Equity Research puzzles, solved step by step

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.

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 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 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.