Mutual Fund Mastery puzzles, solved step by step

About Rs 150 crore a month, with a range of roughly Rs 100 to 200 crore. One crore people at four per household is 25 lakh households. Assume 15% have at least one SIP, 3.75 lakh households, with 1.6 SIPs each, 6 lakh SIPs. At an average Rs 2,500 per SIP that is Rs 150 crore a month, about Rs 1,800 crore a year. Penetration is the assumption to test first.

Where do you start, people or money?

Think of estimating how much a housing society spends on milk. You would count flats, then flats that buy from the dairy, then litres per flat, then price. A sizing answer is judged on the chain: each step one assumption, stated with a number and a reason, so the interviewer can challenge any link without the whole answer falling over. Start with people because they are the one number given, and move to households because SIP decisions are made at home.

How do you defend each assumption?

Give a reason in one breath for each. Four per household reflects a mix of nuclear and joint families in a large city. Fifteen per cent penetration is the weakest link: it assumes a minority of salaried and business households invest monthly through funds, and you should say you would check it against published folio or SIP account data for the city. Families with an SIP often run more than one, one per goal or per earner, hence 1.6. A Rs 2,500 average blends small starter SIPs with larger ones.

Then check the result a second way. Rs 150 crore a month is Rs 150 per person, or Rs 4,000 per investing household. If an investing household in this city earns around Rs 50,000 a month, that is about 8% of income going into SIPs, which is plausible. A figure that implied half of income would tell you an assumption has gone wrong.

Roughly Rs 560 to 784 crore, on Rs 56 crore of operating profit at assumed multiples of 10 to 14 times. Fees are 8,000 times Rs 2 lakh, Rs 160 crore; a 35% margin leaves Rs 56 crore. The case for buying is durability: a brand, accreditation and a campus that keep the seats full for decades. The multiple you ask for depends on how sure the buyer can be of that.

What is the interviewer really testing?

Think of selling the tea stall outside a busy railway station. The buyer is not paying for the kettle; he is paying for the queue that shows up every morning and the confidence it will keep showing up. Any institution can be valued as a stream of cash plus a judgement about how long and how reliably that stream lasts, and the question has two halves because those are the two halves of a valuation. "Why should I buy" asks for the durability story; "how much" asks for the numbers.

How do you get from fees to a value?

Revenue is students times fees: 8,000 times Rs 2 lakh is Rs 160 crore a year. A 35% operating margin leaves Rs 56 crore, and the multiple you put on that profit is where the durability argument turns into a number. At 10 times it is Rs 560 crore, at 14 times Rs 784 crore. These multiples are assumptions for the exercise; say you would set them against what comparable education businesses have changed hands for, and against a cash flow valuation.

Then sell the durability and test it. The selling points are a waiting list larger than the intake, accreditation that a new entrant would take years to earn, land owned rather than leased, and alumni who send their children. The tests are the risks: if enrolment falls 10% while costs stay fixed, operating profit drops from Rs 56 crore to about Rs 40 crore, because every rupee of lost fees falls straight to profit. A per-seat check helps too: Rs 560 crore over 8,000 seats is Rs 7 lakh a seat, three and a half years of fees.

Name one structural limit. Many colleges are run by trusts or societies that cannot distribute profit, so in practice a buyer may be acquiring a management contract, the land or a related company rather than the college itself; the cash a buyer can actually take out may be smaller than the operating profit. Asking who can receive the cash shows the interviewer you think like an owner.

About Rs 20 crore a year. A basis point is 0.01%, one rupee in every ten thousand. Rs 2 lakh crore is Rs 2,00,000 crore, and dividing by 10,000 gives Rs 20 crore. A handy anchor: one basis point on Rs 1 lakh crore is Rs 10 crore. To an investor holding Rs 1 lakh the same basis point is Rs 10 a year, which is why a fund house fights over fees its investors barely notice.

How do you get the zeros right under pressure?

A basis point is a hundredth of a per cent, so it is one rupee in every ten thousand, the way a paisa is one part in a hundred of a rupee. Convert the AUM into crore first, then move the decimal four places to the left; one basis point on Rs 1 lakh crore is Rs 10 crore, and every other size scales from that anchor. Rs 2 lakh crore is Rs 2,00,000 crore, so one basis point is Rs 20 crore.

