Investment Banking puzzles, solved step by step

Puzzles: 100
Traced to a firm: 36
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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?
Show the worked solution
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
072A property is bought at a 7% cap rate with a 60% loan-to-value loan at 9% interest-only. What is the cash-on-cash return on the equity?Rates, risk and optionsCoreWells Fargo SecuritiesNew York · 2026
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Before you work it: does borrowing raise or lower the equity return here?
Show the worked solution
About 4%, below the unlevered 7%. Per Rs 100 of property, a 7% cap rate means Rs 7 of net operating income. A 60% loan is Rs 60, and at 9% interest-only it costs Rs 5.4 a year. That leaves Rs 1.6 of cash for the Rs 40 of equity, which is 4%. Because the loan costs more than the property yields, this is negative leverage: borrowing lowers the equity return rather than raising it.
Why is the cash-on-cash below the cap rate?
Suppose you borrow money at 9% to put in a deposit paying 7%. Every rupee borrowed loses you 2 paise a year, and the more you borrow the worse it gets. Leverage lifts the equity return only when the asset yields more than the debt costs; when the cap rate sits below the interest rate, every rupee of debt subtracts from the equity's return. Here the Rs 60 of debt earns 7% inside the property, Rs 4.2, but costs 9%, Rs 5.4, so it drags Rs 1.2 off the Rs 7 that the equity would otherwise keep on Rs 100 unlevered.
Per Rs 100 of property, Rs 7 of net operating income less Rs 5.4 of interest on Rs 60 of debt at 9% leaves Rs 1.6 for Rs 40 of equity, a 4% cash-on-cash return, and the same loan at 5% would give 10% while at 7% it would leave the return unchanged at 7%.
How do you say the answer in a way the interviewer can follow?
Fix the value at Rs 100 so every input becomes a rupee figure. Cap rate times value is the income; loan-to-value times value is the debt; debt times the rate is the interest; the rest is cash on the equity, and the equity is value minus debt. That is four multiplications and two subtractions, and saying each one aloud keeps you honest. Then say the comparison that matters: 4% levered against 7% unlevered, so the loan has cost the equity 3 points of yield.
The relationship
$\text{CoC} = \frac{\text{NOI} - \text{interest}}{\text{equity}} = \frac{7 - 60 \times 9\%}{100 - 60} = \frac{1.6}{40} = 4\%$
NOI net operating income, the cap rate times the value
interest the loan times its rate, interest-only so no principal
equity value less the loan, here Rs 40 per Rs 100
What it says in wordsCash-on-cash is the income left after interest, divided by the cash the equity put in.
Loan rate Interest on Rs 60 Cash to Rs 40 of equity Cash-on-cash
5% 3.0 4.0 10%
7% 4.2 2.8 7%
9% 5.4 1.6 4%
The cash-on-cash return crosses the unlevered 7% exactly when the loan rate equals the cap rate, rising above it at cheaper rates and falling below it, to 4%, at the 9% in the question.
Why would anyone buy with negative leverage?
Because cash-on-cash is a snapshot of year one. A buyer accepting 4% today is betting on rent growth lifting the income, on refinancing when rates fall, or on selling at a lower cap rate, none of which is in this calculation. Say that the figure ignores principal repayment, because the loan is interest-only, and ignores any appreciation. A total return would add both, and a lender would also look at the debt service coverage, which here is 7 over 5.4, about 1.3x, thin for most lenders.
Where candidates lose it
The common loss is assuming leverage must raise the return and answering something above 7%. The interviewer has set the loan rate above the cap rate on purpose to see whether you check the sign before you multiply.
The second loss is dividing the cash by the whole Rs 100 of value instead of the Rs 40 of equity, which gives 1.6% and a confused look. Cash-on-cash is measured on the cash the equity actually put in.
What the interviewer asks next
At what loan rate does the cash-on-cash equal the cap rate, and why?
Now the loan amortises over 25 years. Does the cash-on-cash rise or fall, and what does it leave out?
If rents grow 3% a year, what is the cash-on-cash in year 3?
Asked at Wells Fargo Securities, Real Estate, New York, 2026 (Wall Street Oasis): What is the CoC when you have _ Interest Rate, _ LTV, and _ Cap rate?
075A tech company is worth 10x EBITDA and carries net debt of 7x EBITDA. If its enterprise value falls 10%, what happens to its equity value?Enterprise value and dilutionCoreMoelis & CompanyNew York · 2026
