Private Equity puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 22
- Topics
- 12
- Hard
- 30
008A real estate fund is looking at a chain of wedding banquet halls. Roughly how many banquet halls can a city of 50 lakh people support?Real estate PEIndian mid-market PE
Try it first
Which number sets how many halls the city needs?
Show the worked solution
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.
The same 27,000 hall bookings a year need 74 halls if spread over 365 days, 180 if spread over a 150-day season, and 360 if 40% of them fall on 30 peak dates, so the busiest evenings set the number of halls. 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.
Where candidates lose it
The common answer divides annual weddings by 365 and lands near 75 halls. It looks tidy and misses the whole point of the question, which is that the wedding calendar is lumpy and halls cannot store capacity.
The other loss is spending three minutes on the wedding count and none on the conclusion. The interviewer wants the investor's reading: peak sets supply, off-peak sets profit.
What the interviewer asks next
- How would you check the 40% peak share without data?
- What revenue would one hall need per booking to earn back a build cost you assume?
- How does the answer change for a city where many weddings happen in hometowns elsewhere?
015An Indian mid-market fund is looking at a regional dairy. Roughly how many litres of milk does a city of 1 crore people consume in a day?Indian mid-market PE
Try it first
Which unit should the estimate be built on?
Show the worked solution
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.
Twenty-five lakh households using about 0.8 litres a day consume 20 lakh litres at home, and out-of-home use at tea stalls, hotels and sweet shops adds about 5 lakh, giving roughly 25 lakh litres a day, or 250 ml a person. 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.
Where candidates lose it
The common loss is reaching for a remembered national per-person figure and multiplying. Even if the number were right, the interviewer cannot follow it, and a recalled statistic offered as fact is exactly what they are testing you not to do.
The second miss is forgetting out-of-home use. Tea stalls and sweet shops are a large part of urban milk demand, and leaving them out produces a clean, confident and low answer.
What the interviewer asks next
- How would the estimate change for a city with many single migrant workers?
- What share of this volume is likely to be packaged rather than loose, and how would you estimate it?
- How many delivery vehicles would a dairy need to serve 10% of this market?