Investment Banking puzzles, solved step by step

Puzzles: 100
Traced to a firm: 36
Topics: 12
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037Estimate how many cups of tea street vendors in Mumbai sell in a day.Estimation and market sizingCoreBulge bracket IBConsulting style brainteasers

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Which order of magnitude feels right?

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Roughly 1.2 crore cups a day. Take about 2 crore people as a round assumption, 75% adults, 40% of them buying street tea on a given day and two cups each: 1.2 crore cups. Check it from the supply side: about one stall per 400 people gives 50,000 stalls, each selling about 252 cups a day, which is 1.26 crore. Two routes landing within 5% make the estimate credible.

How do you structure the estimate before any number?

Think of how you would guess the rotis a hostel mess makes in a day: count the students, how many eat in the mess, and how many rotis each one eats. A market sizing is a chain of multiplications, and the interviewer scores the chain more than the final figure. Say the chain first: people, then adults, then the share who buy street tea on a given day, then cups per buyer. Each link is one assumption you can defend or change, and round numbers keep the arithmetic in your head.

The demand route, 2 crore people to 1.5 crore adults to 60 lakh buyers at two cups, gives 1.20 crore cups; the supply route, 50,000 stalls at 252 cups each, gives 1.26 crore, within 5% of the first.

Why does a demand estimate need a supply check?

Each link in the demand chain is a guess, and errors multiply. A second route built from different assumptions, here stalls and cups per stall, tests the first: if both land close together, neither is likely to be badly wrong. One stall per 400 people gives 50,000 stalls. A busy stall open 14 hours and selling 18 cups an hour sells about 252 cups a day, so supply comes to about 1.26 crore cups, within 5% of demand.

Step	Demand route	Supply route
Start	2.0 crore people (assumed)	2.0 crore people (assumed)
First filter	75% adults: 1.5 crore	1 stall per 400 people: 50,000 stalls
Rate	40% buy today: 60 lakh buyers	14 hours x 18 cups: 252 a stall
Cups a day	1.20 crore	1.26 crore

Every input is an assumption stated out loud; the demand route gives 1.20 crore cups a day and the independent supply route 1.26 crore, so the answer is about 1.2 crore.

What do you say about the weakest link?

Name it before the interviewer does. The share of adults buying street tea on a given day drives the answer one for one: 30% instead of 40% cuts the demand estimate to 90 lakh cups. Office workers, drivers and shopkeepers buy several cups a day; many households brew at home and buy none. Then say which number you would go and observe, the stalls along one busy street, because that is the input you can check. The population figure is a round assumption to confirm against the latest census estimate, not a fact.

Where candidates lose it

Candidates jump to a final number with no chain, or build a ten-step chain and lose the room in the arithmetic. The interviewer wants four or five clear links, each stated as an assumption, with round numbers that multiply in your head.

The second loss is stopping at one route. A supply check costs thirty seconds and is the moment the estimate becomes believable.

What the interviewer asks next

What is the street tea market worth in rupees a year?
How would the estimate change in the monsoon months?
How many stalls would a new tea chain need to win 5% of this market?

