Financial Analysis puzzles, solved step by step

About 2,000 sit-down cafés, as a range of roughly 1,000 to 4,000. Take about 1.3 crore people, 70% of them aged 15 to 64, and assume 20% of those visit a café twice a week. That is about 5.2 lakh cups a day; at 250 cups a café a day, about 2,080 cafés. A supply check, 150 commercial clusters with 10 cafés each plus 500 neighbourhood ones, gives about 2,000.

What exactly are you counting?

Say the definition before any number. In Bengaluru the answer changes several times over depending on whether small standing filter coffee counters count, so define a coffee shop as a sit-down café selling espresso-style coffee and say you are leaving the counters out. Then state the population as an assumption, about 1.3 crore for the metro area, and tell the interviewer you would confirm it. In a market sizing nobody is marking the population figure; they are marking whether your chain of reasoning holds.

How do you build it from demand?

Think of a single café first: how many cups does it need to sell to pay its rent? Then ask how many cups the city drinks. Of 1.3 crore people, about 70% are aged 15 to 64, so 91 lakh. Assume 20% of them use cafés, 18.2 lakh people, at two cups a week each: 36.4 lakh cups a week, or about 5.2 lakh a day. A café open 12 hours selling around 20 cups an hour serves about 250 cups a day, so the city supports about 2,080 cafés.

How do you check it, and which assumption matters most?

Count from the other side: supply. Picture the tech parks, malls and busy high streets, say 150 of them, with about 10 cafés each, plus about 500 standalone neighbourhood cafés. That is about 2,000, close to the demand answer. Then name the swing factor. The 20% share of café users is the softest input: halve it and the answer falls to about 1,040. Say the range out loud, roughly 1,000 to 4,000, because a single precise number from soft inputs sounds less credible, not more.

About 5,100 people, as a range of roughly 3,400 to 5,100. Take a floor plate of 25,000 square feet. After lifts, stairs and services about 80% is usable, 20,000 square feet. At 100 square feet a seat that is 200 seats, and at 85% occupancy about 170 people a floor. Thirty floors gives about 5,100. Roomier offices at 150 square feet a seat bring it down to about 3,400.

Why start from one floor?

Think of estimating the people in a cinema: you count the seats in one row, then the rows. A tower is the same: thirty copies of one floor, so estimate one floor carefully and multiply, because every assumption is easier to defend on a single floor you can picture. Define the answer too: people who work in the building, meaning assigned staff, not visitors and not the count present on any one day.

What goes into one floor?

Four assumptions, each said out loud. A floor plate of about 25,000 square feet, typical for a large commercial tower. About 20% of that is the coreThe central block of a floor holding lifts, stairs, toilets, shafts and service rooms, which cannot be used for desks., leaving 20,000 usable. At 100 square feet a seat, including aisles and meeting rooms, the floor holds 200 seats, and with 85% of seats assigned that is about 170 people. The rest are vacant desks, new hires not yet in, or space held for growth.

Which assumption would you flex, and how would you check it?

Seat density moves the answer most. A dense back office runs near 100 square feet a seat; a bank's front office with larger desks and more meeting rooms nearer 150. At 150 square feet a seat the tower holds about 3,400 people, so give the answer as about 3,400 to 5,100. Then trim for floors that hold no desks: if the lobby and a plant floor take two of the thirty, the dense case falls to about 4,760. A check from another side: assume a dozen lifts, each carrying about 15 people a trip on a round trip of about 3 minutes. That moves about 12 x 15 x 20, or 3,600 people an hour, which fits a building of a few thousand people arriving over a morning, not tens of thousands.

About 106 a year, on stated assumptions. Assume 15 crore domestic trips a year. A 180-seat jet, 85% full, flying 5 sectors a day for 350 days carries about 2.68 lakh passengers, so the fleet is about 560 jets. At 8% traffic growth it needs 1,209 in ten years, 65 more a year, plus about 41 retirements a year on a 20-year life.

How do you turn passengers into aircraft?

Think of a school deciding how many buses to buy. It counts the children who need a seat, divides by how many one bus can carry in a day, then adds buses for next year's bigger intake and for the old ones being scrapped. Aircraft demand is the same: fleet size is passenger trips divided by what one jet carries in a year, and new orders are fleet growth plus replacement. State each number as an assumption, because the interviewer cares about the structure first and the inputs second.

