Investment Banking puzzles, solved step by step

Puzzles: 100
Traced to a firm: 36
Topics: 12
Hard: 29

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015Without a calculator, what is 9 to the power of 6?Mental maths and countingCoreNomuraTokyo · 2025
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Before computing anything, which size is right?
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531,441. Rewrite 9 to the 6th as the square of 9 cubed. 9 cubed is 729. Then square 729 by splitting it into 700 plus 29: 700 squared is 490,000, twice 700 times 29 is 40,600, and 29 squared is 841. They add to 531,441. As a check, it should be a little over half a million, because 0.9 to the 6th is about 0.53.
How do you keep every step in your head?
Think of carrying a heavy box up six floors: you take it in two flights of three with a rest between, not six lifts in a row. Rewriting a power as the square of a smaller power cuts the work to one easy cube and one square you can split. 9 squared is 81, and 81 times 9 is 729, so 9 cubed is 729. Then 9 to the 6th is 729 squared, and squaring a number near a round one is the most practised move in mental maths.
Nine cubed is 729, and squaring 729 as 700 plus 29 gives a 490,000 block, two strips of 20,300 and an 841 corner, which add to 531,441.
The relationship
$9^6 = (9^3)^2 = 729^2 = (700+29)^2 = 490{,}000 + 2(700)(29) + 29^2 = 531{,}441$
9^3 729, nine cubed
(700 + 29)^2 the square split into a round part and a remainder
2(700)(29) the two strips, 20,300 each and 40,600 together
What it says in wordsSquare a number by splitting it into a round part and a remainder; the cross term counts twice.
How do you check it before saying it?
Three quick checks. An even power of 9 ends in 1, because 81 does, and 531,441 ends in 1. Any power of 9 is divisible by 9, so its digits must sum to a multiple of 9: 5 + 3 + 1 + 4 + 4 + 1 is 18. And the size is right: 9 is 10% below 10, and six 10% trims leave about 53% of a million. A digit check and a size check together catch nearly every slip in the cross term, which is where most mental errors happen.
A second route, if you prefer it: 9 to the 6th is also 81 cubed. 81 times 81 is 6,561, and 6,561 times 81 is 6,561 times 80 plus 6,561, which is 524,880 plus 6,561, giving 531,441 again. Saying one route and confirming with the other is worth more than speed.
Where candidates lose it
The usual loss is multiplying 9 by itself six times in a row and dropping a digit somewhere in the five-digit middle steps. By the time you reach 59,049 times 9, the interviewer has watched you struggle for a minute.
The other loss is saying the number without a check. Give the answer, then the two-second test: it ends in 1 and its digits sum to 18.
What the interviewer asks next
What is 11 to the power of 4?
What are 99 squared and 999 squared?
Is 2 to the power of 20 bigger or smaller than a million, and by how much?
Asked at Nomura, Generalist, Tokyo, 2025 (Wall Street Oasis): I think one of the math questions was 9 to the power of 6
016A merger promises Rs 100 crore of pre-tax cost synergies at full run-rate: half in year 1 and all of it from year 2. Achieving them costs Rs 150 crore once, in year 1. Tax is 25% and the market capitalises after-tax earnings at 8x. Roughly what are the synergies worth today?Deal mathsHardNomuraNew York · 2026
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Roughly what are the synergies worth?
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About Rs 450 crore. At full run-rate the synergies add Rs 75 crore of after-tax earnings, which the market capitalises at 8x: Rs 600 crore. Two things the headline ignores come off. Year 1 delivers only half, a shortfall of Rs 37.5 crore after tax, and the one-off cost of Rs 150 crore is Rs 112.5 crore after its tax saving.
Why can you not just multiply Rs 100 crore by 8?
A shop owner expects a new supplier to cut her costs by Rs 1 lakh a year. Before celebrating, she has to pay tax on the extra profit, wait for the new contract to start, and pay the one-off cost of switching. A synergy is worth the after-tax earnings it adds, capitalised, less everything it costs to achieve and every rupee that arrives late. The 8x multiple applies to after-tax earnings, so the pre-tax Rs 100 crore first becomes Rs 75 crore at 25% tax, and 75 x 8 is Rs 600 crore.
The pre-tax headline of Rs 800 crore overstates the synergies: after tax the run-rate is worth Rs 600 crore, and taking off the after-tax year-1 shortfall of Rs 37.5 crore and integration cost of Rs 112.5 crore leaves about Rs 450 crore.
What comes off the Rs 600 crore?
Two things. Phasing: the market value assumes the full run-rate, but year 1 delivers only half, so Rs 50 crore of pre-tax savings, Rs 37.5 crore after tax, never arrive. Cost to achieve: Rs 150 crore of severance, systems work and site closures, assumed tax deductible, so it costs Rs 112.5 crore after tax. Net of phasing and the cost to achieve, the synergies are worth about Rs 450 crore, a quarter less than the after-tax figure and 44% less than the pre-tax headline.
The relationship
$V = \underbrace{100 \times 0.75 \times 8}_{600} - \underbrace{50 \times 0.75}_{37.5} - \underbrace{150 \times 0.75}_{112.5} = 450$
100 x 0.75 x 8 run-rate synergies after 25% tax, capitalised at 8x
50 x 0.75 the half of year 1's savings that does not arrive, after tax
150 x 0.75 the one-off cost to achieve, after its tax saving
What it says in wordsCapitalise the after-tax run-rate, then subtract the after-tax value of the savings that arrive late and the cost of getting them.
What does this rough answer leave out?
