Financial Analysis puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 47
- Topics
- 13
- Hard
- 30
066Estimate how many litres of packaged milk Mumbai buys in a day.Corporate FP&AConsulting-style case
Try it first
Which order of magnitude is plausible before you build anything?
Show the worked solution
About 32 lakh litres a day, inside a plausible range of roughly 18 to 47 lakh. Assume about 1.3 crore people in four-person homes, 32.5 lakh households. If 80% buy packaged milk at about a litre a day, that is 26 lakh litres. Tea stalls, restaurants and sweet shops add perhaps a quarter more. Each input is an assumption to state aloud and test.
What is the natural unit for a daily staple?
Think about your own home: someone buys one or two packets every morning, and the number depends on how many people share the kitchen, not on who drinks what. For something bought every day by almost every home, the household is the unit, because the buying decision and the quantity are set per kitchen. Start from people, convert to homes, decide what share buys the product, and multiply by the daily quantity. Then add the buyers who are not homes.
About 1.3 crore people make 32.5 lakh homes, 80% of which buy about a litre of packaged milk a day, and a quarter more for tea stalls and restaurants gives about 32.5 lakh litres, a figure that checks out at 250 ml a head and about 217 tankers a day. Every number in the chain is an assumption, not a fact, and should be said that way. The population depends on where you draw the boundary: the city proper and the wider metropolitan region differ by a large factor, so confirm the latest census or municipal estimate and say which one you are using. The 80% packaged share leaves room for loose milk from local dairies, which is still common in parts of the city.
Case Packaged share Litres a home Trade uplift Litres a day Low 70% 0.7 15% 18.3 lakh Base 80% 1.0 25% 32.5 lakh High 90% 1.2 35% 47.4 lakh Moving the three softest assumptions together gives a range of about 18 to 47 lakh litres a day around a base case of 32.5 lakh, so the order of magnitude is secure even though the point estimate is not. How do you cross-check it without reusing the same assumptions?
Use a check that rests on different inputs. Per head, 32.5 lakh litres across 1.3 crore people is about 250 ml a day: two or three cups of tea at about 50 ml of milk each plus a glass for a child. That is believable. From the supply side, if a road tanker carries about 15,000 litres, which is an assumption to state, the city needs about 217 tankers a day. A good estimate survives a check built from a different direction; if the per-head number had come out at two litres, you would know a step was wrong.
What would sharpen the estimate most?
The packaged share is the biggest swing, so it is the first thing to research, followed by the trade uplift, which is hard to observe because tea stalls and sweet shops often buy loose milk in bulk. Seasonality matters too: festival weeks lift demand for sweets and milk. The limit to say: this is a demand estimate on an average day, and a dairy planning supply would also need the peak day and the share each brand holds.
Where candidates lose it
The common loss is starting from cows, dairies or the national milk output, numbers few candidates know and none can check in the room. The estimate collapses into guesses about guesses.
The other slip is silent assumptions. An interviewer cares more about hearing 'I will assume four people a household, and I would want to check that' than about the final number, and a candidate who never states the city boundary has an answer that could be off by half.
What the interviewer asks next
- How would the estimate change for the whole metropolitan region?
- Estimate the daily revenue of the packaged milk market from your volume.
- Which single assumption would you research first, and where would you look?
095Estimate the annual revenue of one multiplex screen in a tier-1 Indian city.Equity researchCorporate finance
Try it first
Which input moves the answer most, and is hardest to guess?
Show the worked solution
Roughly Rs 4.4 crore a year, on the assumptions below. Five shows a day, 200 seats and 30% average occupancy give about 1.1 lakh admissions a year. At an average ticket of Rs 250 that is Rs 2.74 crore; food and beverage at Rs 130 a head adds Rs 1.42 crore; on-screen advertising adds perhaps Rs 0.2 crore. Every input is an assumption to state and then test.
What is the structure before any number?
Estimating what a hall earns is like estimating a restaurant: count the covers, then what each cover spends, then any income that does not depend on covers. Estimate each revenue stream separately: tickets and food both hang off admissions, while advertising depends on the screen, not the audience on the day. So the first job is admissions: shows a day times seats times occupancy times days.
Assume five shows a day on a 200-seat screen, open every day. Occupancy is the soft input: a weekend evening may be nearly full while a Tuesday matinee is mostly empty. Build it rather than guess it: if weekdays run at 20% and weekends at 55%, the weighted average is (5 x 20% + 2 x 55%) / 7, about 30%.
Stream Driver Assumption Rs crore a year Tickets admissions x average ticket 109,500 x Rs 250 2.74 Food and beverage admissions x spend per head 109,500 x Rs 130 1.42 Advertising per screen Rs 20 lakh 0.20 Total 4.36 Every price, occupancy and spend figure is an illustrative assumption, not an industry statistic. About 1.09 lakh admissions a year support Rs 2.74 crore of tickets and Rs 1.42 crore of food and beverage, with advertising a small extra, for about Rs 4.4 crore a year from one screen. How do you know the number is sensible?
Check it three ways. Per day: Rs 4.4 crore over 365 days is about Rs 1.19 lakh, which is 300 admissions spending about Rs 400 each in total, plausible for a screen with five shows. Per seat: about Rs 2.2 lakh a year. And the mix: food at about a third of revenue is the kind of share multiplex operators discuss, and it is high-margin money. The softest input is occupancy: every 10 points on it moves revenue by about Rs 1.4 crore, because it drives tickets and food together.
Say what revenue is not. Gross ticket revenue includes entertainment taxes in some form, and a large share of net ticket income goes to the film's distributor. Confirm current tax rates and typical revenue-sharing terms before using the figure for anything beyond a size estimate. Food, by contrast, the operator keeps in full, which is why its share matters to profit far more than its share of revenue suggests.
Where candidates lose it
The common error is assuming full houses: 5 shows x 200 seats x 365 days at Rs 250 is over Rs 9 crore from tickets alone, more than three times the ticket estimate. Average occupancy across every show, including weekday mornings, is far below a packed Friday night.
The second loss is stopping at tickets. Food and beverage is roughly a third of revenue on these assumptions and a larger share of profit. An interviewer asking about a multiplex wants to hear that you know the business is partly a restaurant with a screen attached.
What the interviewer asks next
- How would a premium recliner screen with 60 seats compare, and why?
- What share of this revenue would you expect the operator to keep after paying the distributor and taxes, and what would you check?
- A new release fills the screen to 70% for two weeks. How much does that add to the year?