039A company earns Rs 10 a share, has a 10% cost of equity, does not grow and pays out everything. It decides to retain half its earnings and reinvest them at a 10% return. Does the share price change?Valuation riddlesCoreElite boutique IBBulge bracket IB
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Does the price move?
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No, the price stays at Rs 100. Paying out Rs 10 forever at a 10% cost of equity is worth 10 over 10%, Rs 100. Retaining half and reinvesting at 10% gives growth of 50% times 10%, which is 5%, on a Rs 5 dividend: 5 over (10% minus 5%) is also Rs 100. Reinvesting at exactly the cost of capital swaps cash today for cash later at a fair rate, so value does not change.
Why does growth not add value here?
Imagine lending your bonus to a friend at exactly the rate your bank pays. You will have more money later, but you are no richer today, because the bank would have paid you the same. Retained earnings create value only if the company reinvests them at more than shareholders could earn elsewhere at the same risk, which is the cost of equity. At exactly 10% the company is just the bank: the growth is real, but it is paid for rupee for rupee by the dividend given up.
Rs 10 a year forever and Rs 5 a year growing at 5% are both worth Rs 100 at a 10% cost of equity, even though the growing stream only overtakes after about 14 years; reinvesting at 15% would lift the price to Rs 200, at 6% it would cut it to Rs 71.
How do the two dividend streams compare?
The flat stream pays Rs 10 every year. The growing one starts at Rs 5 and rises 5% a year, so it overtakes Rs 10 only after about 14 years. Discounted at 10%, the early shortfall and the later surplus cancel exactly, and both streams are worth Rs 100. The tool is the Gordon growth modelA valuation of a stream that grows at a constant rate forever: the next payment divided by the discount rate minus the growth rate.: price equals next year's dividend over the cost of equity minus growth, and growth equals the share retained times the return on the money reinvested.
The relationship
$P = \frac{D_1}{r - g} = \frac{5}{0.10 - 0.5 \times 0.10} = \frac{5}{0.05} = 100$
D1 next year's dividend, half of Rs 10
r the cost of equity, 10%
g growth: half retained, times a 10% return on it
What it says in wordsA smaller dividend that grows is worth exactly the same as the full dividend when the growth is bought at the cost of capital.
When would the decision change the price?
Change the return on the reinvested money. At 15%, growth is 7.5% and the price doubles to Rs 200; at 6%, growth is 3% and the price falls to about Rs 71. The same retention policy creates or destroys value depending only on whether the return beats 10%. That is the sentence the interviewer is waiting for: growth is not good in itself, profitable growth is.
Where candidates lose it
The usual answer is that the price rises because the company now grows. Growth sounds good, but it is bought with the dividend given up, and at a 10% return it costs exactly what it is worth.
The opposite slip is saying the price halves because the dividend halves. That ignores the growth the retained cash buys. Run both legs through the same formula and they cancel.
What the interviewer asks next
What if the retained earnings are reinvested at 15%?
Why might the market still cheer a company that announces growth at its cost of capital?
How does this connect to return on invested capital in a DCF?
040You have eight gold bars that look identical, and one is lighter than the rest. Using a balance scale, what is the fewest weighings that guarantees you find the light bar?Logic and brainteasersCoreConsulting style brainteasersSales and trading
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What is the minimum?
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Two weighings. Put three bars on each side and leave two off. If the scale balances, the light bar is one of the two left off, and weighing them against each other finds it. If one side is lighter, the light bar is among those three: weigh one against one, and if they balance it is the third. A weighing has three outcomes, so two weighings separate up to 3 x 3 = 9 bars.
Why is halving the wrong instinct?
Think of guessing a number with questions that can be answered higher, lower or spot on. Each answer splits the possibilities three ways, not two. A balance scale gives three outcomes, left lighter, right lighter or level, so each weighing should split the suspects into three groups, not two. Halving, four against four, uses only two of those outcomes and needs 3 weighings for eight bars.
Weighing bars 1, 2 and 3 against 4, 5 and 6 sends the search down one of three branches, and a single second weighing inside each branch names the light bar, so two weighings cover all eight bars.
Why can it not be done in one weighing?
One weighing has only three possible results, and any of the eight bars could be the light one. Three outcomes cannot point to eight different answers, so one weighing is never enough, and two weighings, with 3 x 3 = 9 outcome paths, are the fewest that can cover eight bars. That counting argument is the proof the interviewer wants: it shows two is a floor, not just a method that happened to work.
The relationship
$3^{w} \ge 8 \;\Rightarrow\; w \ge \log_3 8 \approx 1.89 \;\Rightarrow\; w = 2$
w the number of weighings
3^w the number of different outcome paths that many weighings can produce
What it says in wordsYou need enough weighings for the outcome paths to outnumber the bars.