Why does a fund house fight over a few basis points?

Scale it up. A 10 basis point cut on Rs 2 lakh crore is Rs 200 crore a year of revenue gone, every year, with no saving in cost. At fund-house scale a basis point is real money, and a fee change is a large change in revenue for a business whose costs barely move with it. If the house earns, say, an average 0.50% across its book, its revenue is Rs 1,000 crore, and a 10 basis point cut takes away 20% of it. Those figures are illustrations; the shape of the arithmetic is the point.

Why is the same basis point invisible to the investor?

Because it is spread thin. An investor with Rs 1 lakh pays Rs 10 a year per basis point, the price of a cup of tea. The benefit of a fee change is concentrated in one balance sheet and its cost is spread across lakhs of folios, so the fund house argues hard and each investor shrugs. That is also why fee caps exist: in India the regulator caps the total expense ratioThe yearly cost of running a scheme, charged to the fund as a percentage of its assets and taken out of the NAV. in slabs that fall as a scheme grows. Confirm the current slabs before quoting them; they have been revised before.

About 10 crore 5G phones a year, on stated assumptions. Take 70 crore smartphone users replacing every 4 years: 17.5 crore replacement phones a year. Add about 1.5 crore first-time buyers for 19.0 crore phones. If 55% of new handsets are 5G, that is about 10.5 crore. Each input is an assumption to state and defend; reasonable changes give a range of about 8 to 14 crore.

Why start from replacements and not from users?

A town with ten thousand households does not buy ten thousand refrigerators a year. It buys the ones that wear out, plus a few for new homes. The user base is a stock and yearly sales are a flow, and the replacement cycle is what converts one into the other. Stating that structure first is most of the marks, because it shows the interviewer how you will build the number before you pick any inputs.

How do you justify each input?

Say where each comes from and how you would check it. Users: a large share of a population of roughly 140 crore, here taken as 70 crore, half the population, to be confirmed against current telecom data. Replacement cycle: budget phones tend to be replaced sooner and premium phones later; 4 years is a middle assumption. First-time buyers: people moving from basic phones, assumed at 1.5 crore a year. 5G share: the share of new models sold with 5G, assumed at 55%. None of these are facts; they are reasoned guesses, and the interviewer is grading the reasoning and the sense check, not the decimal.

How do you sense check the answer?

Two quick checks. First, 19 crore phones a year for a country of roughly 140 crore people is about one phone per seven people each year, which is plausible for a market where most adults already own one. Second, the value: at an assumed average price of Rs 18,000, 10.5 crore phones is about Rs 1.9 lakh crore of sales. If either check looks absurd, revisit the inputs. Then give the range: a 3.5-year cycle and a 65% share give about 14.0 crore; a 4.5-year cycle and a 45% share give about 7.7 crore. The replacement cycle and the 5G share move the answer most, so those are the two to research first.

About 20 full-time distributors. Five lakh people in households of four is 1,25,000 households. If 12% invest Rs 3 lakh each, the town holds Rs 450 crore. Suppose half comes through distributors: Rs 225 crore, which at an assumed 0.8% trail pays Rs 180 lakh a year. A distributor needing Rs 9 lakh a year in gross trail means about 20 can live on it.

What actually limits the number of distributors?

Ask how many tailors a colony can support and you do not count the people; you count the stitching work and divide by what keeps one tailor going. A distributor is paid from trail commissionA yearly commission paid to a distributor as a percentage of the client assets they hold in a fund, for as long as the money stays invested., so the town's capacity is the trail pool divided by one livelihood, not the population divided by some ratio of advisers to people. That tells you the order of the chain before you guess a single number: people, then households, then investors, then assets, then the share that pays a distributor, then the trail.

How do you defend each guess, and which one moves the answer most?