Three refinements, each worth naming. The year-1 items fall a year from now, so discounting them would trim the deductions slightly. The 8x assumes the market gives synergies the same multiple as the core earnings, while in practice cost synergiesSavings from combining two businesses, such as closing duplicate offices or merging purchasing. earn more credit than revenue synergies and both are discounted for execution risk. The deductibility of integration costs is an assumption to confirm for the jurisdiction. The answer to give is the method and Rs 450 crore, then one line on which assumption you would test first.
The number matters because it caps what a buyer can sensibly pay away. A premium above roughly Rs 450 crore hands the target's shareholders more than the whole value the deal creates, before any risk that the savings slip.
Where candidates lose it
The common slip is Rs 800 crore: a pre-tax saving multiplied by a multiple meant for after-tax earnings. Interviewers hear it constantly, because announcements usually quote synergies before tax.
The second slip is stopping at Rs 600 crore. The question gave you a phasing schedule and a cost to achieve for a reason; both come off, and the cost comes off after tax.
What the interviewer asks next
If the buyer pays a Rs 500 crore premium for the target, is the deal worth doing on these synergies alone?
How would you value Rs 100 crore of revenue synergies at a 20% EBITDA margin?
Why do markets often give cost synergies more credit than revenue synergies?
Asked at Nomura, Investment Banking, New York, 2026 (Wall Street Oasis): Asked about what synergies were in a merger and in-depth questions about how my experiences
017Free cash flow of Rs 100 crore arrives every year for five years and the discount rate is 10%. How much does the mid-year convention add to the value, and why?DCF and cost of capitalCoreLazardNew York · 2026
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How much does the mid-year convention add?
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It adds about Rs 18.5 crore, or 4.9%, taking the value from Rs 379.1 crore to Rs 397.6 crore. The mid-year convention assumes each year's cash arrives evenly through the year, so on average halfway through rather than at the end. Every cash flow is then discounted for half a year less, which multiplies each present value by 1.10 to the power of one half, 1.0488.
Why would cash arrive in the middle of the year?
A shop does not collect its year's takings in one lump on the last day of March; money comes in every day. A DCF that discounts each year's cash flow as if it all arrived on the final day is too harsh. The mid-year convention treats each year's cash flow as arriving, on average, halfway through the year, so it is discounted for t minus one half years instead of t. For a business with steady receipts that is the more accurate assumption, and it is the default in many banks' models.
Moving each Rs 100 crore cash flow from the end of its year to the middle lifts its discount factor by the same ratio, so the five-year value rises from Rs 379.08 crore to Rs 397.58 crore, an uplift of 4.88%.
The relationship
$\sum_{t=1}^{5} \frac{100}{1.10^{\,t-0.5}} = 1.10^{0.5} \times \sum_{t=1}^{5} \frac{100}{1.10^{\,t}} = 1.0488 \times 379.08 = 397.58$
t - 0.5 each year's cash treated as arriving at the middle of the year
1.10^0.5 the gain from discounting every cash flow for half a year less
What it says in wordsShifting every cash flow six months earlier multiplies the whole value by the square root of one plus the discount rate.
Why is the uplift exactly the square root of 1.10 minus one?
Because the shift is the same for every cash flow. Moving a payment six months earlier multiplies its present value by 1.10 to the power of one half, whatever year it sits in. Since every cash flow gets the same uplift, the whole value rises by the same 4.88%, and neither the size nor the pattern of the cash flows changes that. Half the discount rate, 5%, is a fair first approximation to say out loud; at a 20% rate the exact uplift is 9.5%, against the 10% the approximation would give, so the shortcut weakens as rates rise.
Where should you not apply it?
Two cautions. A terminal valueThe value of all cash flows beyond the forecast years, usually from a growing perpetuity or an exit multiple. built on a perpetuity of flows is usually discounted on the same mid-year basis, but one built on an exit multiple is not, because a sale happens at a point in time, the end of the final year. Shifting an exit-multiple terminal value half a year earlier overstates the answer, and an interviewer who asks about the convention is often fishing for exactly that. For seasonal businesses that collect most cash late in the year, the convention itself flatters the value.
Where candidates lose it
The usual slip is to say the convention changes the cash flows, or that it only affects the first year. It changes timing only, and it moves every cash flow by the same six months, so the uplift applies to all of them.
The second slip is applying it to a terminal value built on an exit multiple. A sale happens at a moment, so that value stays discounted for the full five years; candidates who shift it too overstate the value and get caught on the follow-up.
What the interviewer asks next
If the discount rate were 20%, what would the convention add?
Should the mid-year convention apply to a terminal value built on an exit multiple?
For a business that bills most customers in its final quarter, is the convention still appropriate?
Asked at Lazard, Investment Banking, New York, 2026 (Wall Street Oasis): Asked about SBC, LBOs, Advanced accounting questions and mid-year conventions
019Explain the Black-Scholes intuition by pricing, in your head, a one-year at-the-money call on a Rs 100 stock with 20% volatility and near-zero interest rates.Rates, risk and optionsHardGoldman SachsZurich · 2025