What does the puzzle teach beyond the scale?
The same counting sits behind any search. The fewest questions you need is set by how many answers each question can give, not by how clever the questions are. With nine bars, two weighings still suffice; with ten, you need a third. Saying where the method breaks shows the interviewer you understand why it works, which is the point of asking it.
Where candidates lose it
Most candidates halve: four against four, then two against two, then one against one, and answer three. The method finds the bar but misses that a level scale is an outcome too, and it carries information.
The second loss is giving two with no lower-bound argument. Say why one weighing cannot do it: three outcomes cannot separate eight bars.
What the interviewer asks next
What is the largest number of bars that two weighings can handle?
Now the odd bar could be lighter or heavier, and you do not know which. How many weighings for 12 bars?
What changes if two of the eight bars are light?
041Your pay is 60% fixed salary and 40% bonus, and the bonus moves twice as much as the market. What is your personal beta, and what does it say about the market risk you carry before you invest a rupee of savings?Rates, risk and optionsCoreRothschild & CoNew York · 2026
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What is your personal beta?
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Your personal beta is 0.8. Salary does not move with the market, a beta of 0; the bonus moves twice as much, a beta of 2. Weighted by share of pay, 0.6 x 0 plus 0.4 x 2 gives 0.8. If the market falls 20%, the bonus falls 40% and total pay falls 16%. Your earnings already carry most of the market risk of an index fund before you invest a rupee of savings.
How do you get a beta for a person?
Think of a household with two earners, a schoolteacher on a fixed salary and a salesperson paid on commission. In a downturn the teacher's pay holds while the commission falls sharply, and the household's income falls by a blend of the two. The beta of a mix is the weighted average of the betas of its parts, so a pay packet's beta is each component's beta weighted by its share of pay. Salary has a beta of 0 and the bonus a beta of 2, so the blend is 0.8.
Salary is 60% of pay with a beta of 0 and the bonus 40% with a beta of 2, which blends to 0.8; on pay of Rs 25 lakh, a 20% market fall cuts the bonus to Rs 6 lakh and total pay to Rs 21 lakh, a 16% fall.
What does 0.8 look like in rupees?
Take pay of Rs 25 lakh: Rs 15 lakh of salary and Rs 10 lakh of bonus. If the market falls 20%, the bonus falls 40% to Rs 6 lakh, and total pay falls from Rs 25 lakh to Rs 21 lakh, a 16% drop, which is 0.8 times the market's fall. The salary cushions the swing, but the bonus is exactly the part that shrinks in the years the market is weakest.
The relationship
$\beta_{\text{pay}} = 0.6 \times 0 + 0.4 \times 2 = 0.8$
0.6, 0.4 each component's share of total pay
0, 2 how much each component moves when the market moves
What it says in wordsWeight each part of pay by its share and add up how much each moves with the market.
Why does it matter for your savings?
Your future earnings are an asset, often the largest one you own early in a career, and finance calls it human capitalThe value today of the earnings a person expects to make over the rest of a working life.. If that asset already has a beta of 0.8, your total wealth carries market risk before your savings add any, and the worst years for markets are the years your bonus, and perhaps your job, are most at risk. This is a way of counting risk, not a recommendation for anyone's savings: the point the interviewer wants is that risk is measured across everything you own, including your pay.
Where candidates lose it
Candidates answer 2, the bonus beta, or 0.4, the bonus weight, because they reach for one number instead of a weighted average. The beta of a mix always blends by weight.
The second loss is stopping at the number. The question asks what it says, and the answer is that a banker's pay is already a leveraged bet on markets, which is why the follow-up is about savings.
What the interviewer asks next
What is the personal beta of a civil servant on a fixed salary, and what does it suggest?
Your bonus rises to 60% of pay. What is your personal beta now?
How would you put a value on your future earnings as an asset?
Asked at Rothschild & Co, Generalist, New York, 2026 (Wall Street Oasis): How would you value your favorite animal? What is your personal beta?
042A company has revenue of Rs 730 crore and collects from customers in 45 days. Next year revenue grows 20% and collection slows to 60 days. How much cash does the receivables line absorb?Accounting riddlesCoreBulge bracket IBMiddle market IB
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How much cash does the receivables line absorb next year?
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About Rs 54 crore. Receivables today are Rs 730 crore times 45 over 365, which is Rs 90 crore. Next year revenue is Rs 876 crore and collection takes 60 days, so receivables are Rs 144 crore. The increase of Rs 54 crore is cash the business has earned but not collected. Rs 18 crore of it comes from growth and Rs 36 crore from slower collection, twice as much.
Why does growth eat cash at all?