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Before you work it: how far does the equity fall?
Show the worked solution
The equity falls by about 33%, a third. Equity value is enterprise value less net debt: 10 minus 7, so 3 turns of EBITDA. A 10% fall takes enterprise value to 9 turns, and the lenders are still owed 7, so equity is 2 turns. From 3 to 2 is a one third fall. At 7 turns of debt on a 10 turn valuation the equity is a thin slice, and every move in the business's value is magnified 3.33 times on it.
Why does the equity fall more than the business?
Picture a flat bought for Rs 1 crore with a Rs 70 lakh loan. If the flat's price falls 10% to Rs 90 lakh, the bank is still owed Rs 70 lakh, so the owner's stake falls from Rs 30 lakh to Rs 20 lakh, a third. Net debt is fixed in rupees, so the whole of any fall in enterprise value comes out of the equity, and the thinner the equity slice, the larger the percentage hit. Here the equity is 3 turns of EBITDA under 7 turns of debt, so a 1 turn fall in value is a third of it.
With net debt fixed at 7 turns of EBITDA, a fall in enterprise value from 10 turns to 9 takes the equity from 3 turns to 2, a 33% fall, and the multiplier of 3.33 works the same way upwards, where a 10% rise in EV would lift the equity 33%.
What is the general rule, and what does 7x tell you about sensitivity?
The percentage move in equity is the percentage move in EV times EV over equity. At 10x EV and 7x debt that multiplier is 10 over 3, 3.33, so each 1% in enterprise value is 3.33% on the equity, up or down. That is what an interviewer means by sensitivity: 7 turns of leverage on a 10 turn valuation makes the equity a geared bet on the business. If EBITDA or the multiple slips 30%, the equity is worth nothing and the lenders start taking losses, which is why debt at that level prices as if it carried some of the equity risk.
The relationship
$\frac{\Delta E}{E} = \frac{\Delta EV}{EV} \times \frac{EV}{E} = -10\% \times \frac{10}{3} = -33.3\%$
E equity value, EV less net debt, 3 turns of EBITDA
EV enterprise value, 10 turns of EBITDA
Delta EV / EV the 10% fall in enterprise value
What it says in wordsThe equity moves by the EV move scaled up by how many times EV covers the equity.
Move in EV EV, x EBITDA Net debt, x EBITDA Equity, x EBITDA Move in equity
+10% 11.0 7.0 4.0 +33%
+0% 10.0 7.0 3.0 +0%
-10% 9.0 7.0 2.0 -33%
-20% 8.0 7.0 1.0 -67%
-30% 7.0 7.0 0.0 -100%
With net debt fixed at 7 turns, each 10% step in enterprise value is a one third step in the equity, and a 30% fall in enterprise value leaves the equity worth nothing.
Why does a banker ask a tech company this?
Because 7 turns is a lot of debt for a business valued on growth rather than assets. If the valuation multiple compresses, as growth multiples do when rates rise or growth slows, the enterprise value can fall 10% with no change in EBITDA at all, and the equity takes a third of that on the chin. Say the assumption you leaned on: net debt stays fixed, which holds over a short window but not if the company is burning or generating cash. The question tests whether you can see leverage as a magnifier before you build a single model.
Where candidates lose it
The common loss is answering 10%, as if equity and enterprise value moved together. The debt sits between them and does not move, so the equity absorbs the whole fall.
The second loss is giving 33% and stopping. The interviewer asked what 7x tells you about sensitivity, so name the multiplier, 10 over 3, and say that it works both ways.
What the interviewer asks next
EBITDA falls 10% and the multiple stays at 10x. What happens to the equity, and is it the same answer?
At what fall in enterprise value is the equity worth nothing?
How does this magnifier relate to the beta of a levered company?
Asked at Moelis & Company, Generalist, New York, 2026 (Wall Street Oasis): A tech company has leverage rate of 7X. What does it tell you about the about the impact on sensitivity?
079A company has EBITDA of Rs 100 crore and can borrow at 10%. Lenders require interest cover of at least 2.5x and leverage of no more than 5.0x EBITDA. How much can it borrow, and which test binds?Deal mathsCoreWells Fargo SecuritiesNew York · 2025
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Before you calculate: how much debt can the company raise?
Show the worked solution
