Equity Research puzzles, solved step by step

About 325 to 420 million tonnes, on these illustrative inputs. The per capita route, 1,400 million people at 0.30 tonnes each, gives 420. Adding up housing, repairs, infrastructure and commercial building gives 325. The 95 million tonne gap points at the two softest inputs: the per capita anchor and the number of homes built each year. Check either against published industry data.

How does the per capita route work?

It is the way a household guesses its monthly rice: people times how much each eats. Take a population of about 1,400 million and an assumed consumption of 0.30 tonnes, 300 kg, a head. That gives 420 million tonnes. The route is quick but hangs on a single number you cannot see, the per capita figure, so it is only as good as your anchor. Say that you would check the anchor against published data rather than quoting one from memory.

How do you build the end use route, and why does it disagree?

Now count what gets built. Assume 10 million new homes a year at 600 sq ft and a builder's thumb rule of about 20 kg of cement per sq ft: 120 million tonnes. Repairs and extensions: 250 million existing homes, 6% doing a job a year, about 2 tonnes each: 30. Infrastructure: assume Rs 15 lakh crore of spending a year, cement at 5% of project cost and Rs 6,000 a tonne: 125. Commercial and industrial: 2,000 million sq ft at 25 kg: 50. Total 325.

When two routes disagree, the gap tells you which assumption to test, not which answer to average. Close the 95 million tonne gap from each side in turn. A per capita figure of 0.23 tonnes instead of 0.30 would close it alone. So would roughly 18 million new homes instead of 10, which is a big move, so the home count is less likely to be the whole story. Self-built rural homes are the category most often missed, which is where you would dig.

About Rs 271 crore a year, on these assumptions. A weekday carries 240,000 boardings: six peak hours at 25,000, four shoulder hours at 12,000 and seven quiet hours at 6,000. Weekends and holidays run at 60% of a weekday, giving 77.5 million trips a year. At an average fare of Rs 35, that is about Rs 271 crore.

How do you estimate a weekday's ridership?

Think about any busy road near an office district: jammed from 8 to 11 and from 5 to 8, calm in between. A metro line has the same shape. Ridership is concentrated in two peaks, so build the day hour by hour; a flat hourly average taken from the peak overstates it badly. Assume the line runs 6 am to 11 pm, 17 hours, with 25,000 boardings in each of six peak hours, 12,000 in four shoulder hours and 6,000 in seven quiet hours. That gives 240,000.

How do you check it and turn it into revenue?

Check from the stations. A line of 25 stations at 240,000 boardings a day is about 9,600 per station, which is plausible for a mix of busy interchanges and quiet suburban stops. Two routes that land close together give you licence to use the number; if they did not, the gap would tell you which assumption to test. Then annualise: 260 weekdays at 240,000 and 105 weekend and holiday days at 60% of that give 77.52 million trips.

Say which input you trust least: the average fare, since metro fares usually rise with distance and a line's trip-length mix is hard to guess. A research analyst would also note that fare revenue is only part of a metro's income, with advertising and property often material, and would check the operator's published ridership rather than rely on the estimate.

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 Rs 19,000 crore a year on these assumptions. Take an assumed fleet of 25 crore two-wheelers, 1.8 crore in each of the last five years and 1.6 crore in each older year. All young vehicles are insured; after year five the insured share falls from 60% to 20%. That leaves 14.6 crore insured vehicles paying Rs 800 to Rs 1,500 a year, a pool near Rs 18,700 crore.

Where do you start, the vehicles or the policies?

Think of a gym. Counting everyone who ever signed up tells you little; the revenue comes from the members who still renew. Start from the fleet, but the number that decides the pool is how many vehicles are still insured, not how many are on the road. In India third-party cover is compulsory by law and new two-wheelers are sold with a multi-year third-party policy, so the young fleet is close to fully insured. Confirm the current rules before quoting them. Once that upfront cover runs out, many owners of older, cheaper bikes let it lapse.

How do you show the interviewer which assumption matters?

Run one sensitivity out loud. If ten more vehicles in every hundred older than five years renewed their cover, the pool would rise by about Rs 1,440 crore, roughly 8% of the total. That is the lever an insurer or a regulator can pull: enforcement of the third-party requirement at the roadside. The premium per vehicle matters less because it is set in narrow bands for third-party cover. The limitation to say: premiums, fleet and lapse rates here are assumptions for the method, and an analyst would replace each with a sourced number before writing it into a note.

