Investment Banking puzzles, solved step by step
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- 29
003A pond has one lily pad on day 1. The lily pads double every day and the pond is completely covered on day 30. On what day was the pond half covered?Harris WilliamsRichmond · 2025
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Answer inside five seconds.
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Day 29. The coverage doubles every day, so it halves when you step back one day. Full on day 30 means half on day 29, a quarter on day 28 and one thirty-second on day 25. Most of the growth in a doubling process arrives right at the end.
Why is day 15 wrong?
Day 15 would be right if the pond gained the same area every day, like a tank filling from a tap. Doubling is different: it is money compounding at 100% a day. Under doubling, each step back in time halves the amount, so half full is always exactly one step before full. On day 15 the pond is only one part in about 32,768 covered.
The pond is one thirty-second covered on day 25 and still only one quarter covered on day 28. It reaches half on day 29 and is full on day 30, because each day's bar is double the one before. Why would a banking interviewer ask this?
It is a test of whether you think in growth rates or in straight lines. The same instinct that answers day 15 also overestimates how much of a compounding investment's value arrives early. Say that link in one sentence after you answer: it shows you know why the question is on the table.
Where candidates lose it
Answering day 15 is the whole trap, and many strong candidates say it because they are answering fast. The interviewer is watching whether you pause for one second and ask what kind of growth this is.
Say day 29, then give the one-line reason: doubling forward means halving backward.
What the interviewer asks next
- On which day is the pond a quarter covered?
- If you start with two lily pads, when is the pond full?
- Where do you see this pattern in a DCF or an LBO?
Asked at Harris Williams, Generalist, Richmond, 2025 (Wall Street Oasis):
The lilypad doubles in size everyday, until the 30th day, when the pond is full
005A stock falls 10% one day. How much does it need to rise the next day to get back to where it started?JefferiesLondon · 2026
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Pick the answer before you calculate.
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About 11.1%. A price of 100 falls 10% to 90. Getting back to 100 needs a rise of 10 on a base of 90, which is 10 divided by 90, or 11.1%. The general rule: to recover a loss of L, you need L divided by (1 minus L), which grows much faster than the loss itself.
Why is the recovery bigger than the fall?
A 10% discount on a 100 rupee shirt takes it to 90. If the shop then marks it up by 10%, the tag reads 99, not 100, because the markup is taken on 90. Percentages are always measured against a base, and after a fall the base is smaller, so the same rupee gain is a bigger percentage.
A fall from 100 to 90 is 10%, but the climb from 90 back to 100 is 11.1% because it starts from a smaller base. The gap widens with the size of the loss: 30% needs 42.9% to recover and 50% needs a full 100%. The relationshipL the loss, as a decimal g the gain needed to get back to the start What it says in wordsThe gain needed to recover equals the loss divided by what is left after the loss.What do you add to sound like a banker rather than a calculator?
Give the number, then the pattern. Large drawdowns are hard to climb out of: a fund that loses 50% has to double just to break even. That one sentence shows you see why lenders and investors care about downside, which is the real reason the question is asked.
Where candidates lose it
Saying 10% is the whole trap, and it happens because the question is asked fast and sounds symmetric. The interviewer wants to see you notice the base changed.
If you say 11% rather than 11.1%, that is fine; say 10 over 90 so the method is audible.
What the interviewer asks next
- A stock rises 50% and then falls 50%. Where does it end?
- Two days of minus 10% and plus 10%: are you up or down, and by how much?
- Why does this matter for how a fund reports its drawdowns?
Asked at Jefferies, Generalist (IBD spring week), London, 2026 (Wall Street Oasis):
if a stock goes down 10% one day how much does it need to go up by the day after to get back
044A company finds Rs 10 crore of cash lying on the street. What happens to its enterprise value and its equity value?UBSAnonymous interview candidate in · 2024
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What happens to enterprise value?
