Financial Analysis puzzles, solved step by step

Puzzles: 100
Traced to a firm: 47
Topics: 13
Hard: 30

Showing 1–10 of 100

001Two store chains run identical stores and earn the same Rs 100 crore a year before property costs. One owns its stores; the other leases them at Rs 12 crore a year for 10 years. Once the lease is capitalised at 9%, the leaser's EBITDA rises by Rs 12 crore and a lease liability of about Rs 77 crore appears. How do you compare the two on EV/EBITDA fairly?Accounting flow riddlesHardMizuhoNew York · 2026
Try it first
The owner trades at 8.0x. The leaser's shares and debt are worth Rs 723 crore and its EBITDA, rent added back, is Rs 100 crore. Which multiple is the fair one to set beside 8.0x?
Show the worked solution
Put the lease liability inside EV whenever the rent is outside EBITDA. After capitalisation the leaser's EBITDA is Rs 100 crore, like the owner's. Its shares and debt are worth Rs 723 crore, so dividing those alone gives 7.2x and makes it look cheaper. Add the Rs 77 crore lease and it is 8.0x, the owner's multiple. The numerator and denominator must describe the same claims.
Why does a lease behave like debt?
Think of two families in identical flats. One bought with a home loan; the other rents on a ten year agreement it cannot walk away from. Both owe fixed payments for years. A long lease is a loan from the landlord, repaid in rent, so the rent contains both the use of the asset and the financing of it. Under IFRS 16, and Ind AS 116 in India, the leaser now shows that promise as a lease liabilityThe present value of the rent the company is contractually committed to pay over the lease term, carried on the balance sheet like a borrowing.: Rs 12 crore a year for ten years, discounted at 9%, is about Rs 77 crore.
The relationship
$L = 12 \times \frac{1 - 1.09^{-10}}{0.09} = 12 \times 6.418 \approx 77.0$
12 yearly rent, Rs crore
0.09 the discount rate applied to the lease
10 years left on the lease
What it says in wordsThe lease liability is the rent stream discounted back to today, exactly as you would value a loan's repayments.
What changes in the numbers, and what does not?
Capitalisation moves the rent out of operating costs. It comes back as depreciation on a right-of-use asset and interest on the lease, both below EBITDA. So the leaser's EBITDA jumps by the full Rs 12 crore while nothing about its stores, customers or cash has changed. The same move puts about Rs 77 crore of lease on the balance sheet. The two changes are a pair, and a fair multiple has to use both halves or neither.
After capitalisation the leaser's EBITDA rises from Rs 88 crore to Rs 100 crore and a Rs 77 crore lease appears. Dividing only its Rs 723 crore of shares and debt by Rs 100 crore gives 7.2x, while adding the lease to EV gives 8.0x, the same as the owner.
Where does this bite in real comparables work?
Data providers and peer tables do not always treat leases the same way, and a peer set can mix companies reporting under different standards. Before trusting a multiple, check whether its EV includes lease liabilities and whether its EBITDA is before or after rent, then make every company in the table match. A retailer, airline or restaurant chain that leases most of its sites can look 11% cheaper than an owner purely from this mismatch, which is the whole of the gap in this example.
Say the limitation too. The capitalised figure depends on the discount rate and the lease term the company chose, so two leasers with the same rent can carry different liabilities. Lease-adjusted multiples are better, not exact.
Where candidates lose it
The common loss is quoting the leaser at 7.2x and calling it cheap. The candidate has taken the EBITDA uplift from the new standard and forgotten the liability that came with it, so the comparison rewards a company for renting instead of owning.
The second miss is going the other way and deducting rent from one company's EBITDA while leaving the other's untouched. Whichever basis you choose, say it once and apply it to every company in the set.
What the interviewer asks next
Before lease capitalisation, how would you have compared the two chains, and what is EBITDAR?
What happens to the leaser's net income in year 1 compared with the old rent expense?
Does lease capitalisation change the leaser's free cash flow?
How should a DCF treat lease payments if EBITDA already excludes rent?