Think of a tailor who lets regular customers pay a month and a half after collecting their clothes. If the business grows, more money is out with customers at any moment, even though nobody is paying late. Receivables are revenue earned but not yet collected, so when revenue grows at the same collection period the balance grows with it, and the increase is cash the business has to fund. Here 20% more revenue at 45 days lifts receivables from Rs 90 crore to Rs 108 crore.
Receivables rise from Rs 90 crore to Rs 144 crore: Rs 18 crore of the increase comes from 20% growth at the old 45 days and Rs 36 crore from collecting in 60 days instead, so slower collection absorbs twice as much cash as growth.
How do you split the Rs 54 crore?
Take the two changes one at a time. Growth first: Rs 876 crore at the old 45 days is Rs 108 crore, so growth absorbs Rs 18 crore. Then slower collection: going from 45 to 60 days on Rs 876 crore adds 15 days of sales, Rs 36 crore. Fifteen extra days of collection on the larger business costs twice as much cash as 20% growth. The line to watch is days sales outstandingReceivables divided by revenue, times 365: the average number of days customers take to pay..
The relationship
$\Delta AR = \left(876 \times \tfrac{45}{365} - 90\right) + 876 \times \tfrac{60-45}{365} = 18 + 36 = 54$
876 x 45/365 next year's receivables if collection had not slowed
90 today's receivables, 730 x 45/365
876 x 15/365 the extra 15 days of sales tied up by slower collection
What it says in wordsThe change in receivables is the growth effect at the old collection period plus the slower collection on the new revenue.
Does the order of the split matter?
A little. Slower collection first, on today's revenue, costs Rs 30 crore, and growth then adds Rs 24 crore; the Rs 6 crore difference is growth and slower collection compounding each other. The total is Rs 54 crore whichever way you split it, and slower collection is the bigger cause either way. Say which order you used. Then say what it means: a business growing fast while collecting slowly can report rising profit and falling cash at the same time, which is the pattern a lender looks for first.
Where candidates lose it
Candidates answer Rs 144 crore, the new balance, rather than Rs 54 crore, the change. Cash is absorbed by the increase in receivables, not by their level.
The second loss is blaming it all on growth. Splitting the change shows that slower collection costs twice as much, and that is the insight the question is built to draw out.
What the interviewer asks next
Collection improves to 30 days instead. How much cash does the receivables line release?
Payables also stretch from 30 to 45 days of costs. How does that change the answer?
Why might a company's collection period lengthen as it grows?
043Comparable companies have an unlevered beta of 0.8. Your target will run at a debt-to-equity ratio of 50% with a 25% tax rate. The risk-free rate is 7% and the equity risk premium 6%. What is the target's cost of equity?DCF and cost of capitalCoreMoelis & CompanyLos Angeles · 2026
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What cost of equity do you get?
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About 13.6%. The peers' 0.8 is an unlevered beta, the risk of the business with no debt. The target carries debt equal to 50% of its equity, so relever it: 0.8 times (1 plus 75% times 0.5) is 1.1. CAPM then gives 7% plus 1.1 times 6%, which is 13.6%. Using the unlevered 0.8 directly would understate the cost at 11.8%.
Why can you not use the peer beta as it is?
Think of two people with the same job and salary, one with no loan and one with a large home loan. A pay cut hurts the borrower more, because the loan payment does not shrink. Debt magnifies the swings that reach shareholders, so the same business carries a higher equity beta the more it borrows. Peers' betas are first stripped of their own debt to give an unlevered betaThe beta a business would have with no debt: the risk of its operations alone., then relevered at the target's own mix of debt and equity.
The peers' unlevered beta of 0.8 relevers to 1.1 at a 50% debt-to-equity ratio and a 25% tax rate, giving a cost of equity of 13.6%, while the three common slips give 11.8%, 13.0% and 14.2%.
How does the relevering work?
Use the standard formula, which assumes the debt itself carries no market risk. Levered beta equals unlevered beta times one plus (one minus the tax rate) times debt over equity: 0.8 times (1 + 0.75 x 0.5), which is 0.8 times 1.375, or 1.1. The tax term is there because interest is tax deductible, so the tax saving softens a quarter of the debt's burden on shareholders. Then CAPM: 7% plus 1.1 times 6% is 13.6%.
The relationship
$\beta_L = \beta_U\left[1 + (1-t)\frac{D}{E}\right] = 0.8 \times 1.375 = 1.1 \qquad k_e = 7\% + 1.1 \times 6\% = 13.6\%$
beta_U the peers' unlevered beta, 0.8
t the tax rate, 25%
D/E the target's debt divided by its equity, 50%
What it says in wordsAdd back the target's own debt to the business risk, then price that risk with CAPM.
Which slips change the answer?
Three, each worth naming. Skipping the relevering gives 11.8%, using debt over total capital instead of debt over equity gives 13.0%, and ignoring tax gives 14.2%. A spread of 2.4 points in the cost of equity moves a DCF a long way, so the interviewer wants to hear which ratio you are plugging in. State the limit too: the rates here are illustrations, and a live model takes the current government bond yield and the premium the bank uses.
Where candidates lose it
The fast loss is plugging 0.8 straight into CAPM. The peers' beta has been cleaned of debt, so using it unadjusted values the target as if it had none, and the cost of equity comes out too low.
