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.

Roughly 607 million 5G phones worth about US$ 351 billion, on stated assumptions. Assume 4 billion smartphones in use, replaced every 3 years, so about 1.33 billion are sold in 2022. Assume all premium phones, 60% of mid-range and 15% of entry phones are 5G, a blended 45.5%, which gives 607 million units. At a blended price near $579, the value is about US$ 351 billion.

Where do you start: people, phones or networks?

Think of estimating how many pairs of school shoes a town buys. You do not count shops; you count children and ask how often a pair wears out. Annual phone sales are the phones in use divided by how many years a phone lasts, so start from the installed base and the replacement cycle, then split the year's sales by price band. Say every number as an assumption: an installed base of 4 billion and a 3 year cycle are round figures for the method, to be checked against an industry tracker before they go into a note.

How do you show the interviewer you know where the estimate is weak?

Run the sensitivity on the widest step. A cycle of 2.5 years gives 728 million 5G units and 3.5 years gives 520 million, a swing larger than any plausible error in the price assumptions. Then sanity check the output: 45% of phones sold being 5G in 2022 should sit sensibly against what you know about network rollouts, and a blended price near $579 says premium phones carry most of the value. The limitation: first-time buyers are folded into the cycle, which slightly understates sales in markets still adding users.

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 450 crore. Revenue is 5,000 students x Rs 3 lakh, Rs 150 crore a year. A 25% EBITDA margin gives Rs 37.5 crore, and at 12 times that is an enterprise value of Rs 450 crore, before subtracting any debt. The case for buying is fees paid in advance, a campus and approvals that are slow to copy, and demand that renews with a new batch every year.

How do you structure an open question like this?

The question has two halves and the interviewer wants both. It is like selling a flat: first you say what makes it worth having, the light, the location, the building, and then you give a price per square foot times the area. Give the reasons to own it in three short points, then build the price as revenue times margin times multiple, naming every input so the interviewer can push on any one of them. Leading with the structure also buys you time to do the arithmetic.

What makes the case for buying convincing?

Pick the features an investor would pay for. The strongest is that customers pay a term or a year in advance and come back every year, so the business funds its own working capital and its revenue is visible well before the year starts. Add that a campus, a faculty and regulatory approvals take years to replicate, which protects the fee level, and that demand refreshes with every new batch. Then name the risk that decides the price: how full the seats are. One caution belongs here too: in many countries, including India, degree-granting colleges are commonly run through not-for-profit trusts or societies, so confirm the legal structure first, because it decides whether an investor can own the profit at all.

Which number would you defend hardest?

The margin and the multiple, because each moves the answer one for one. At a 20% margin the value falls to Rs 360 crore, and at 10 times EBITDA it falls to Rs 375 crore; every input in the chain carries equal weight. Justify 12 times with the visibility of fee income and 25% with a campus that is nearly full. If asked for a range rather than a point, Rs 360 to 450 crore on those two sensitivities is honest.

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.