Asked at Mizuho, Generalist, New York, 2026 (Wall Street Oasis): How does a $10 increase for depreciation Finance lease vs operating lease (which effect valuation)
002Company X trades at 12x earnings but 9x EV/EBITDA. Its peers trade at 15x earnings and 7x EV/EBITDA. Give two reasons, with numbers, that make both facts true at once.Valuation and multiples riddlesHardBarclaysNew York · 2026
Try it first
Which single fact could, on its own, push X's P/E down and its EV/EBITDA up at the same time?
Show the worked solution
X carries more debt and owns a stake in an associate. Debt of Rs 750 crore at 8% costs 5.6% after tax, less than the 6.7% its operations earn on their value, so levering lowers the P/E. The associate adds Rs 22 crore to net income but nothing to EBITDA, while its Rs 300 crore value sits inside EV. Strip it out and X is 7.0x, like its peers.
Why can two multiples on the same company disagree?
Picture a house with a mortgage. Its price compared with the rent it earns is one ratio; your equity in it compared with the rent left after the mortgage payment is another. The two only agree if there is no loan. EV/EBITDA looks at the whole business before financing, while P/E looks at the shareholders' slice after interest, tax and anything non-operating. Every gap between them is explained by something that sits between EBITDA and net income, or between EV and equity value.
What numbers make both facts true?
Give both companies the same operations: EBITDA Rs 150 crore, depreciation Rs 50 crore, operating profit Rs 100 crore, tax 30%. The peer has no debt, earns Rs 70 crore and is worth Rs 1,050 crore: 15.0x earnings and 7.0x EBITDA. X borrows Rs 750 crore at 8%, so interest of Rs 60 crore leaves Rs 28 crore from operations, and it books Rs 22 crore as its share of an associateA company in which the group holds a significant minority stake, usually 20% to 50%. The group books its share of that company profit below operating profit, never in revenue or EBITDA.'s profit. Net income of Rs 50 crore at 12x is equity of Rs 600 crore, and with the debt that is an EV of Rs 1,350 crore, 9.0x EBITDA.
Company X's EV of Rs 1,350 crore is funded by Rs 600 crore of equity and Rs 750 crore of debt, and pays for the same Rs 1,050 crore of core operations as the peer plus a Rs 300 crore associate stake. Taking the stake out brings X back to 7.0x EBITDA.
Which reason moves which multiple?
Separate them, because the follow-up always asks. Debt lowers the P/E when its after-tax cost is below the earnings yield of the operations. Here debt costs 8% times 0.7, which is 5.6%, while the operations earn 70 on 1,050, or 6.7%. Swapping expensive equity for cheaper debt leaves the operating slice at about 10.7x earnings. The associate does the other job: its Rs 300 crore of value sits inside EV while its profit sits below EBITDA, which lifts EV/EBITDA from 7.0x to 9.0x.
Name a third candidate if you have time: a lower tax rate than peers raises net income without touching EBITDA, so it also lowers P/E alone. Say what you would check to choose between them: the notes on debt, associates and the effective tax rate.
Where candidates lose it
Most candidates say X must have more debt and stop. Debt alone explains the lower P/E, but it does not raise EV/EBITDA if the business is worth the same, because EV is the same whoever funds it. The interviewer is waiting for something that sits inside EV but outside EBITDA.
The other loss is giving reasons with no numbers. Build one small example in which both multiples land where the question says; it proves the reasons work together.
What the interviewer asks next
Would you subtract the associate stake from X's EV in a comps table, and at what value?
If X's debt cost 11% instead of 8%, would its P/E still be below its peers'?
Which of the two multiples would you use to value X, 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
003A company earns a 20% after-tax return on the capital it invests and wants operating profit to grow 15% a year. What share of operating profit must it reinvest each year? What changes if the return on capital is 10%?Ratio and margin riddlesHardEquity researchCorporate finance
Try it first
At a 20% return on capital, how much of each year's operating profit has to go back into the business to grow 15%?
Show the worked solution
It must reinvest 75% of operating profit at a 20% return, and 150% at a 10% return. Growth equals return on capital times the share of profit reinvested, so the reinvestment rate is 15% divided by the return. At 20% that leaves Rs 25 of every Rs 100 free. At 10% the company must invest Rs 150 for every Rs 100 it earns, raising Rs 50 from lenders or shareholders to keep growing.