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Roughly what is the call worth?
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About Rs 8. With near-zero rates, an at-the-money call is worth roughly 0.4 times the price times the volatility times the square root of time: 0.4 x 100 x 0.20 x 1 = 8.0. The full Black-Scholes formula gives Rs 7.97. The intuition: the option collects the upside of a bell-shaped spread of outcomes and nothing on the downside, and the average of that upside half is about 0.4 of one standard deviation.
What is Black-Scholes actually doing?
Picture a ticket that pays you whatever a stock gains over the next year and nothing if it falls. You would pay something for it, even though an at-the-moneyAn option whose strike price equals the current stock price, so exercising it today would pay nothing. ticket is worth nothing if cashed in today. Black-Scholes prices that ticket as the average payoff across all the ways the stock could move, with the spread of those moves set by volatility and time. Its inputs are the stock price, strike, time, volatility and interest rate, and with zero rates the formula reduces to S times N(d1) minus K times N(d2), where the two N terms come from the bell curve.
At a stock price of 100 the call pays nothing if exercised today, yet with a year to run at 20% volatility it is worth Rs 7.97, almost exactly the rule of thumb of 0.4 times the Rs 20 one-year standard deviation.
Where does the 0.4 come from?
Over a year at 20% volatility, the stock's likely outcomes form a bell curve around Rs 100 with a standard deviation of about Rs 20. The call keeps the right half and treats the left half as zero. The average of the positive half of a bell curve, counting the negative half as zero, is the standard deviation divided by the square root of 2 pi, about 0.4 of it. So the call is worth about 0.4 x Rs 20, which is Rs 8. Halve the time to six months and the spread shrinks by the square root of 2, so the option is worth about Rs 5.6, not Rs 4.
The relationship
$C \approx \frac{1}{\sqrt{2\pi}}\,S\,\sigma\sqrt{T} = 0.399 \times 100 \times 0.20 \times 1 = 7.98 \qquad C_{BS} = 100\,[N(0.1) - N(-0.1)] = 7.97$
S the stock price, Rs 100, equal to the strike
sigma volatility, 20% a year
T time to expiry in years, here 1
N(.) the cumulative bell-curve probability used in the full formula
What it says in wordsAn at-the-money option is worth about 0.4 of one standard deviation of the stock's price over the life of the option.
What does the shortcut leave out?
It holds for at-the-money options with modest volatility and low rates. Away from the strike, the payoff is no longer the clean right half of the curve, and with meaningful rates the forward price drifts above the spot, which raises a call's value. The rule is a sanity check on a quoted price, not a replacement for the formula. Black-Scholes itself assumes constant volatility and smooth price moves, which is why traders quote options in implied volatility and adjust for the skew they see in the market. Doubling volatility to 40% roughly doubles this call's value, to about Rs 15.9.
Where candidates lose it
The common slip is to say an at-the-money option is worth nothing because exercising it today pays zero. That is intrinsic value; the whole price of this option is time value, the chance of a favourable move before expiry.
The second slip is reciting the formula without any feel for the number. Give the 0.4 rule, reach Rs 8, and then say the exact formula agrees; that is what explaining Black-Scholes sounds like in an interview.
What the interviewer asks next
What is the matching at-the-money put worth here, and why?
If volatility doubles to 40%, roughly what happens to the call's value?
What is the delta of this call, roughly, and what does it tell you?
Asked at Goldman Sachs, 2026 | EMEA | Zurich | Wealth Management | Summer Analyst Interview, Zurich, 2025 (Wall Street Oasis): Moreover, I was asked to explain Black and Scholes.
020Company A trades at 12x earnings and 9x EV/EBITDA. Its closest peer B trades at 15x earnings and 8x EV/EBITDA. Build one set of numbers that explains how A is cheaper on P/E yet dearer on EV/EBITDA.Valuation riddlesHardBarclaysNew York · 2026
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Which difference does most of the work in a good answer?
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Give B heavy depreciation and more debt, so much less of its EBITDA reaches shareholders. Both earn EBITDA of Rs 100 crore. A has D&A of 2 and interest of 18, keeps net income of 60, and at equity value 720 trades on 12x; its EV of 900 is 9x EBITDA. B has D&A of 25 and interest of 35, keeps only 30, and at equity value 450 trades on 15x, though its EV of 800 is 8x.
How can one company be cheaper on one multiple and dearer on another?
Two shops each take in Rs 1 lakh a month before equipment and loan costs. One works from a simple counter with a small loan; the other leases costly machines it must keep replacing and carries a large loan. Priced on takings before those costs, they look alike; priced on what the owner keeps, they do not. EV/EBITDA values the business before depreciation and before financing, while P/E values what is left for shareholders after both, so a company with heavy D&A or heavy interest can look cheap on one and dear on the other.
Both companies earn EBITDA of Rs 100 crore, but B's heavier D&A and interest leave it net income of Rs 30 crore against A's Rs 60 crore, so B looks cheaper on EV/EBITDA at 8.0x against 9.0x and dearer on P/E at 15.0x against 12.0x.
Which line explains how much of the gap?