The quieter loss is the ratio. The formula takes debt over equity, 50%, not debt over total capital, one third. Say the ratio out loud before you multiply.
What the interviewer asks next
The target's debt rises to 100% of equity. What is the cost of equity now?
What is the WACC if the target's debt costs 10% before tax?
Why do you unlever each peer before averaging, rather than averaging the levered betas?
Asked at Moelis & Company, Investment Banking, Los Angeles, 2026 (Wall Street Oasis): high-level technical questions aimed at accounting (NWC) and valuation topics (EV, DCF, UFCF, Cost of Equity)
051Estimate the number of two-wheelers sold in India in a year.Estimation and market sizingCoreBulge bracket IBConsulting style brainteasers
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Pick a ballpark before you build it.
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About 2 crore a year. India has about 140 crore people in roughly 30 crore households. If about half of households own a two-wheeler, 15 crore are in use. A vehicle lasts about 10 years, so 1.5 crore are replaced each year, and a fleet growing 3% adds about 45 lakh more, close to 2 crore. A top-down check, 18 crore vehicles on the road over a 9-year life, lands at 2.0 crore too. The published industry figure is the thing to confirm, not to recall.
Where do you start, and what do you refuse to guess?
Think of guessing how many birthday cakes a town buys in a year. Nobody knows the number, but everybody can picture the pieces: people, birthdays per person, the share with a cake. Market sizing works from a number you can picture to the number you cannot, and the only figure taken on trust is the population. About 140 crore people at 4.5 per household is 31 crore households, call it 30. The one real judgement is the ownership rate, the penetrationThe share of possible buyers who already own the product. Half of households here.: higher in towns, lower in villages, so about half overall.
Working up from 30 crore households, half owning a two-wheeler that lasts 10 years, gives 1.95 crore sales a year once 3% fleet growth is added, and working down from 18 crore vehicles on the road over a 9-year life gives 2.0 crore, so the two routes agree within 4%.
How does the bottom-up build go?
Thirty crore households at 50% is 15 crore two-wheelers in use. Sales are what it takes to keep that fleet going plus what it takes to grow it. Yearly sales of a durable are the fleet divided by its life, plus the fleet's growth, so the life assumption matters as much as the ownership rate. At a 10-year life, 1.5 crore are replaced each year; a fleet growing 3% a year needs another 45 lakh; together about 1.95 crore. Say each assumption as you use it, so the interviewer can push on the one they disagree with.
The relationship
$S = \frac{H \times p}{L} + H \times p \times g = \frac{30 \times 0.5}{10} + 15 \times 0.03 \approx 1.95\text{ crore}$
H households, about 30 crore
p the share of households with a two-wheeler, 50%
L the vehicle's life, 10 years
g growth in the fleet, 3% a year
What it says in wordsSales replace the vehicles that wear out and add the ones that a growing fleet needs.
Why build a second route, and what if it disagrees?
Come at it from the fleet instead. About 13 two-wheelers per 100 people is 18 crore on the road, and dividing by a 9-year average life gives 2.0 crore a year, within 4% of the first route. A demand estimate is credible only once an independent route lands near it; agreement does not prove either number, but disagreement tells you which assumption to revisit. Stress the two judgements: 40% ownership and a 12-year life give 1.4 crore, 60% and 8 years give 2.8 crore. So the honest answer is a range of about 1.5 to 3 crore with 2 crore most likely, and the published sales figure from the industry body is the check to look up afterwards.
Where candidates lose it
Candidates reach for a remembered figure, right or wrong, and have nothing to say when asked how they got it. The interviewer is marking the structure and the stated assumptions, not the number.
The second loss is forgetting replacement. A fleet of 15 crore does not mean 15 crore sales; sales are the fleet divided by its life plus growth, which is why the life assumption deserves its own sentence.
What the interviewer asks next
How would the estimate change if you were asked for cars instead?
What share of those sales would you expect to be first-time buyers rather than replacements?
How would you estimate the number of two-wheeler dealerships in India?
053You roll a fair die and are paid its face value in lakh rupees. After seeing the first roll you may roll once more and take the second result instead, whatever it turns out to be. What is the game worth, and what is your stopping rule?Expected value and gamesCoreBulge bracket IBConsulting style brainteasers
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On which first rolls do you roll again?
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The game is worth Rs 4.25 lakh, and you roll again on a 1, 2 or 3. A single roll is worth 3.5 lakh on average, so the chance to roll again is worth exactly that. Keep any first roll above 3.5, which means 4, 5 or 6. Half the time you keep, averaging 5 lakh; half the time you roll again for 3.5. Half of 5 plus half of 3.5 is 4.25 lakh. The option to re-roll adds 0.75 lakh over a single roll.
Why is the rule to compare against 3.5?