Where does growth in operating profit come from?
Picture a tailor who earns 20% a year on every rupee of sewing machines she owns. If she wants next year's profit 15% higher, she needs 15% more machines' worth of profit, and each rupee of machines earns only 20 paise. Growth equals the return on new capital multiplied by the share of profit put back in. That share is the reinvestment rate, and it is the price the company pays today for tomorrow's growth.
The relationship
$g = \text{ROC} \times b \quad\Rightarrow\quad b = \frac{g}{\text{ROC}} = \frac{15\%}{20\%} = 75\%$
g growth in operating profit, 15% a year
ROC after-tax return on the new capital invested
b the share of after-tax operating profit reinvested
What it says in wordsDivide the growth you want by the return you earn, and that is the share of profit you must plough back.
To grow operating profit 15% a year, a company earning 30% on capital reinvests 50% of its profit, one earning 20% reinvests 75%, one earning 15% reinvests all of it, and one earning 10% must invest 150%, raising the gap from outside.
What does the 10% case tell an analyst?
Below a 15% return, 15% growth cannot be paid for out of profit at all. At 10%, for every Rs 100 earned the company must invest Rs 150, so Rs 50 comes from new debt or new shares every year and free cash flow is negative. The table shows how the free cash left for owners changes with the return on capital.
Return on capital Reinvestment rate Free cash per Rs 100 of profit
30% 50% 50
20% 75% 25
15% 100% 0
10% 150% (50)
Same 15% growth in every row. Free cash is operating profit less reinvestment; a bracket means cash must be raised from outside.
Growth at a low return can still be worth having if the return beats the cost of capital, and it destroys value if it does not. Say the limitation: the formula assumes new capital earns what old capital earns. Price increases and efficiency gains are growth that needs no reinvestment, so real companies sometimes beat it.
Where candidates lose it
The quick wrong answer is 15%, treating the growth rate as the share you reinvest. That ignores the return: the same growth costs very different amounts of capital at 10% and at 30%.
The second loss is stopping at 150% without saying what it means. A reinvestment rate above 100% is a funding need, and the interviewer wants to hear that growth at a low return on capital burns cash.
What the interviewer asks next
At a 12% cost of capital, is 15% growth at a 10% return good or bad for shareholders?
How would you estimate return on capital for a company from its annual report?
What happens to the valuation if growth falls to 5% with the return held at 20%?
004A comparable company's unlevered beta is 0.8. Your company targets a debt-to-equity ratio of 0.5 and pays 25% tax. The risk-free rate is 7% and the equity risk premium is 6%. What is your company's cost of equity? What if its debt-to-equity rises to 1.0?Cost of capital, leverage and ratesCoreLazardSan Francisco · 2026
Try it first
With debt-to-equity of 0.5, what is the levered beta?
Show the worked solution
The cost of equity is 13.6% at debt-to-equity of 0.5, and 15.4% at 1.0. Relevering puts your own debt back onto the peer's business risk: 0.8 times (1 plus 0.75 times 0.5) gives a beta of 1.10, and 7% plus 1.10 times 6% is 13.6%. At 1.0 the beta is 1.40, so the cost of equity is 15.4%.
Why unlever the peer's beta and then relever it?
Two friends buy identical flats. One pays cash; the other borrows 60% of the price. When flat prices move 10%, the cash buyer's wealth moves 10%, while the borrower's stake moves far more, because the loan does not shrink with the price. A peer's observed beta mixes two things, the risk of its business and the risk its own debt adds, so you strip out its debt before borrowing its business risk. Then you add back your own debt, because your shareholders carry your leverage, not the peer's.
The relationship
$\beta_L = \beta_U\left[1 + (1-t)\frac{D}{E}\right] = 0.8\,[1 + 0.75 \times 0.5] = 1.10$
β_U unlevered beta, the business risk alone, 0.8
t tax rate, 25%
D/E your target debt to equity, 0.5
β_L levered beta your shareholders bear
What it says in wordsYour shareholders' beta is the business beta scaled up by how much after-tax debt sits in front of them.