Work down from EBITDA. B carries Rs 23 crore more D&A and Rs 17 crore more interest than A, which after 25% tax is Rs 17.25 crore and Rs 12.75 crore of net income: together exactly the Rs 30 crore gap between A's 60 and B's 30. Here depreciation does more of the work than debt, which you can show with EV/EBIT, a multiple that charges D&A but ignores financing: A is 9.2x and B 10.7x, so A is cheaper there too.
Rs crore A B
Enterprise value 900 800
Net debt, at 10% interest 180 350
Equity value 720 450
EBITDA 100 100
D&A 2 25
Interest 18 35
Net income, 25% tax 60 30
EV / EBITDA 9.0x 8.0x
EV / EBIT 9.2x 10.7x
P/E 12.0x 15.0x
Two invented companies built to match the multiples in the question.
So which company is actually cheaper?
It depends on whether B's D&A is a real cost. If it reflects equipment that must be replaced, which capital expenditureCash spent on buying or replacing long-term assets such as machines and buildings. running close to depreciation would confirm, then EBITDA flatters B and A is better value on every measure that counts the cost of staying in business. If B's D&A is mostly amortisation of acquired intangibles with no cash replacement, EBITDA is the fairer lens and B may be the cheap one. The answer the interviewer wants is the diagnosis: check capex against D&A and check leverage before trusting either multiple.
Where candidates lose it
The common slip is to say the market simply disagrees or that one multiple must be wrong. Both are correct; they measure different things, and the job is to name what sits between EBITDA and net income.
The second slip is naming only debt. Leverage can push P/E either way depending on the cost of debt, while heavy D&A reliably depresses earnings relative to EBITDA. Give both, with numbers, and say which one does more of the work.
What the interviewer asks next
How would you check whether B's D&A is a real economic cost?
If B refinanced its debt at 5% instead of 10%, what would its P/E become?
Which multiple would you use to compare a capital-heavy telecoms operator with a software company, and why?
Asked at Barclays, Investment Banking, New York, 2026 (Wall Street Oasis): A company is trading at a lower P/E but a higher EV/EBITDA than peers
024Size the annual market for wedding catering in India, in Rs crore.Estimation and market sizingCoreRothschild & CoNew York · 2026
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Which structure gives the most defensible answer?
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Roughly Rs 2.3 lakh crore a year, on stated assumptions. Assume about 90 lakh weddings a year, from a population of about 140 crore. Split them into budget, mid-range and premium tiers, each with its own plate count and cost per plate. Budget weddings contribute about Rs 47,000 crore, mid-range Rs 81,000 crore and premium about Rs 1 lakh crore: 5% of weddings, 44% of the spend.
How many weddings happen a year?
Start from people, not from a remembered statistic. Assume a population of about 140 crore, a figure to confirm, and an average lifespan near 70 years, so roughly one seventieth of people, 2 crore, reach marrying age each year. Assume 90% marry: 1.8 crore people, or 90 lakh weddings. A count built from cohorts can be checked line by line, which is what makes it defensible in the room. One caveat is worth saying: a young population has larger cohorts than one seventieth, so this may undercount a little.
Why split by tier rather than use one average wedding?
Think of a school canteen and a five-star hotel both serving lunch. Averaging their prices and their customer counts separately, then multiplying, gives a number neither of them earns. Big weddings have both more guests and a higher cost per plate, so averaging guests and price separately understates the market. On the tiers below, the average-wedding shortcut, 435 plates at Rs 400, gives Rs 1.57 lakh crore, about 32% less than the tiered Rs 2.29 lakh crore. Plates here count every guest meal across all the functions of a wedding, and catering means food only, not venue or decoration.
About 90 lakh weddings a year, split into budget, mid-range and premium tiers with their own plate counts and prices, give about Rs 2,29,500 crore of catering, while one average wedding multiplied out gives only Rs 1,56,600 crore.
Tier Share of weddings Weddings Plates Rs per plate Rs crore
Budget 70% 63 lakh 300 250 47,250
Mid-range 25% 22.5 lakh 600 600 81,000
Premium 5% 4.5 lakh 1,500 1,500 1,01,250
Total 100% 90 lakh 2,29,500
Every input is an illustrative assumption stated for the estimate, not a measured figure.
Which assumption moves the answer most?
The premium tier. It is 5% of weddings and 44% of the value, so a change in its plate count or price moves the total more than any change in the budget tier. When one segment dominates the value, spend your sanity checks there: is 1,500 plates across several functions at Rs 1,500 a plate plausible for the top twentieth of weddings? Halve the premium tier's value and the total falls to about Rs 1.8 lakh crore, which is the honest low end of the range to quote.
Where candidates lose it
The common loss is one average wedding: a few hundred guests at a few hundred rupees a plate, times the number of weddings. It sounds reasonable and quietly drops about a third of the market, because the weddings with the most guests also pay the most per plate.
The second loss is reciting a wedding-industry figure from an article. The interviewer wants a structure built from people, tiers and plates, with every number said as an assumption.
What the interviewer asks next
How would you size the decoration market for the same weddings?
How does the wedding season affect the capacity a caterer needs?
How would you check the premium tier's assumptions with a few phone calls?
Asked at Rothschild & Co, Generalist, New York, 2026 (Wall Street Oasis): 1st round all technical focused mainly on DCF and Eq Val and Enterprise Value questions, mental math, and some market sizing