Think of boarding a train with one visible seat by the door and the rest of the carriage out of sight. You walk on only if the seat you can see is worse than the average seat down the carriage, because once you walk you take whatever is there. Work backwards: the last decision has no choices left, so its value is the plain average, 3.5 lakh, and any earlier roll is kept only if it beats that. A 4, 5 or 6 beats 3.5; a 1, 2 or 3 does not; no face equals it, so the rule has no ties. The number you are comparing with is the expected valueThe average outcome if the same gamble were repeated many times: each result weighted by its probability. of rolling again.
A first roll of 1, 2 or 3 falls below the 3.5 that a second roll is worth, so you roll again, while a 4, 5 or 6 is kept, and the kept faces contribute 2.5 and the re-rolls 1.75 for a game worth 4.25 lakh.
How does the 4.25 come together?
Three faces out of six are kept and contribute (4 + 5 + 6) over 6, which is 2.5 lakh; three are re-rolled and contribute three sixths of 3.5, which is 1.75; the total is 4.25 lakh. Check the rule by moving it. Keep the 3 as well: (3 + 4 + 5 + 6) over 6 plus two sixths of 3.5 is 4.17. Re-roll the 4 too: (5 + 6) over 6 plus four sixths of 3.5 is 4.17. Both sit below 4.25, about Rs 8,333 a game, so 3.5 is the only bar that gives the full value.
The relationship
$V = \frac{4 + 5 + 6}{6} + \frac{3}{6} \times 3.5 = 2.5 + 1.75 = 4.25$
(4 + 5 + 6)/6 the kept faces, each one in six
3/6 the chance the first roll is a 1, 2 or 3 and you roll again
3.5 what the second roll is worth on average
What it says in wordsAdd what you keep, weighted by its chance, to what you get from rolling again, weighted by its chance.
What happens with a third roll, and why do interviewers ask?
Allow two re-rolls. The game from the second roll onward is now worth 4.25, so on the first roll you keep only a 5 or 6: (5 + 6) over 6 plus four sixths of 4.25 is 4.67 lakh. Every extra chance to try again raises both the value of the game and the bar for stopping, and that is the whole logic of an option: the right to swap a known result for an uncertain one is worth paying for only when the known result is poor. The same reasoning prices walking away from a signed deal or waiting for a better bid. The limit: this assumes you care only about the average. Someone who badly needs 3 lakh might keep a 3, and that is a preference, not an error.
Where candidates lose it
The common miss is a rule based on feel, such as re-rolling anything below 5 because 5 and 6 feel like wins. That throws away a 4 that beats the 3.5 you get by rolling again, and costs about Rs 8,333 of value per game.
The second loss is valuing the game at 3.5 lakh because it is still just a die. The option to re-roll is worth 0.75 lakh here, and pricing an option at zero is the error the interviewer is listening for.
What the interviewer asks next
You may re-roll twice. What is the game worth and what is the rule on the first roll?
The re-roll costs Rs 50,000. Do you still take it, and when?
How does this connect to the decision to walk away from a signed deal?
063A company has Rs 10 crore of revenue, variable COGS of 60% of revenue and fixed operating costs of Rs 2 crore, so EBITDA is Rs 2 crore. Which would you rather have: a 10% rise in revenue, a 5% fall in COGS, or a 5% rise in EBITDA?Accounting riddlesCoreNomuraSan Francisco · 2026
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Which option adds the most EBITDA?
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Take the 10% revenue rise: it adds Rs 0.4 crore of EBITDA. Revenue rises by Rs 1 crore, and with variable COGS at 60%, Rs 0.4 crore of it reaches EBITDA, a 20% jump. A 5% cut in COGS saves 5% of Rs 6 crore, Rs 0.3 crore. A 5% rise in EBITDA is 5% of the smallest number, Rs 0.1 crore. Translate every option into rupees of EBITDA before choosing.
Why can't you compare the three percentages directly?
Ten per cent off a car and ten per cent off a cup of coffee are not the same saving. Each percentage is taken on a different base, so convert all three into one unit, rupees of EBITDA, before you choose. Revenue is the biggest base at Rs 10 crore, COGS is Rs 6 crore and EBITDA is the smallest at Rs 2 crore. A small percentage of a big number can beat a big percentage of a small one, and here it does.
On Rs 10 crore of revenue with 60% variable COGS and Rs 2 crore of fixed costs, a 10% revenue rise adds Rs 0.4 crore of EBITDA, a 5% COGS cut adds Rs 0.3 crore and a 5% EBITDA rise adds only Rs 0.1 crore.
What should you ask before you answer?
Two readings change the numbers, and asking about them is part of the answer. First, is the revenue rise from volume or from price? Selling 10% more units drags 60% of the new revenue away as COGS, but a 10% price rise costs nothing extra, so all Rs 1 crore reaches EBITDA. Second, does a 5% fall in COGS mean 5% of COGS, or COGS falling from 60% to 55% of revenue? The first saves Rs 0.3 crore; the second saves Rs 0.5 crore and would beat a volume-led revenue rise.
Reading of the option EBITDA gain, Rs crore New EBITDA, Rs crore
Revenue +10% from volume 0.4 2.4
Revenue +10% from price 1.0 3.0
COGS down 5% of itself 0.3 2.3
COGS down 5 points of revenue 0.5 2.5
EBITDA +5% 0.1 2.1
The EBITDA option comes last under every reading. The revenue rise wins unless the COGS cut means five points of revenue and the revenue rise comes from volume, in which case the cut adds Rs 0.5 crore against Rs 0.4 crore.