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Enterprise value stays the same and equity value rises by Rs 10 crore. Shareholders own the extra cash, so their equity is worth Rs 10 crore more. Enterprise value is equity plus debt minus cash: equity is up 10 and cash is up 10, so EV does not move. EV measures the operating business, and picking money up off the street does not change what that business earns. Ignoring tax on the windfall keeps the numbers clean.
What is enterprise value actually measuring?
Think of buying a shop whose till holds Rs 10,000. You would pay for the business plus the cash in the till, and the cash is worth exactly its face value to you, no more and no less. Enterprise value prices the operating business on its own, so cash, which is worth its face value to whoever holds it, is taken out of the bridge. Equity value is what shareholders own, and they own both the business and the cash.
Finding Rs 10 crore lifts equity value from Rs 500 crore to Rs 510 crore and cash from Rs 50 crore to Rs 60 crore, and because cash is subtracted in the bridge, enterprise value stays at Rs 750 crore. How does the bridge move?
Take a company with equity worth Rs 500 crore, debt of Rs 300 crore and cash of Rs 50 crore, so enterprise value is Rs 750 crore. Find Rs 10 crore: cash becomes Rs 60 crore and equity Rs 510 crore, and EV is 510 plus 300 minus 60, still Rs 750 crore. Nothing in the operating business changed, so multiples of EBITDAEarnings before interest, tax, depreciation and amortisation: a rough measure of the cash profit the operating business produces. or revenue do not change either.
The relationshipE equity value, what the shareholders own D debt C cash, subtracted because it is not part of the operating business What it says in wordsEquity and cash rise by the same amount, so their effects on enterprise value cancel.What assumptions should you say out loud?
Two. First, tax: the windfall is probably taxable income, so at a 25% rate equity and cash each rise by Rs 7.5 crore rather than Rs 10 crore. Whatever amount sticks, cash and equity move together and enterprise value stays put. Second, the cash sits idle. If the company used it to repay debt, EV would still not change, but the split between lenders and shareholders would. Naming both shows the interviewer you know which line each event touches.
Where candidates lose it
The common wrong answer is that enterprise value rises by Rs 10 crore because the company is worth more. The owners are richer, but the operating business is not, and EV only measures the business.
The opposite slip is saying EV falls because cash is subtracted. That forgets equity rises by the same amount. Walk the bridge line by line and the two moves cancel.
What the interviewer asks next
- The company uses the Rs 10 crore to repay debt. What happens to EV and equity value?
- The company issues Rs 100 crore of new shares for cash. What happens to EV?
- Why might a buyer pay less than face value for cash trapped in a foreign subsidiary?
Asked at UBS, Investment Banking, Anonymous interview candidate in, 2024 (Wall Street Oasis):
explain the assumptions behind it - if pick up 10 bucks, what happens to EV
058A company trades at 15x earnings and pays out 40% of its earnings as dividends. What is its dividend yield?JefferiesChicago · 2026
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Which is the dividend yield?
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About 2.67%. A P/E of 15 means each Rs 100 of share price buys Rs 6.67 of yearly earnings, an earnings yield of 1 over 15. The company pays out 40% of that, Rs 2.67, as dividend. Dividend yield is dividend over price, Rs 2.67 over Rs 100. In one line: the payout ratio divided by the P/E, 0.40 over 15.
How do you turn a P/E into something you can multiply?
Flip it. A P/E of 15 says you pay 15 rupees for every rupee of yearly profit, so every rupee of price buys one fifteenth of a rupee of profit. Inverting the P/E gives the earnings yieldEarnings per share divided by the share price: the inverse of the P/E., 1 over 15 or about 6.67%, and every other per-share ratio then falls out by multiplication. Picking a round share price of Rs 100 makes it concrete: earnings per share are Rs 6.67.
A Rs 100 share at 15x earnings carries Rs 6.67 of earnings; paying out 40% gives a Rs 2.67 dividend, a 2.67% yield, while the other Rs 4.00 stays in the business. Why is the dividend only part of the shareholder's return?