Rs 400 crore, and the coverage test binds. Leverage of 5.0x allows Rs 500 crore. Coverage of 2.5x caps interest at 100 divided by 2.5, which is Rs 40 crore, and at 10% that interest supports Rs 400 crore of debt. The borrower must pass both tests, so the lower number is the ceiling. Below an 8% rate, leverage would bind instead.
Why are there two answers, and why take the smaller?
A bank deciding your home loan asks two things: is the loan too large against your salary, and can you afford the monthly payment? You can pass one and fail the other. Lenders to a company ask the same pair. Leverage limits the size of the debt; coverage limits the cost of carrying it, and the borrower must clear both, so the binding test is whichever gives less. Compute both every time, then name the one that bites.
Leverage is one step: 5.0 times EBITDA of 100 is Rs 500 crore. Coverage works backwards from the payment. Interest coverEBITDA divided by interest expense: how many times over the operating profit pays the interest bill. of at least 2.5 means interest can be at most 100 divided by 2.5, which is Rs 40 crore. At a 10% rate, Rs 40 crore of interest corresponds to Rs 400 crore of debt.
The leverage test allows Rs 500 crore but the coverage test, with interest capped at Rs 40 crore at a 10% rate, allows only Rs 400 crore, so the company can borrow Rs 400 crore and the extra 100 the leverage test permits is unusable.
When would the answer flip to the leverage test?
The coverage ceiling moves with the rate; the leverage ceiling does not. Set the two equal: interest of 40 on 500 of debt is an 8% rate. Below 8%, leverage binds; above it, coverage binds, which is why debt capacity shrinks when rates rise even if earnings do not move. At 7%, coverage would allow about Rs 571 crore, so the 500 leverage cap becomes the limit.
The relationship
$D_{\max} = \min\Big(L \times E,\; \frac{E / C}{r}\Big) = \min(500,\; 400) = 400$
E EBITDA, Rs 100 crore
L maximum leverage, 5.0x
C minimum interest cover, 2.5x
r interest rate, 10%
What it says in wordsDebt capacity is the smaller of the size limit and the debt the maximum affordable interest bill can carry.
Say the limitation too. Real covenants often test cover on EBITDA less capex, or on a fixed charge basis that includes leases, and lenders size a deal with headroom below both ceilings rather than at them. The two-test logic stays the same.
Where candidates lose it
Most candidates multiply 5.0 by 100, say Rs 500 crore and stop, because leverage is the covenant they have read about. The interviewer has deliberately set the rate high enough that coverage bites first.
The other loss is treating the two tests as alternatives to pick from. They are both conditions. Say both numbers, then say which binds and the rate at which it would switch.
What the interviewer asks next
What interest rate makes the two tests give the same answer?
If EBITDA falls 20%, which ceiling falls further?
How would a cash sweep or amortisation change the coverage picture in later years?
Asked at Wells Fargo Securities, Investment Banking, New York, 2025 (Wall Street Oasis): Simple 400 guide questions, walk through DCF, how much leverage is too much leverage, walk through 3 statemets.
085A software company's free cash flow is Rs 130 crore if Rs 30 crore of stock-based compensation is added back as a non-cash charge, and Rs 100 crore if it is treated as a cash cost. With a WACC of 10% and perpetual growth of 3%, how far apart are the two perpetuity values, and which treatment is right?DCF and cost of capitalHardLazardNew York · 2026
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Which treatment gives the right value for today's shareholders?
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About Rs 441 crore apart: Rs 1,913 crore with the add-back against Rs 1,471 crore without, a 30% gap. Treat the compensation as a real cost. It is paid in shares rather than cash, but existing holders bear it through dilution. Either deduct it from cash flow and use today's diluted share count, or add it back and count every future share it will create. Adding it back and ignoring the dilution counts the cost as zero.
If no cash leaves, why is stock compensation a cost?
Imagine a family business that pays its manager not in salary but by handing over a slice of the shop every year. No cash leaves the till, but each year the family owns less of the shop. Stock compensation is a real expense paid in ownership instead of money, and today's shareholders pay it through dilution. If the company had paid staff Rs 30 crore in cash, everyone would deduct it. Paying in shares changes who bears the cost, not whether there is one.