Rs crore	A	B
Enterprise value	900	800
Net debt, at 10% interest	180	350
Equity value	720	450
EBITDA	100	100
D&A	2	25
Interest	18	35
Net income, 25% tax	60	30
EV / EBITDA	9.0x	8.0x
EV / EBIT	9.2x	10.7x
P/E	12.0x	15.0x

Tier	Share of weddings	Weddings	Plates	Rs per plate	Rs crore
Budget	70%	63 lakh	300	250	47,250
Mid-range	25%	22.5 lakh	600	600	81,000
Premium	5%	4.5 lakh	1,500	1,500	1,01,250
Total	100%	90 lakh			2,29,500

027Equity value is Rs 1,000 crore. The company has Rs 400 crore of debt, Rs 150 crore of cash, Rs 100 crore of preference shares, Rs 50 crore of minority interest and a stake in an associate worth Rs 80 crore. What is enterprise value?Enterprise value and dilutionCoreBarclaysLondon · 2026

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Which of these items are subtracted on the way from equity value to enterprise value?

Show the worked solution

Enterprise value is Rs 1,320 crore. Start with equity value of Rs 1,000 crore. Add the claims that rank alongside or ahead of the ordinary shareholders on the consolidated business: debt of Rs 400 crore, preference shares of Rs 100 crore and minority interest of Rs 50 crore. Subtract what the company owns that is not part of that operating business: cash of Rs 150 crore and the Rs 80 crore associate stake. 1,000 plus 550 less 230 is 1,320.

Why are some items added and others subtracted?

Picture buying a shop. You pay the owner for her shares, but you also take on the bank loan, you owe the silent partner his share of the profits, and you inherit the cash in the till and the shop's small stake in the bakery next door. The price of the shop itself is what you paid, plus the loan and the partner's claim, minus the cash and the bakery stake, which you could sell on day one without touching the shop. Enterprise value is the value of the consolidated operating business, so you add every claim on that business and subtract every asset whose earnings sit outside it.

Equity value of Rs 1,000 crore steps up by debt, preference shares and minority interest to Rs 1,550 crore and down by cash and the associate stake to an enterprise value of Rs 1,320 crore, because the additions are claims on consolidated EBITDA and the subtractions are assets whose income sits outside it.

What is the test for each line?

Ask where the item's earnings appear. Minority interestThe share of a consolidated subsidiary owned by outside shareholders. Its profit is inside consolidated EBITDA but belongs to someone else. is added because consolidation puts 100% of the subsidiary's EBITDA into the group figure even though outsiders own part of it; leave it out and EV is too small for the EBITDA it is set against. Preference shares are added because their dividend is a claim ahead of the ordinary equity. The associateA company in which the group holds a significant but not controlling stake, usually 20% to 50%, shown as one line of share of profit below operating profit. is subtracted for the mirror reason: its profits arrive as a single line below EBITDA, so its value must come out of the numerator to keep the multiple consistent. The rule is consistency between numerator and denominator: EV must describe exactly the business whose EBITDA you divide it by.

Item	Rs crore	Why
Equity value	1,000	the ordinary shares, the starting point
Debt	+400	a claim on consolidated EBITDA
Preference shares	+100	a claim ranking ahead of the ordinary equity
Minority interest	+50	outsiders' share of a subsidiary whose EBITDA is fully consolidated
Cash	-150	not needed to run the business; netted against debt
Associate stake	-80	its profit arrives below EBITDA, so its value comes out
Enterprise value	1,320	1,000 + 550 - 230

An illustrative bridge; every figure is from the question, not from any real company.

The relationship

EV = 1{,}000 + 400 + 100 + 50 - 150 - 80 = 1,320

1,000	equity value, the ordinary shares
400 + 100 + 50	debt, preference shares and minority interest: claims on the consolidated business
150 + 80	cash and the associate stake: value whose income is not in consolidated EBITDA

What it says in wordsAdd the claims on consolidated EBITDA and subtract the assets whose income sits outside it.

What would you say the question leaves out?

Three things an interviewer may push on. Net debt here is Rs 250 crore, but a company needs some cash to run, so only the excess is truly surplus; most desks ignore that in an interview and net all of it, which is the assumption to state. Debt-like items such as unfunded pension deficits, lease liabilities and earn-outs also belong on the add side, and an interviewer who adds a convertible bond is checking whether you treat it as debt or as equity at the current share price. Give the Rs 1,320 crore, then name one debt-like item you would ask about, because the bridge in a live deal is longer than the one in the question. The multiple this feeds, EV/EBITDA, is only as clean as the bridge beneath it.

Where candidates lose it

The usual slip is the associate: candidates add it because it is an asset, or ignore it. It is subtracted, because its earnings sit below EBITDA and its value would otherwise inflate the multiple. The other common slip is subtracting minority interest because it belongs to outsiders; it is added, because the EBITDA it earns is counted in full.

Say the test out loud before you add a single number: claims on consolidated EBITDA are added, assets whose income sits outside it are subtracted. Then the arithmetic is five steps and the answer, Rs 1,320 crore, is the easy part.