Close with what a banker adds beyond the arithmetic. Operating leverageHow much profit swings for a given change in sales, because fixed costs do not move with volume. is why the revenue rise is so strong: with Rs 2 crore of fixed costs, a 10% rise in sales lifts EBITDA by 20%. The same leverage works in reverse, so a 10% fall in volume would cut EBITDA by 20% as well.
Where candidates lose it
Candidates pick the 10% because it is the biggest number, or the EBITDA option because EBITDA is what gets valued, without converting anything. Both are guesses; the interviewer wants rupees on one line.
The other loss is answering without asking whether the revenue rise is volume or price and what the COGS cut means. Asking takes ten seconds and shows you know the answer can flip.
What the interviewer asks next
At what variable COGS percentage would the 5% COGS cut and the 10% volume rise be worth the same?
Which option would a buyer of the business value most, and why might it not be the biggest EBITDA gain?
How does the answer change if fixed costs were Rs 3.5 crore instead of Rs 2 crore?
Asked at Nomura, Generalist, San Francisco, 2026 (Wall Street Oasis): $10 million in revenue. Do u want a 10% increase in revenue, 5% decrease in COGS, or 5% increase in EBITDA
064Estimate the annual revenue of a single petrol pump on a busy national highway.Estimation and market sizingCoreBulge bracket IBConsulting style brainteasers
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Before building it: which assumption deserves the most of your time?
Show the worked solution
About Rs 82 crore a year, built as vehicles, stop rate, litres and price. Say 15,000 vehicles pass a day and 5% stop, which is 750 fills. At 30 litres a fill that is 22,500.0 litres, and at Rs 100 a litre about Rs 22.5 lakh a day. Times 365 gives roughly Rs 82 crore. The stop rate is the shakiest input: 3% gives Rs 49 crore and 8% gives Rs 131 crore.
How do you turn a vague question into a chain you can multiply?
Think of a chai stall outside a railway station. You would not guess its takings in one go; you would ask how many people walk past, how many stop, what they buy and what it costs. A petrol pump is the same chain. Revenue is vehicles passing, times the share that stop, times litres per fill, times the price per litre, and the whole job is to say a defensible number for each link out loud. A busy national highway might carry 15,000 vehicles a day past one spot. If one in twenty pulls in, that is 750 fills. A car takes 25 to 35 litres and a truck far more, so 30 litres is a fair blended figure once you note that most vehicles are cars. Use Rs 100 a litre as a round illustrative price and say that the live pump price should be checked, because it moves.
Starting from 15,000 vehicles a day, a 5% stop rate, 30 litres a fill and Rs 100 a litre, the pump sells 22,500.0 litres and takes about Rs 22.5 lakh a day, roughly Rs 82 crore a year, and moving the stop rate between 3% and 8% swings that between Rs 49 crore and Rs 131 crore.
Which assumption should you shake, and which can you leave alone?
Not every link is equally uncertain. Shake the input you know least, because the answer moves one for one with every link and the widest range sits in the stop rate. Litres per fill is boxed in by the size of a fuel tank: 25 to 35 litres moves the annual figure only from Rs 68 crore to Rs 96 crore. The stop rate could honestly be 3% on a stretch with pumps every few kilometres or 8% at the only station for an hour, and that range takes the answer from Rs 49 crore to Rs 131 crore. Saying which input is soft is worth more to the interviewer than the point estimate.
Input Low Base High Revenue swing, Rs crore a year
Share of vehicles that stop 3% 5% 8% 49 to 131
Litres per fill 25 30 35 68 to 96
Price per litre Printed on the pump Rs 100 Known, confirm the current figure
With everything else at the base case, the stop rate swings the annual revenue across a range of Rs 82 crore while litres per fill swings it only Rs 27 crore, so the stop rate is where the estimate lives or dies.
The relationship
$\text{Revenue} = 15{,}000 \times 5\% \times 30 \times 100 \times 365 \approx \text{Rs }82\text{ crore}$
15,000 vehicles passing the pump in a day
5% the share that stop to fill
30 litres in an average fill
100 an illustrative price per litre, in rupees
365 days a year, a highway pump rarely closes
What it says in wordsAnnual revenue is the number of fills a day, times the litres and the price, times the days in the year.
What does a banker add after the number?
Say what the number is not. Revenue is not profit: a dealer keeps a margin of a few rupees a litre, so Rs 80 crore of sales is a small fraction of that in gross margin, and the rest passes through to the oil company and the exchequer. Then offer one sanity check: Rs 80 crore a year is about Rs 22 lakh a day, which at Rs 3,000 a fill is roughly 750 customers, about one every two minutes across an 18-hour day. If that sounds like a busy forecourt, the estimate hangs together.
Where candidates lose it
The common loss is a single guessed number with no chain behind it, or a chain where every link is stated with equal confidence. The interviewer is marking the structure and the honesty about which link is soft, not the final figure.
The second loss is stopping at revenue. One sentence on margin, and one sanity check from the other direction, separates a market-sizing answer from a guess.
What the interviewer asks next
How would you estimate the pump's annual profit rather than its revenue?
What changes if the pump sits inside a city rather than on a highway?
The owner wants to add a convenience store. How would you size that revenue?