The two values follow from the perpetuity formula. With the add-back, 130 x 1.03 / (10% - 3%) is about Rs 1,913 crore. Treated as a cost, 100 x 1.03 / 7% is about Rs 1,471 crore. The gap, about Rs 441 crore, is exactly the present value of paying Rs 30 crore a year, growing at 3%, in shares.
Adding back Rs 30 crore of stock compensation lifts the perpetuity value from Rs 1,471 crore to Rs 1,913 crore, and the Rs 441 crore gap is the present value of the shares handed to staff, so it must be deducted or counted as dilution.
Can the add-back version ever be right?
Yes, if you finish the job. Add the Rs 30 crore back, value the firm at Rs 1,913 crore, then recognise that the company will issue Rs 30 crore of new shares every year, growing at 3%, forever. Those future holders own a stream worth Rs 441 crore of the total, leaving Rs 1,471 crore for today's shareholders. Both consistent methods land on the same value for existing holders; the error is adding back the expense and then dividing by today's share count, which counts the cost nowhere. In practice, deducting it is simpler, because projecting every future grant into the share count is hard.
The relationship
$V_{\text{add}} - V_{\text{ded}} = \frac{\text{SBC} \times (1+g)}{r - g} = \frac{30 \times 1.03}{0.07} \approx 441$
SBC stock-based compensation, Rs 30 crore a year
r WACC, 10%
g perpetual growth, 3%
What it says in wordsThe difference between the two values is the present value of paying staff in shares forever.
One honest limitation: existing options and restricted shares already granted are a separate matter, counted in today's diluted share count by the treasury method. The question here is future grants, which the cash flow treatment decides.
Where candidates lose it
The standard slip is saying stock compensation is non-cash, so it is added back like depreciation, and stopping there. Depreciation is the echo of cash already spent; stock compensation is a cost paid now, in a different currency.
The second loss is saying deduct it without being able to explain why the add-back can be made consistent. Name both consistent routes and the one wrong one: that is the answer an associate-level interviewer is looking for.
What the interviewer asks next
How do already-granted options enter the valuation?
If the company buys back shares each year to offset dilution, how does that change the cash flow treatment?
Why do many sell-side models still add stock compensation back?
Asked at Lazard, Investment Banking, New York, 2026 (Wall Street Oasis): SBC treatment in DCF
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?Mental maths and countingWarm upBarclaysNew York · 2026
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Which division contributed most to total growth?
Show the worked solution
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 relationship
$g_{\text{total}} = \sum_i w_i\, g_i = \tfrac{420}{800}(10\%) + \tfrac{260}{800}(15\%) + \tfrac{120}{800}(25\%) = 13.9\%$
w_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

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

NOI	net operating income, the cap rate times the value
interest	the loan times its rate, interest-only so no principal
equity	value less the loan, here Rs 40 per Rs 100

Loan rate	Interest on Rs 60	Cash to Rs 40 of equity	Cash-on-cash
5%	3.0	4.0	10%
7%	4.2	2.8	7%
9%	5.4	1.6	4%

E	equity value, EV less net debt, 3 turns of EBITDA
EV	enterprise value, 10 turns of EBITDA
Delta EV / EV	the 10% fall in enterprise value

Try it first

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

Why is the cash-on-cash below the cap rate?

How do you say the answer in a way the interviewer can follow?

Why would anyone buy with negative leverage?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the equity fall more than the business?

What is the general rule, and what does 7x tell you about sensitivity?

Why does a banker ask a tech company this?

Where candidates lose it

What the interviewer asks next

Try it first

Why are there two answers, and why take the smaller?

When would the answer flip to the leverage test?

Where candidates lose it

What the interviewer asks next

Try it first

If no cash leaves, why is stock compensation a cost?

Can the add-back version ever be right?

Where candidates lose it

What the interviewer asks next

Try it first

Why are these two different questions?

How do you do it fast under a timer?

Where candidates lose it

What the interviewer asks next