What the interviewer asks next

If the company also carries Rs 60 crore of lease liabilities, does enterprise value change?
In a sum-of-the-parts valuation, where does minority interest appear, and with what sign?
The associate contributes Rs 10 crore of share of profit. If you kept the stake inside EV, what would you have to do to EBITDA?

Asked at Barclays, Investment Banking, London, 2026 (Wall Street Oasis): 25 minutes of technical questions, covering basics: EV-to-Equity, Valuation, Multiples, Working Capital

028A company's tax rate rises from 25% to 30%. Name three ways this moves a DCF and put numbers on each for a business with EBIT of Rs 200 crore, funded 30% by debt at 8% before tax and 70% by equity at 12%.DCF and cost of capitalHardGoldman SachsSan Francisco · 2025
Try it first
Which way does the valuation move overall?
Show the worked solution
The value falls, by about 4.8% here, because the cut to cash flow outweighs the cheaper debt. One: unlevered free cash flow falls, as NOPAT drops from Rs 150 crore to Rs 140 crore. Two: the after-tax cost of debt falls from 6.0% to 5.6%, taking the WACC from 10.20% to 10.08%. Three: the terminal value, which carries both effects, falls from about Rs 2,516 crore to Rs 2,395 crore at 4% growth.
Why does a tax rate touch both the top and the bottom of the fraction?
A landlord pays more tax on her rent, so the rent she keeps falls; but the interest on her mortgage is deductible, so the loan costs her a little less after tax. Two opposite effects from one change. A DCF is the same fraction: cash flow on top, discount rate below. A higher tax rate shrinks the cash flows directly and shrinks the WACC indirectly through the interest tax shield, and the first effect is almost always larger because it hits every rupee of operating profit while the second touches only the debt slice. Interviewers ask for three ways so that you show both sides and then say which wins.
The tax rise cuts NOPAT from Rs 150 crore to Rs 140 crore, lowers the WACC from 10.20% to 10.08% through the cheaper after-tax debt, and takes the terminal value from Rs 2,516 crore to Rs 2,395 crore, because the cash flow effect of Rs -168 crore outweighs the WACC relief of Rs 46 crore.
How big is each effect on these numbers?
Cash flow. NOPAT is EBIT times one minus the tax rate: Rs 200 crore x 0.75 = Rs 150 crore before and Rs 200 crore x 0.70 = Rs 140 crore after, a fall of Rs 10 crore, or 6.7%, in every forecast year, treating depreciation, capex and working capital as cancelling out. Discount rate. The after-tax cost of debt is 8% x (1 - t): 6.0% before and 5.6% after. Weighted at 30% debt and 70% equity at 12%, the WACC moves from 10.20% to 10.08%, down 12 basis points. Terminal value. At 4% growth, a Gordon growthA terminal value that treats the final cash flow as growing at a constant rate forever: the next cash flow divided by the discount rate less the growth rate. terminal value is Rs 2,516 crore before and Rs 2,395 crore after. Separating the two, the cash flow cut alone takes Rs 168 crore off the terminal value and the lower WACC alone adds Rs 46 crore back, so the net is Rs 121 crore, 4.8% lower.
Line Tax 25% Tax 30% Change
NOPAT, Rs crore 150 140 -6.7%
After-tax cost of debt 6.0% 5.6% -40 bp
WACC 10.20% 10.08% -12 bp
Terminal value at 4% growth, Rs crore 2,516 2,395 -4.8%
Illustrative inputs from the question: EBIT Rs 200 crore, 30% debt at 8%, 70% equity at 12%, long-run growth 4%.
The relationship
$WACC = 0.30 \times 8\%\,(1-t) + 0.70 \times 12\% \qquad TV = \frac{EBIT\,(1-t)\,(1+g)}{WACC - g}$
(1 - t) the share of each rupee left after tax, 0.75 falling to 0.70
0.30, 0.70 the debt and equity weights
g the long-run growth rate, 4% here
What it says in wordsThe tax rate enters the cash flow once and the discount rate once, and the cash flow effect is the larger of the two.
Is there a subtler channel the interviewer might be after?
Yes: the cost of equity. When you relever a beta, the formula carries a (1 - t) term, so a higher tax rate lowers the levered beta a little and the cost of equity with it. With debt to equity of 3 to 7 and a levered beta of 1.0 at 25%, the unlevered beta is 0.757, and relevering at 30% gives 0.984; with an assumed 6% risk-free rate and 6% equity risk premium, the cost of equity slips from 12% to 11.90% and the WACC to 10.01%. Even with that help the value is still about 3.7% lower, so the ranking of the effects does not change. Say the limitation too: the WACC relief assumes the company actually pays tax and keeps its interest deductible, and interest deductions are capped in many jurisdictions, a rule to confirm for the country in question.
Where candidates lose it
The common loss is naming only the cash flow effect, or naming the WACC effect and then concluding that value rises. Three ways means cash flow, the cost of debt inside the WACC, and the terminal value or cost of equity that carries them, and the net is down.
The second loss is putting no numbers on it. The question hands you EBIT, weights and rates so that you can say Rs 150 to Rs 140 crore and 10.20% to 10.08% out loud; a candidate who stays qualitative has not answered.
What the interviewer asks next
If the company had no debt at all, which of the three effects survive?
How would a large tax-loss carryforward change the answer?
Why might a biotech DCF, with years of losses ahead, be almost indifferent to this change?
Asked at Goldman Sachs, Investment Banking, San Francisco, 2025 (Wall Street Oasis): Three ways in which the tax rate affects a DCF?
029What is the beta of a lottery ticket, and what is the beta of a portfolio that is half an index fund and half lottery tickets?Rates, risk and optionsCoreMoelis & CompanyNew York · 2026
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The lottery ticket's beta is?
Show the worked solution
The lottery ticket has a beta of zero, and the half-and-half portfolio has a beta of 0.5. Beta is the covariance of an asset's return with the market's return divided by the market's variance. A lottery draw does not move with the index at all, so its covariance is zero, however wild its payoff. Betas combine in proportion to weights, so half an index fund at beta 1 and half tickets at beta 0 give 0.5 x 1 + 0.5 x 0 = 0.5.
Why is a wildly risky asset given a beta of zero?
Think of two shops on one street. One sells umbrellas, whose takings rise and fall with the weather; the other sells birthday cards, whose takings have nothing to do with it. The card shop's sales swing plenty, but not with the rain. Beta measures only the part of an asset's movement that follows the market, so an asset whose payoff is decided by a draw of numbered balls has a beta of zero no matter how large its swings. On a Rs 10 ticket with an assumed one in a crore chance of a Rs 5 crore prize, the standard deviation of the return is about 1,600 times the stake and the beta is still zero. Volatility is total riskThe full spread of an asset's returns, usually measured by standard deviation, including both the part linked to the market and the part unique to the asset.; beta is only its market-linked part.
On the security market line the index fund sits at beta 1 and 12%, the lottery ticket at beta 0 and about -50%, some 56 points below the 6% the line requires, and the half-and-half blend at beta 0.5 and -19%, because betas average by weight while expected returns do not sit on the line for an asset with a negative-value payoff.