D1	next year's dividend, half of Rs 10
r	the cost of equity, 10%
g	growth: half retained, times a 10% return on it

0.6, 0.4	each component's share of total pay
0, 2	how much each component moves when the market moves

876 x 45/365	next year's receivables if collection had not slowed
90	today's receivables, 730 x 45/365
876 x 15/365	the extra 15 days of sales tied up by slower collection

beta_U	the peers' unlevered beta, 0.8
t	the tax rate, 25%
D/E	the target's debt divided by its equity, 50%

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How do you structure the estimate before any number?

Why does a demand estimate need a supply check?

What do you say about the weakest link?

Where candidates lose it

What the interviewer asks next

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Why does growth not add value here?

How do the two dividend streams compare?

When would the decision change the price?

Where candidates lose it

What the interviewer asks next

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Why is halving the wrong instinct?

Why can it not be done in one weighing?

What does the puzzle teach beyond the scale?

Where candidates lose it

What the interviewer asks next

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How do you get a beta for a person?

What does 0.8 look like in rupees?

Why does it matter for your savings?

Where candidates lose it

What the interviewer asks next

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Why does growth eat cash at all?

How do you split the Rs 54 crore?

Does the order of the split matter?

Where candidates lose it

What the interviewer asks next

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Why can you not use the peer beta as it is?

How does the relevering work?

Which slips change the answer?

Where candidates lose it

What the interviewer asks next

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Where do you start, and what do you refuse to guess?

How does the bottom-up build go?

Why build a second route, and what if it disagrees?

Where candidates lose it

What the interviewer asks next

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Why is the rule to compare against 3.5?

How does the 4.25 come together?

What happens with a third roll, and why do interviewers ask?

Where candidates lose it

What the interviewer asks next

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Why can't you compare the three percentages directly?

What should you ask before you answer?

Where candidates lose it

What the interviewer asks next

Try it first

How do you turn a vague question into a chain you can multiply?

Which assumption should you shake, and which can you leave alone?

What does a banker add after the number?

Where candidates lose it

What the interviewer asks next