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.

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 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.