About Rs 69 crore of revenue and Rs 2.2 crore of gross profit a year, on stated assumptions. Assume 12,000 vehicles a day pass on the pump's side, about 500 an hour. About 384 stop, filling 20,232 litres a day, most of it diesel for trucks. At assumed pump prices near Rs 90 to Rs 100 a litre that is Rs 18.8 lakh a day; at an assumed dealer margin of Rs 3 a litre the pump keeps about Rs 2.2 crore a year.

Where does the estimate start?

Think of a roadside dhaba: its takings depend less on how many vehicles pass than on which ones stop and how much each group eats. Start from the traffic on the pump's side of the road, split it by vehicle type, and apply a stop rate and litres per fill to each, because the three types differ by a factor of forty in what they buy. Every input below is an assumption for the method; fuel prices and dealer margins change and should be checked before use.

How do you turn litres into revenue and profit, and check the answer?

Revenue is litres times the pump price: petrol for two-wheelers and cars at an assumed Rs 100, diesel for trucks at Rs 90, which gives Rs 18.8 lakh a day and Rs 68.6 crore a year. The dealer does not keep the pump price; it earns a commission per litre, so gross profit is litres times margin, about Rs 2.2 crore a year at Rs 3 a litre. Sanity check the stops: 384 a day is about 16 an hour, one fill every four minutes, which a pump with a few nozzles handles easily. The weakest assumption is the truck stop rate, since fleet operators choose pumps by contract and credit terms, not by chance.

About Rs 1,560 crore a year, on stated assumptions. Take 95 crore adults and 10% prevalence for 9.5 crore people with diabetes. Half are diagnosed, 4.75 crore; half of those take regular tablets, 2.38 crore; 60% of them are on this molecule, 1.43 crore patients. At Rs 3 a day for 365 days each patient spends Rs 1,095 a year, which gives about Rs 1,560 crore.

How do you structure a market size before you pick any number?

Sizing a drug market is like working out how many raincoats a town buys: not everyone gets caught in the rain, not everyone who gets wet buys a coat, and those who buy choose among brands. Write the chain first and say it out loud: people, times the share with the disease, times the share who know they have it, times the share treated, times the share on this molecule, times the annual cost. Stating the chain before any number shows the interviewer the logic, and lets them correct one input without the estimate collapsing.

Which assumption deserves the most care?

The one you are least sure of, because in a multiplicative chain every input moves the answer in the same proportion. Raising the diagnosis rate from 50% to 60% lifts the market by 20%, exactly as much as raising prevalence from 10% to 12%. Candidates spend their effort on prevalence because it is the headline statistic and wave the diagnosis rate through, when it is often the less certain number. Every figure here is an assumption for the exercise; check each against a published national survey before using it for anything.

How do you sanity check the answer?

Cross-check from the other end. Taking India's population as roughly 140 crore, also an assumption, Rs 1,560 crore works out to about Rs 11 per person per year, which is plausible for one cheap, widely used tablet. Then name what the estimate leaves out: combination tablets that contain the molecule, patients who take it irregularly, and the price gap between branded and generic packs. Each moves the number, and saying so is worth more than an extra decimal.

About Rs 4.4 crore a year, on stated assumptions. Five shows a day on 200 seats at 30% occupancy is 300 visitors a day, about 1,09,500 a year. At Rs 250 a ticket that is Rs 2.74 crore; at Rs 120 of food per head, Rs 1.31 crore; screen advertising adds about Rs 0.30 crore. Food is under a third of revenue, but because a distributor takes about half of each ticket, it is well over a third of what the screen keeps.

How do you build the visitor count?

Count it the way you would count lunches at an office canteen: seats, times sittings, times how full each sitting is, times days. Visitors are shows x seats x occupancy x days, and occupancy is the number to defend, because most screens are far from full outside weekend evenings. Five shows on 200 seats at 30% gives 300 visitors a day and 1,09,500 a year. Every figure here is an assumption for the exercise, and prices are taken net of GST, whose rates should be confirmed.

Why does food matter more than its price suggests?

Because the two rupees are not shared the same way. A ticket rupee is split with the film's distributor, while a food rupee mostly stays with the screen, so Rs 120 of popcorn and a drink keeps about Rs 90, close to the Rs 125 the screen keeps from a Rs 250 ticket. That is why chains price food high and push it hard, and why an analyst tracks spend per head as closely as ticket prices. The distributor's share and the food cost here are assumptions to check against a company's disclosures.