How does the portfolio beta follow?
Covariance is linear in the weights, so the beta of a portfolio is the weighted average of the betas inside it. An index fund tracking the market has a beta of one by construction. Half at beta 1 and half at beta 0 gives 0.5, the same beta as a portfolio that is half the index and half cash. That comparison is the point: in the capital asset pricing model the lottery half and a cash half demand the same return, the risk-free rate, because neither adds market risk; the lottery's enormous extra risk is diversifiable in theory and simply unrewarded.
The relationship
$\beta_i = \frac{\mathrm{Cov}(r_i, r_m)}{\mathrm{Var}(r_m)} = 0 \qquad \beta_p = 0.5\times 1 + 0.5\times 0 = 0.5$
Cov(r_i, r_m) how the asset's return moves with the market's; zero for a lottery draw
Var(r_m) the market's own variance
beta_p the portfolio beta, a weighted average of the betas inside it
What it says in wordsBeta is the market-linked share of an asset's movement, and portfolio betas are weighted averages of the parts.
What does the security market line say about the blend?
Plot required return against beta. With an assumed 6% risk-free rate and 6% equity premium, the line runs from 6% at beta 0 to 12% at beta 1, and the blend at beta 0.5 would be required to earn 9%. Its expected return is nothing like that: if a ticket pays out an assumed half of its price in prizes, its expected return is -50%, and the blend's is 0.5 x 12% plus 0.5 x -50%, which is -19%. Beta tells you where an asset sits along the line, and the lottery ticket sits about 56 points below it: a zero-beta asset with an appalling expected return. That is the limitation to state: beta says nothing about expected return outside the model's assumptions, and nothing about risk the market does not share.
Why a banker asks it: the same logic decides what goes into a cost of equity. A project whose cash flows do not move with the economy, a regulated pipeline or a contracted toll road, carries a low beta and a low cost of equity even if its engineering risk is large, because that risk is specific and diversifiable. Candidates who confuse volatility with beta tend to over-discount exactly those assets, and to under-discount a cyclical business that happens to look calm.
Where candidates lose it
The usual wrong answer is a high beta, because the ticket is risky. The interviewer wants the distinction said plainly: beta is co-movement with the market, and risk that is not shared with the market does not appear in it at all.
The second loss is the portfolio part: candidates hesitate because they are unsure whether betas average. They do, by weight, because covariance is linear. Say 0.5 at once and add that it equals the beta of half index, half cash.
What the interviewer asks next
What is the beta of cash, and of a gold bar?
Can an asset have a negative beta, and what would such an asset be worth to a portfolio?
The blend has a beta of 0.5 but far more volatility than half index, half cash. Which measure belongs in a cost of equity, and why?
Asked at Moelis & Company, Investment Banking, New York, 2026 (Wall Street Oasis): What is the Beta of a lottery ticket A: Zero, Beta is a measure of volatility RELATIVE to the market
030Someone gives you an elephant. It costs Rs 20 lakh a year to keep, the best price you can get for it is Rs 50 lakh but the sale takes a year of paperwork, and a sanctuary will take it off your hands today for free. At a 10% discount rate, what is the gift worth to you?Valuation riddlesCoreHSBCNew York · 2024
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Before you discount anything: what is the gift worth?
Show the worked solution
About Rs 27.3 lakh, the value of selling it. Keeping the elephant forever costs Rs 20 lakh a year, minus Rs 2 crore in today's money at 10%. Selling means one more year of upkeep and Rs 50 lakh at the end, a net Rs 30 lakh worth Rs 27.3 lakh today. Donating is worth zero. A gift is worth its best use, and the free exit means it can never be worth less than zero.
Why does the elephant not have one value?
Think of being handed an old car that needs Rs 30,000 of repairs before anyone will buy it. The car is not worth its sticker price; it is worth what you can do with it, net of what doing that costs. An asset with a carrying cost has no value of its own: each option for it has a value, and the asset is worth the best of them. So the first move is to list the options out loud, keep it, sell it or give it away, and then price each one at the same 10% rate.
Keeping the elephant forever is worth minus Rs 200 lakh today, selling it after a year of upkeep is worth plus Rs 27.3 lakh, and donating it is worth zero, so the gift is worth Rs 27.3 lakh, the value of its best option.
How do you price each option?
Keeping is a perpetuityA payment that repeats every year forever. Its value today is the yearly amount divided by the discount rate. of costs: Rs 20 lakh a year divided by 10% is minus Rs 200 lakh, or minus Rs 2 crore. Selling means paying one more year of upkeep while the paperwork clears, then collecting Rs 50 lakh. Net of upkeep, the sale delivers Rs 30 lakh at the end of year one, and Rs 30 lakh a year away is worth Rs 27.3 lakh today. Donating costs nothing and brings nothing. The working assumes upkeep is paid at the year end; if it is paid upfront, the sale is worth Rs 25.5 lakh instead, and the choice does not change.
The relationship
$V = \max\left(-\frac{20}{0.10},\; \frac{50-20}{1.10},\; 0\right) = \max(-200,\ 27.3,\ 0) = 27.3$
20/0.10 keeping it: Rs 20 lakh of upkeep a year, forever, at 10%
(50 - 20)/1.10 selling it: the sale price less one year of upkeep, received a year from now
0 donating it today
What it says in wordsThe gift is worth whichever option has the highest present value, here the sale.
When would the gift be worth nothing?
Change one number. If the best sale price were Rs 15 lakh, the sale would net minus Rs 5 lakh at the year end, minus Rs 4.5 lakh today, and donating would win at zero. The free exit puts a floor under the gift: it can be worth nothing, but never less than nothing, as long as someone will take it away for free. Remove the sanctuary and the floor goes too. That is why bankers ask about exit options before valuing a loss-making plant, a lease that cannot be broken or a subsidiary with heavy fixed costs.
Where candidates lose it
The two fast answers are Rs 50 lakh, which ignores the year of upkeep and the wait, and minus Rs 2 crore, which values only the option of keeping the elephant forever. Both value the object instead of the decision.
The interviewer is listening for the list of options before any arithmetic. Say keep, sell or donate, price each, and pick the best; the number then follows in one line.
What the interviewer asks next
The sanctuary now charges Rs 10 lakh to take the elephant. Does your answer change?
The sale could close in six months instead of a year. What is the gift worth now?
Where do you see the same logic when valuing a loss-making subsidiary inside a group?
Asked at HSBC, Generalist, New York, 2024 (Wall Street Oasis): If you received an elephant what would you do with it?