Start with traffic. Assume about 15 crore domestic passenger trips a year, and tell the interviewer you would check the current figure in the aviation regulator's monthly traffic data. A narrow-body has about 180 seats; assume 85% of them are filled, 5 sectors a day and 350 flying days. That is 267,750 passengers a jet a year, so today's fleet is about 560 jets.

Which assumption moves the answer most, and what did you leave out?

Growth carries more of the answer than replacement: at 8% a year the fleet more than doubles in ten years, adding 65 jets a year, while retirements on a 20-year life add 41. The number most worth defending is passengers per jet, because a sixth sector a day would cut the fleet by a sixth and every later number with it. Then name what you left out: international short-haul routes also fly narrow-bodies, airlines hold spare aircraft for maintenance, and engine problems can ground jets for months. Each pushes the true need above 106. Also say that orders and deliveries differ: airlines order years ahead, so order books can be far larger than a decade's need.

About 2,520 ATMs, on stated assumptions. Of one crore people, 70 lakh are adults and 60% of them, 42 lakh, use ATMs about three times a month: 4.2 lakh withdrawals a day. If 12% fall in the busiest hour, that is 50,400 an hour. A machine handles 30 an hour at two minutes each; plan for two-thirds busy, 20 an hour, and you need about 2,520.

Where do you start, demand or supply?

Think of a canteen deciding how many counters to open. It does not divide the day's meals by 24 hours; it counts the lunch rush and opens enough counters for that. Size a service network to its peak load, so the estimate runs from people to withdrawals to the busiest hour, and only then to machines. Start with demand: 70% of one crore are adults, 70 lakh; assume 60% of them use ATMs for cash, 42 lakh, and that each withdraws three times a month. That is 1.26 crore withdrawals a month, or 4.2 lakh a day.

How much does the peak assumption change the answer, and how do you check it?

Machines stand idle at 3 a.m. and have queues at 6 p.m. If you spread 4.2 lakh withdrawals evenly over 24 hours, you would size for 17,500 an hour and buy 875 machines. The peak-hour share is the assumption that moves the answer most: at 12% of the day in one hour, the city needs nearly three times what the average implies. The same logic explains the planning margin: a machine busy 100% of the time has a queue that never clears, so plan for two-thirds use. Then sanity check the result: 2,520 machines for one crore people is about 25 per lakh, a ratio you can compare with the published ATMs-per-lakh figure for the city, which you should look up rather than quote from memory.

Say what you left out. Salary days bring a bigger rush at the start of the month; digital payments are shrinking cash use, so the user share and the withdrawals per month are both falling; and machines sit where people work and shop, so a city with a dense business district needs more than population alone suggests.

Roughly Rs 70,000 to 75,000 crore a year, on the assumptions below. Start from an assumed 1.8 crore two-wheelers sold a year, assume a little over half are bought on credit, and lend about three quarters of the price. Splitting the market into commuter motorcycles, scooters and premium bikes gives about 99 lakh loans averaging Rs 73,600, or Rs 72,832 crore. Every input is an assumption to state and then confirm.

What is the structure before any number?

To estimate what a college canteen sells on credit, you would count meals, the share put on a tab, and the average tab. Loans work the same way. A finance market size is units times financing penetration times ticket size, and saying that structure first lets the interviewer follow every number after it. Here the units are new two-wheelers sold in a year, penetration is the share bought on a loan, and the ticket is the price less the down payment.

Assume about 1.8 crore two-wheelers are sold in India a year. Treat that as an assumption to confirm against the industry body's current sales data, never a fact to quote. Prices range from a basic commuter bike to a premium motorcycle, so one average price is fragile; split the market three ways instead.

How do you check it a second way?

Run it top-down in one line: 1.8 crore units x 55% financed x 75% of an average Rs 1,00,000 price is Rs 74,250 crore. Two routes landing within about 2% of each other is the check, and the segment split earns its place by showing where the uncertainty lives. The softest input is the financed share: every 5 points on it moves the answer by about Rs 6,621 crore. Then a feel check: 99 lakh loans a year is about 27,123 loans a day across the country, which is plausible for a mass market sold through thousands of dealers.

Say what the number is not. It is a yearly flow of new loans. The loan book outstanding at any time is a stock: with loans running about two and a half years and repaid evenly, the average loan is half outstanding for that period, so the book is roughly 1.25 times a year's disbursement, about Rs 91,041 crore. Used-vehicle loans are excluded.