Equity Research puzzles, solved step by step

About 18 million a year, on these assumptions. Take 300 million households, half owning a two-wheeler, at 1.1 each: a fleet of about 165 million. Replacing each every 11 years gives 15 million a year. Ownership rising one point a year adds 3 million first-time buyers. Check the total against published industry sales before relying on it.

Where does demand for new vehicles come from?

Think of a housing society's parking lot. Each year a few old scooters are swapped for new ones, and a few families who never had one buy their first. New vehicle sales are replacement of the existing fleet plus first-time buyers, and splitting the two is what makes the estimate defensible, because each has its own driver. Replacement depends on fleet size and vehicle life; first-time buying depends on how fast ownership spreads.

How do you build each branch, and which assumption matters most?

Start with households: roughly 1,400 million people at a little under five a household gives about 300 million, stated as an assumption. Half own a two-wheeler, and owning households average 1.1, so the fleet is about 165 million. If a vehicle lasts 11 years, about one in eleven is replaced each year, 15 million, which makes replacement most of the market. First-time demand is ownership rising one point a year on 300 million households, 3 million.

Test the most sensitive input out loud. A 9-year life instead of 11 lifts replacement to about 18 million; a 13-year life cuts it to about 13 million. That range, about 6 million, is twice the whole first-time branch, which tells you where to look first. Then say you would check the total against the industry body's published annual sales rather than quoting a figure from memory.

About 1.5 lakh cups a day on these assumptions. Take 5 lakh passengers. The 2 lakh long-distance travellers wait long enough that one in two buys a cup: 1 lakh cups. The 3 lakh commuters rush through, one in ten buys: 30,000. Staff, porters and drivers, say 5,000 people at three cups, add 15,000. That gives 1,45,000, and 50 stalls selling about 3,000 cups each agrees.

Why start from people and not from stalls?

If you wanted to know how many samosas a school canteen sells, you would count students and ask how many buy one at break, not count the frying pans. Demand comes from the people passing through, so the estimate starts with footfall and a buying rate; the stall count is useful only as a check on capacity. Starting from stalls forces you to guess sales per stall, which is the very number you are trying to find.

State every number as an assumption. Assume a busy junction handles about 5 lakh passengers a day. Split them by how long they stay: long-distance travellers wait on the platform for trains that may be late, while suburban commuters walk straight through. The split matters because waiting time drives tea buying far more than the station's size does. Give long-distance travellers a rate of one cup for every two people and commuters one in ten.

How do you check it from the supply side?

Count the sellers. Suppose a big station has about 50 stalls and trolleys. A busy stall can pour a cup every 20 seconds for much of a 17-hour day, about 3,000 cups. 50 sellers at 3,000 cups is 1,50,000, close to the 1,45,000 from the demand side, so the two routes agree. If they had disagreed by a factor of three, you would know one buying rate or the footfall figure was off and could say which one you distrust.

What would you refine with more time?

The long-distance buying rate carries most of the answer, so refine it first. Waiting time varies with delays, time of day and weather: a winter morning sells far more tea than a summer afternoon. A sharper estimate would split the day into blocks and apply a rate to each, which is what the hourly chart does. The limitation is that footfall itself is an assumption here; railway data on passengers per day for the specific station would replace it.