9^3	729, nine cubed
(700 + 29)^2	the square split into a round part and a remainder
2(700)(29)	the two strips, 20,300 each and 40,600 together

100 x 0.75 x 8	run-rate synergies after 25% tax, capitalised at 8x
50 x 0.75	the half of year 1's savings that does not arrive, after tax
150 x 0.75	the one-off cost to achieve, after its tax saving

t - 0.5	each year's cash treated as arriving at the middle of the year
1.10^0.5	the gain from discounting every cash flow for half a year less

S	the stock price, Rs 100, equal to the strike
sigma	volatility, 20% a year
T	time to expiry in years, here 1
N(.)	the cumulative bell-curve probability used in the full formula

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How do you keep every step in your head?

How do you check it before saying it?

Where candidates lose it

What the interviewer asks next

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Why can you not just multiply Rs 100 crore by 8?

What comes off the Rs 600 crore?

What does this rough answer leave out?

Where candidates lose it

What the interviewer asks next

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Why would cash arrive in the middle of the year?

Why is the uplift exactly the square root of 1.10 minus one?

Where should you not apply it?

Where candidates lose it

What the interviewer asks next

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What is Black-Scholes actually doing?

Where does the 0.4 come from?

What does the shortcut leave out?

Where candidates lose it

What the interviewer asks next

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How can one company be cheaper on one multiple and dearer on another?

Which line explains how much of the gap?

So which company is actually cheaper?

Where candidates lose it

What the interviewer asks next

Try it first

How many weddings happen a year?

Why split by tier rather than use one average wedding?

Which assumption moves the answer most?

Where candidates lose it

What the interviewer asks next

Try it first

Why are some items added and others subtracted?

What is the test for each line?

What would you say the question leaves out?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a tax rate touch both the top and the bottom of the fraction?

How big is each effect on these numbers?

Is there a subtler channel the interviewer might be after?

Where candidates lose it

What the interviewer asks next

Try it first

Why is a wildly risky asset given a beta of zero?

How does the portfolio beta follow?

What does the security market line say about the blend?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the elephant not have one value?

How do you price each option?

When would the gift be worth nothing?

Where candidates lose it

What the interviewer asks next