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 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 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 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.