Which assumption would the interviewer push on?

Occupancy first. It moves both big lines at once: at 35% instead of 30%, revenue rises to about Rs 5.03 crore. A screen's economics turn on filling empty seats, because rent, staff and power are the same whether the hall is a third full or packed. Then the average ticket price, which blends weekday discounts with weekend premiums, and the number of shows, which depends on film lengths. Name all three and you have shown how the business works, not just its size.

About Rs 50,000 crore a year on these assumptions, with the two routes landing within 5% of each other. Bottom up, urban repaints give Rs 35,000 crore, rural repaints Rs 9,000 crore and new homes Rs 7,200 crore, Rs 51,200 crore in all. Top down, 140 crore people spending Rs 350 a head gives Rs 49,000 crore. Every input is an assumption to be checked against published data.

Where do you start the bottom-up build?

Start from what gets painted, not from who sells paint. A home is repainted every few years, and each repaint uses a number of litres set by the wall area. So the market is homes, divided by the repaint cycle, times litres per job, times the price of a litre, plus the new homes painted for the first time. Split urban and rural before you multiply anything, because they differ on every input: bigger walls, shorter cycles and costlier emulsions in cities; smaller homes, longer cycles and cheaper finishes in villages.

State each number as an assumption and move on. Assume 140 crore people in about 30 crore households, a third urban. Urban homes are repainted every five years, with 3,000 square feet of wall and ceiling; rural homes every eight years, with 1,200 square feet. A litre covers about 60 square feet for a two-coat finish, and a litre costs a blended Rs 350 in cities and Rs 180 in villages. About 60 lakh new homes a year take 40 litres each at Rs 300. None of these is a published figure; each is a round number you can defend in one sentence and replace later. Confirm household counts against the latest census or survey data.

How does a top-down check work, and why does it help?

Go the other way with a number you can feel. A family of four that repaints a flat for about Rs 7,000 of paint every five years spends Rs 1,400 a year, which is Rs 350 a head. Across 140 crore people that is Rs 49,000 crore. Two routes built from different inputs that land within a few percent of each other are worth more than one route worked to the last rupee. If they had landed a factor of two apart, you would know one assumption was wrong and go looking for it.

Then name your weakest input. Urban repaints are about 68% of the answer, so the urban cycle carries the most risk: at six years instead of five, the urban figure falls to Rs 29,167 crore. An analyst would close by saying which number to check first, and where: the decorative revenue that listed paint makers publish in their annual reports is the natural cross-check.

About Rs 28,800 crore a year on these assumptions, most of it from private schools. Government schools: 13 crore children, 2 sets a year at Rs 300, Rs 7,800 crore. Private schools: 12 crore children, 2.5 sets at Rs 700, Rs 21,000 crore. A single blended average would have given Rs 20,000 crore, so the split matters more than any one input. Confirm enrolment against the latest official school data.

Why split by school type before anything else?

Think of two families on the same street. One sends a child to the government school, where the uniform is supplied through the state at a fixed allowance. The other pays a private school's appointed tailor for a blazer, a house t-shirt and two sets of the regular uniform. Who pays decides both how many sets are bought and what each costs, so the segments must be sized separately and then added. A national average price describes neither family.

State the assumptions plainly and treat each as a placeholder to be replaced with data. Assume about 25 crore children in school, 13 crore in government schools and 12 crore in private ones; confirm against the latest UDISE+ report. Assume 2 sets a year at about Rs 300 a set in government schools, where many states fund uniforms through schemes, and 2.5 sets at about Rs 700 in private schools, allowing for sports and house uniforms. Each number is round on purpose; the point is a structure you can defend.

How do you sanity check it?

Turn it into a number a parent can feel. The market works out to about Rs 1,152 a child a year, roughly Rs 1,750 for a private school child and Rs 600 for a government school child. If a private school parent you know spends about that on uniforms each year, the build is in the right range. A second check comes from the supply side: the number of uniform makers and school tailors in one town, times their annual sales, scaled by the number of similar towns.

What would you refine with more time?

The private segment carries almost three quarters of the value, so refine it first. Private schools range from low-fee neighbourhood schools, where uniforms cost little more than in government schools, to premium schools with branded kits. Splitting private schools into two or three fee bands is the next step, because price varies most there. Replacement is a second lever: younger children outgrow uniforms every year, while older ones may make one set last two.

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.