Say each assumption with a reason. Four people to a household is a fair Indian average. Twelve percent of households holding funds is a cautious guess for a district town. Rs 3 lakh is a modest balance once systematic plans have run a few years. Half through distributors leaves the rest to direct plans, apps and bank branches. Trail rates vary by scheme and over time, so 0.8% is an assumption to confirm. The answer is a product of guesses, so a change in any one moves it in proportion: halve the trail and the town supports half as many.

Close with the sanity check and the limit. Twenty distributors for 15,000 investing households is about 750 families each, which is a full book for one person with a small office. In reality many towns have far more registered distributors than this, because most are part-time, also sell insurance or deposits, or work for a bank, so their fund trail is only part of their income. The estimate sizes the full-time capacity, not the head count on a register.

About 1,600 a year, on stated assumptions. Take a global narrow-body fleet of about 20,000 jets. If a jet flies for about 25 years, 800 retire each year and need replacing. If traffic grows about 4% a year and the fleet grows with it, another 800 are needed. Replacement plus growth gives roughly 1,600, with a sensible range of about 1,300 to 2,000.

Why split deliveries into replacement and growth?

Think about how many pairs of school shoes a town buys in a year. You do not count shoe shops; you count children. Shoes wear out after about a year, and each year the town has a few more children. Annual sales of anything durable are the flow that keeps a stock alive: what wears out plus what the stock grows by, and both are proportions of the stock. So the whole estimate hangs on one number, the fleet, and two rates you can reason about aloud: how long a jet lasts and how fast flying grows.

How do you get the fleet number if you do not know it?

Build it from passengers, and say that every input is an assumption. Suppose narrow-body jets carry about 4.5 billion passenger trips a year. A typical jet has 150 seats and flies 80% full, so 120 passengers a flight. If it flies five short sectors a day, every day, that is 1,825 flights and about 2.19 lakh passengers a year. Divide and you get roughly 20,500 jets. Two independent routes landing near 20,000 is the check an interviewer wants to hear, even when both routes are rough.

Where is this estimate weakest?

In three places. Service life is not fixed: when fuel is dear, airlines retire old jets early, and when new jets are scarce they keep old ones flying. Traffic growth is lumpy, and a shock year can turn it negative. And, most important for anyone valuing a maker, deliveries are capped by how many jets the factories can build, so demand can sit above actual deliveries for years, with the difference piling up as a backlog of orders. If the interviewer asks about one maker, split the 1,600 by an assumed market share and say the share is the assumption most worth checking.

About Rs 600 crore, or 2.4 days of the stock's entire trading. Passive funds must hold the stock at its index weight: 1.2% of Rs 50,000 crore is Rs 600 crore. Against Rs 250 crore of daily trading, that is 2.4 days of every share traded, and they want to own it by the day the change takes effect. If they took only a quarter of each day's volume, the buying would take about 9.6 days.

Why is index buying forced rather than optional?

Picture a school that announces every student must own a particular textbook by Monday, and the only shop stocks a few dozen copies a day. The shopkeeper knows exactly how many will be needed and by when. An index fund has no view on the stock; its job is to hold every stock at its index weight, so when a stock enters the index, every passive fund tracking it must buy, in a known amount, by a known date. That predictability is what makes inclusion a trading event, not just a news item.

How do you size it, and why measure it in days?

The rupee amount is just the weight times the passive money: 0.012 x Rs 50,000 crore is Rs 600 crore. On its own that number means little, because Rs 600 crore is trivial in one stock and enormous in another. Dividing by daily traded value turns it into a measure of difficulty: 2.4 days means the funds must buy every share traded for more than two full days, which nobody can do without pushing the price up. A desk usually assumes a buyer can take only a fraction of the day's volume quietly; at a quarter, the job takes about 9.6 days.

Who positions for it, and what does the estimate leave out?

Traders who expect the inclusion buy ahead of the effective date and sell to the index funds on it, so part of the price move usually happens before the passive funds trade at all. The passive funds also pay for the purchase by selling a slice of every other stock, about Rs 600 crore spread across the rest of the index, which barely registers in each. The estimate leaves out active funds that hug the same benchmark and buy for similar reasons, which makes the real demand larger, and it assumes the weight is set by the stock's full market value; index providers commonly weight by the shares freely available for trading, so check the actual weight before relying on the size.