotels and sweet shops are large buyers, and leaving them out understates demand in a city where many people take their tea at a stall. Adding a quarter to household use gives 5 lakh litres more and a total of about 25 lakh. Then do the sanity check: 25 lakh litres over 1 crore people is 250 ml a person a day, roughly one glass. If that sounds wrong for the city you have in mind, adjust the assumption you trust least.

How would a fund use this number?

As a frame, not a forecast. For a dairy deal the question is what share of that daily volume the target already sells and what share it could plausibly win, which needs the packaged versus loose milk split more than the total. A dairy selling 2 lakh litres a day here would hold about 8% of the market. Say the weakest assumption out loud, probably the out-of-home share, and say how you would test it: by counting the tea stalls on a few streets.

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.

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.

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.

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.

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.

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.

About 9 crore tyres a year, on the assumptions stated. Take about 20 crore two-wheelers in use, each riding about 7,000 km a year on 2 tyres: that is 2.8 lakh crore tyre-kilometres. If a tyre lasts about 30,000 km, roughly 9.3 crore tyres wear out each year. Tyre life is the sensitive input: 20,000 km gives 14 crore and 40,000 km gives 7 crore.

Why start from the bikes on the road rather than new sales?

Think of how many toothbrushes a household buys. It depends on how many people live there and how often a brush wears out, not on how many babies were born this year. A replacement market is sized off the installed base, the stock in use, multiplied by how fast each unit wears out. New two-wheelers arrive with tyres already fitted at the factory, which is a separate market sold to manufacturers, so counting new sales here would mix two different customers.

How do you defend each assumption out loud?

Say where each number comes from and how you would check it. Registered vehicle counts overstate the bikes in use, because scrapped vehicles stay on the register, so cut the registered figure down and say you are doing so. Seven thousand km is about 20 km a day, a commute and errands. Then run the cross-check a rider can judge: at 7,000 km a year a 30,000 km tyre lasts about four years, which sounds right for a commuter bike. All three inputs are illustrations to be confirmed against current industry data, not facts.

Close by naming the input you would research first. Tyre life halves or doubles the answer across a plausible range, and rear tyres wear faster than front ones, so a sharper version splits the two. A sponsor looking at a tyre retailer would care about exactly that split, because the rear tyre is the more frequent purchase.

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.

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.

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.

Break-even is Rs 5,000 a passenger; a 10% margin on revenue needs about Rs 5,556. A 2-hour flight costs 2 x Rs 3.6 lakh, Rs 7.2 lakh. An 80% load factor fills 144 of 180 seats, so each passenger must cover Rs 7.2 lakh / 144, Rs 5,000. For cost to be 90% of revenue, divide by 0.9, not multiply by 1.1, which gives about Rs 5,556.

Why divide by passengers and not by seats?

Think of a shared taxi to the airport that costs Rs 1,000 whether four people ride or two. If only two turn up, each pays Rs 500, not Rs 250. A flight costs the same to operate with empty seats, so the fare has to be set on the seats that are actually sold. That is why the load factor sits at the centre of airline economics: at 80%, every paying passenger carries a quarter of an empty seat.

What would you ask the interviewer for next?

In this format you can ask for more data, and asking well scores points. The two inputs that move the answer most are the load factor and what is inside the cost per hour, because fuel and aircraft leases dominate it. At a 70% load factor the break-even rises to about Rs 5,714. You might also ask about ancillary revenue, bags and seats, which lets the base fare sit lower. The interviewer's follow-up, why airlines have often earned poor returns, sits on the same logic: high fixed cost per flight and thin margins mean small swings in load factor or fuel swing profit hard.

About Rs 21,250 crore a year on these assumptions. Take roughly 25 crore school students, assume 85% attend schools that require uniforms, two sets a year and an average of Rs 500 a set: 25 x 0.85 x 2 x 500. Then say which input is weakest. Price is, because government and private sets differ several times over.

How do you structure the estimate before any number?

Say the chain out loud first: students, times the share who must wear a uniform, times sets a year, times price. It is how a shopkeeper would size the season: how many children in the area, how many of their schools insist on a uniform, how many sets each family buys, what they pay. The structure earns most of the marks, because the interviewer can disagree with a number and still follow your answer.

Then put a number on each branch and label it an assumption. Enrolment is the one input with a public source, the government's school statistics; use about 25 crore and say you would confirm the current figure. The uniform share, sets a year and price are judgement calls: 85%, two sets and Rs 500 a set are reasonable starting points, not facts.

Which branch do you name as the biggest uncertainty, and why?

Swing each input across a range you could defend, holding the others. The uniform share from 75% to 95% moves the pool by about Rs 5,000 crore. Sets a year from 1.5 to 2.5 moves it by about Rs 10,625 crore. Price from Rs 300 to Rs 800 moves it by Rs 21,250 crore, so price is where you would spend your first hour of real work. The reason is the mix: many state schools supply uniforms cheaply in bulk, while private schools sell branded sets at a premium.

A strong close splits the pool into those two segments and says which one a buyout fund would care about: the private school segment, where the price is set by the school and the supplier relationship is sticky.

About 2,000 shops on these assumptions. Of 2 crore people, assume 30% drink coffee, a cup a day each: 4.2 crore cups a week. If 10% are bought outside the home, that is 42 lakh a week, 6 lakh a day. At 300 cups a shop a day the metro supports about 2,000. The share bought outside is the branch to test.

What is the chain, and why build it before any number?

Shops exist to serve demand, so go from people to cups to shops. Picture a single street: how many of the people passing drink coffee, how often, and how many of those cups are bought rather than made at home. A sizing answer is a chain of stated assumptions, and the interviewer is testing the chain, not the final figure. Say the chain first, then fill it.

How do you sanity check the supply side?

Three hundred cups a day is the number to defend. A shop open twelve hours selling 25 cups an hour reaches it; a quiet neighbourhood outlet may sell half that and a busy office-district one double. Check the answer from the other end: about one shop for every 10,000 people, which you can compare with what you see on a busy street. If your answer implied a shop for every 500 people, a branch is wrong, and you would say which.

A growth equity interviewer often follows with how many of those shops a single chain could own, which turns the sizing into a market share question. Have the number of shops in your answer split into chains and independents if you can, even roughly.