Mutual Fund Mastery puzzles, solved step by step

Puzzles: 100
Traced to a firm: 29
Topics: 13
Hard: 30

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021"Why should I buy your college, and how much would you sell it for?" Value a college with 8,000 students each paying Rs 2 lakh a year in fees, at a 35% operating margin.Estimation and market sizingHardWellington ManagementBoston · 2024
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What is the college's yearly operating profit?
Show the worked solution
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.
Fees of Rs 160 crore less Rs 104 crore of costs leave Rs 56 crore of operating profit, which at assumed multiples of 10 to 14 times values the college at roughly Rs 560 to 784 crore.
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.
The relationship
$V = m \times (N \times F \times M) = m \times (8{,}000 \times 2 \text{ lakh} \times 0.35) = m \times 56 \text{ crore}$
N students, 8,000
F yearly fee per student, Rs 2 lakh
M the operating margin, 35%
m the multiple of operating profit, assumed 10 to 14
What it says in wordsProfit is students times fee times margin, and value is that profit times a multiple that reflects how durable it is.
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.
Where candidates lose it
The common failure is answering only one half: a heartfelt speech about the college with no number, or a quick multiple with no reason a buyer should believe the profit lasts. The interviewer asked both questions on purpose.
The second failure is multiplying revenue instead of profit, or quoting a multiple as if it were a market fact. Build revenue, then profit, then state the multiple as your assumption and the range it gives.
What the interviewer asks next
What would a buyer pay if fees are capped by a regulator and costs rise 6% a year?
How would you value the college with a discounted cash flow instead of a multiple?
Which single number would you most want to verify before agreeing a price?
Asked at Wellington Management, Investment Research, Boston, 2024 (Wall Street Oasis): Why should I buy your College and how much would you sell it for?
063Estimate how many full-time mutual fund distributors a district town of 5 lakh people can support. Build it from households, the share that invests, average fund assets and the trail income a distributor needs to make a living.Estimation and market sizingHardIndian AMCsDistribution and sales
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Which is the right place to start the estimate?
Show the worked solution
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.
Five lakh people become 1,25,000 households, 15,000 investing households and Rs 450 crore of fund assets, of which Rs 225 crore through distributors pays a trail pool of Rs 180 lakh a year, enough for about 20 full-time distributors at Rs 9 lakh each.
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.
Change one input Distributors supported
Base case 20
Trail 0.5% instead of 0.8% 12.5
20% of households invest instead of 12% 33.3
Each needs Rs 18 lakh instead of Rs 9 lakh 10
Each row changes one assumption from the base case and leaves the rest alone.
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.
Where candidates lose it
The common loss is starting from the population and dividing by an invented ratio of advisers to people. That produces a number with no economics behind it, and the interviewer cannot check any step.
The second is giving one number with no sensitivity. Say which assumption you are least sure of, usually the trail rate or the share that invests, and show how the answer moves when it changes.
What the interviewer asks next
How would the answer change if the town's investors move steadily to direct plans?
Estimate the same town's total yearly flow into systematic investment plans.
Why might an AMC still want a branch in a town that supports only 20 full-time distributors?
093Passive funds tracking an index hold an assumed Rs 50,000 crore. A stock is added to the index at a weight of 1.2%, and it trades about Rs 250 crore a day. How much must the passive funds buy, and how many days of the stock's trading is that?Estimation and market sizingHardPassive and index teamsIndian AMCs
Try it first
How many days of the stock's normal trading does the passive buying equal?
Show the worked solution
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.
Passive funds holding Rs 50,000 crore must buy Rs 600 crore of a stock entering at a 1.2% weight, which is 2.4 days of all its trading at Rs 250 crore a day, and about 9.6 days if they take only a quarter of each day's volume.
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.
The relationship
$\text{Days} = \frac{w \times AUM}{ADV} = \frac{0.012 \times 50{,}000}{250} = 2.4$
w the stock's weight in the index, 1.2%
AUM money in funds tracking the index, Rs 50,000 crore, an assumption
ADV average daily traded value of the stock, Rs 250 crore
What it says in wordsForced buying in rupees, divided by what trades in a day, gives the number of days of all trading the funds need.
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.
Where candidates lose it
Candidates compute Rs 600 crore and stop. The rupee figure is the easy half; the interviewer wants it set against liquidity, because Rs 600 crore tells you nothing until you know whether the stock trades Rs 25 crore a day or Rs 2,500 crore.
The second slip is assuming the funds can simply take all the volume. Say that a buyer can only take part of each day's trading without moving the price, and that traders front-run the known demand.
What the interviewer asks next
The stock is removed from the index instead. Who is on the other side of the passive selling?
Passive assets double over five years. What happens to the days-of-volume figure for the same stock?
Why might a stock rise after the inclusion is announced but fall back after the effective date?

N	students, 8,000
F	yearly fee per student, Rs 2 lakh
M	the operating margin, 35%
m	the multiple of operating profit, assumed 10 to 14

Change one input	Distributors supported
Base case	20
Trail 0.5% instead of 0.8%	12.5
20% of households invest instead of 12%	33.3
Each needs Rs 18 lakh instead of Rs 9 lakh	10

w	the stock's weight in the index, 1.2%
AUM	money in funds tracking the index, Rs 50,000 crore, an assumption
ADV	average daily traded value of the stock, Rs 250 crore

Try it first

What is the interviewer really testing?

How do you get from fees to a value?

Where candidates lose it

What the interviewer asks next

Try it first

What actually limits the number of distributors?

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

Where candidates lose it

What the interviewer asks next

Try it first

Why is index buying forced rather than optional?

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

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

Where candidates lose it

What the interviewer asks next