Mutual Fund Mastery puzzles, solved step by step

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

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008Estimate the monthly SIP inflow into mutual funds from a single city of 1 crore people. State each assumption as you go.Estimation and market sizingCoreAllianceBernsteinNew York · 2021
Try it first
Which assumption will move your answer the most?
Show the worked solution
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.
One crore people become 25 lakh households, 3.75 lakh investing households at an assumed 15% penetration, 6 lakh SIPs and about Rs 150 crore a month at a Rs 2,500 average, and moving penetration between 10% and 20% moves the answer between Rs 100 and Rs 200 crore.
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.
The relationship
$\text{Inflow} = \frac{10^7}{4} \times 0.15 \times 1.6 \times 2{,}500 = \text{Rs } 150 \text{ crore a month}$
10^7 / 4 households, one crore people at four each
0.15 the assumed share of households with an SIP
1.6 and 2,500 SIPs per investing household and the average SIP in rupees
What it says in wordsMultiply down the chain, one stated assumption per step, and the product is the monthly flow.
Where candidates lose it
The common failure is jumping to a number without the chain, or quoting a national SIP figure from memory and scaling it by population. The interviewer cannot test a number with no steps, and a remembered figure may be wrong or out of date.
The second failure is precision theatre: carrying decimals through assumptions that are only good to one significant figure. Give Rs 150 crore, the range, and which link you would check first.
What the interviewer asks next
How would the answer change for a city of the same size with a much younger population?
How would you size the stoppage rate, the SIPs that end each month?
Build the same estimate top-down from a national figure. What would you need to look up?
Asked at AllianceBernstein, Investment Banking, New York, 2021 (Wall Street Oasis): Case study market sizing question
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?
050Estimate the number of 5G smartphones sold in India in a year, working from the number of smartphone users, how often people replace their phones, and the 5G share of new handsets.Estimation and market sizingCoreAllianceBernsteinNew York · 2022
Try it first
Which number drives yearly phone sales most directly?
Show the worked solution
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.
Seventy crore smartphone users on a 4-year replacement cycle buy 17.5 crore phones a year; adding 1.5 crore first-time buyers gives 19.0 crore, and a 55% 5G share of new handsets gives about 10.5 crore 5G phones a year.
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.
The relationship
$Q_{5G} = \left(\frac{U}{c} + F\right) \times s = \left(\frac{70}{4} + 1.5\right) \times 0.55 \approx 10.5 \text{ crore}$
U smartphone users, 70 crore assumed
c replacement cycle, 4 years assumed
F first-time buyers a year, 1.5 crore assumed
s 5G share of new handsets, 55% assumed
What it says in wordsYearly 5G sales are the phones bought each year, replacements plus first-time buyers, times the share that are 5G.
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.
Where candidates lose it
The trap is multiplying the user base by the 5G share and announcing 38 crore phones a year, as if every user bought a new phone every year. That confuses the stock of users with the yearly flow of purchases.
The second loss is giving one number with no range and no source for the inputs. Say which inputs are assumptions, which one matters most, and how you would check it.
What the interviewer asks next
How would the answer change if the replacement cycle shortened to 3 years?
How would you estimate the 5G share of new handsets without published data?
Turn this into a revenue estimate for a phone maker with a 15% share of 5G units.
Asked at AllianceBernstein, Equity Research, New York, 2022 (Wall Street Oasis): Estimate the market size of 5G smartphone sales in 2022.
077Estimate how many new narrow-body passenger jets the world's airlines take delivery of in a year. Build it from the size of the fleet, how long a jet stays in service, and how fast air traffic grows.Estimation and market sizingCoreRothschild & CoParis · 2026
Try it first
Which two flows make up a year's deliveries?
Show the worked solution
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.
A fleet of 20,000 jets needs 800 replacements a year at a 25-year life and 800 extra jets at 4% growth, about 1,600 deliveries in all; building the fleet from passenger trips instead gives about 20,500 jets, which supports the starting assumption.
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.
The relationship
$D = \frac{F}{L} + gF = \frac{20{,}000}{25} + 0.04 \times 20{,}000 = 1{,}600$
D deliveries a year
F the fleet in service, assumed 20,000
L service life in years, assumed 25
g fleet growth a year, assumed 4%
What it says in wordsDeliveries are the fleet divided by its life, for replacement, plus the fleet times its growth rate.
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.
Where candidates lose it
Candidates start from passengers, arrive at a fleet, and give the fleet as the answer. That confuses a stock with a flow: 20,000 jets in service is not 20,000 jets delivered this year. The interviewer is waiting for the step that turns a stock into an annual number, and never hears it.
The other loss is one number with no range. Give 1,600, then say what moves it: a 20-year life and 5% growth push it to 2,000; a 30-year life and 3% growth pull it to about 1,300.
What the interviewer asks next
If one maker holds about half this market, how many jets does it deliver a year, and what would you check first?
Fuel prices double. Which of your two flows moves, and which way?
How would you turn this into an annual revenue figure for the industry?
Asked at Rothschild & Co, Asset Management, Paris, 2026 (Wall Street Oasis): Can You estimate number of flights solds by airbus

10^7 / 4	households, one crore people at four each
0.15	the assumed share of households with an SIP
1.6 and 2,500	SIPs per investing household and the average SIP in rupees

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

U	smartphone users, 70 crore assumed
c	replacement cycle, 4 years assumed
F	first-time buyers a year, 1.5 crore assumed
s	5G share of new handsets, 55% assumed

D	deliveries a year
F	the fleet in service, assumed 20,000
L	service life in years, assumed 25
g	fleet growth a year, assumed 4%

Try it first

Where do you start, people or money?

How do you defend each assumption?

Where candidates lose it

What the interviewer asks next

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

Why start from replacements and not from users?

How do you justify each input?

How do you sense check the answer?

Where candidates lose it

What the interviewer asks next

Try it first

Why split deliveries into replacement and growth?

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

Where is this estimate weakest?

Where candidates lose it

What the interviewer asks next