Think of a shopkeeper who takes home 40% of each year's profit and leaves 60% in the shop to buy more stock. The retained Rs 4.00 is not lost to shareholders; it is reinvested, and if it earns a decent return it should lift future earnings and dividends. That is why a low dividend yield on its own says little about whether a share is cheap. A company paying out everything would show a 6.67% yield and little room to grow.
The relationshipDPS dividend per share EPS earnings per share payout the share of earnings paid as dividend, 40% P/E price over earnings per share, 15 What it says in wordsDividend yield is the payout ratio divided by the P/E, because both are measured against the same share price.Say the general rule after the number, because the follow-up usually changes one input. If the P/E doubles to 30 with the same payout, the yield halves to 1.33%; if the payout doubles to 80% at the same P/E, the yield doubles to 5.33%. Having the one-line formula ready means you answer those in a breath.
Where candidates lose it
The trap is answering 6.67%, the earnings yield, because 1 over 15 is the first thing anyone computes. Dividends are the part of earnings paid in cash, not all of it.
The other slip is multiplying instead of dividing, 40% times 15, and saying 6.0. Pinning a share price of Rs 100 and walking down to earnings and then to the dividend keeps the direction right.
What the interviewer asks next
- If dividends grow at 5% a year forever, what cost of equity does this price imply?
- The payout rises to 60% and the share price does not move. What is the new yield, and what might the market be thinking?
- Why might a fast-growing company pay no dividend at all?
Asked at Jefferies, Mergers and Acquisitions, Chicago, 2026 (Wall Street Oasis):
what are specific line items in the BS, some very simple P/E calculations, etc.
100Online numerical test style: three divisions had revenue of Rs 420, 260 and 120 crore last year and Rs 462, 299 and 150 crore this year. Which division grew fastest, and which contributed most to the growth in total revenue?BarclaysNew York · 2026
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Which division contributed most to total growth?
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Division C grew fastest, at 25%, but Division A contributed most, adding Rs 42 crore of the Rs 111 crore increase. Growth rates are 42/420 = 10%, 39/260 = 15% and 30/120 = 25%. Rupee increases are 42, 39 and 30. A's slower rate on a much bigger base adds more. Total revenue grew 13.9%, and A supplied 37.8% of that growth.
Why are these two different questions?
A child's pocket money rising from 100 to 150 is 50% growth; a parent's salary rising from 1 lakh to 1.1 lakh is 10%. The household budget still cares far more about the salary. A growth rate measures change relative to each part's own size; contribution measures change in rupees, which is what adds up to the total. Online tests ask both in one question because candidates who rush answer the same division twice.
Adding a growth column and an increase column to the table shows Division C growing fastest at 25% while Division A adds the most, Rs 42 crore or 37.8% of the Rs 111 crore rise, and total revenue grows 13.9%. How do you do it fast under a timer?
Compute the increases first, because they are subtractions: 42, 39, 30. Then compute rates only where needed, using easy fractions: 42 on 420 is a tenth, 30 on 120 is a quarter, 39 on 260 sits between them at 15%. Write the two added columns next to the table rather than holding the numbers in your head, because the next question in the set often reuses them.
The relationshipw_i each division's share of last year's revenue g_i each division's growth rate What it says in wordsTotal growth is the average of the divisions' growth rates weighted by their starting size.That weighting is the third trap a test can set. The simple average of 10%, 15% and 25% is 16.7%, which is wrong because it gives the small division the same say as the large one. Total revenue went from 800 to 911, a rise of 13.9%. If an option shows 16.7%, it is there to catch exactly that shortcut.
Where candidates lose it
The trap is answering C to both parts, because the 25% is the most striking number on the page. The test separates fast readers from careful ones by asking for two different measures in one question.
The second loss is averaging growth rates to get total growth. Always weight by size, or simply add the totals and compute once.
What the interviewer asks next
- If Division C keeps growing 25% and A keeps growing 10%, in how many years does C add more rupees than A?
- What share of total revenue will each division have next year if growth rates repeat?
- How would you present these numbers on one slide for a client?
Asked at Barclays, Investment Banking, New York, 2026 (Wall Street Oasis):
The numerical section involved interpreting tables and charts quickly