This is the Hamada relation, which assumes debt carries no market risk of its own. Then the capital asset pricing model does the rest: cost of equity is the risk-free rate plus beta times the equity risk premium, so 7% plus 1.10 times 6% is 13.6%. At debt-to-equity of 1.0, beta becomes 0.8 times 1.75, or 1.40, and the cost of equity is 15.4%.
With an unlevered beta of 0.8, cost of equity rises in a straight line from 11.8% with no debt to 13.6% at debt-to-equity of 0.5 and 15.4% at 1.0, because each extra 1.0 of debt-to-equity adds 0.6 to beta after the tax shield.
Does more debt make the company more expensive to fund overall?
Not by this alone. Equity gets dearer as debt rises, but debt is cheaper than equity and its interest is tax-deductible, so the weighted cost of capital can fall even while the cost of equity climbs. Where it turns is where lenders start charging more and distress becomes real, which this formula does not capture. Say that limit out loud: the straight line only holds while debt is safe.
Where candidates lose it
The common error is using the peer's beta of 0.8 directly. That prices your equity as if you had no debt, which understates the cost of equity by nearly two points at a debt-to-equity of 0.5.
The second is dropping the tax term and getting 1.20. Say the formula before the numbers, so a slip in arithmetic does not look like a gap in understanding.
What the interviewer asks next
Your pre-tax cost of debt is 9%. What is the WACC at debt-to-equity of 0.5 and at 1.0?
The peer's observed beta was 1.2 at a debt-to-equity of 0.6. Check that its unlevered beta is about 0.8.
Why might you use a median of several peers' unlevered betas instead of one?
Asked at Lazard, Investment Banking, San Francisco, 2026 (Wall Street Oasis): They tested core valuation concepts (full DCF walkthrough, WACC, unlevering/relevering beta, and LBO basics)
005A dairy cow gives 10 litres of milk a day for 300 days a year. Milk sells at Rs 40 a litre and the cow costs Rs 70,000 a year to keep. It will produce for 6 more years and then be sold to another farm for Rs 20,000. At a 12% required return, what would you pay for the cow?Compounding and time valueCoreRothschild & CoNew York · 2026
Try it first
Before discounting, what is the cow's net cash each year?
Show the worked solution
About Rs 2.16 lakh. The cow earns Rs 1,20,000 of milk a year and costs Rs 70,000, leaving Rs 50,000 of net cash for six years. At 12% that stream is worth about Rs 2,05,570, and the Rs 20,000 sale in year 6 adds about Rs 10,133. Paying more than about Rs 2,16,000 means earning less than 12% on the purchase.
How do you value something that is not a company?
The same way you value a company. A shop, a flat you rent out and a cow are all machines that turn money in now into money out later. Anything that produces cash can be valued as the present value of the cash it will hand you, after the costs of keeping it running. So the first job is to find the net cash each year, then the life, then the value left at the end.
Net cash: 10 litres a day for 300 days is 3,000 litres, worth Rs 1,20,000 at Rs 40. Upkeep of Rs 70,000 leaves Rs 50,000 a year. The six years and the Rs 20,000 sale at the end complete the cash flows.
The cow's Rs 50,000 of yearly net cash is worth Rs 44,643 today in year 1 but only Rs 25,332 in year 6, and the Rs 20,000 sale is worth Rs 10,133. Added up, the cow is worth about Rs 2.16 lakh at 12%.
The relationship
$V = 50{,}000 \times \frac{1 - 1.12^{-6}}{0.12} + \frac{20{,}000}{1.12^{6}} = 50{,}000 \times 4.111 + 10,133 \approx 215,703$
50,000 net cash each year, Rs
4.111 the six-year annuity factor at 12%
20,000 sale value at the end of year 6, Rs
What it says in wordsValue is the six equal yearly cash flows discounted as an annuity, plus the final sale discounted six years.
What would make you pay less?
Every assumption in this answer is a risk to price: yield falling with age, illness, milk price, feed cost. If milk yield drops 10% a year, net cash falls fast because upkeep does not fall with it, and the value drops sharply. A higher required return for a risky asset does the same. The interviewer who asks you to value an animal is checking that you name the cash, the life, the end value and the risk, in that order, and do not stop at the milk bill.
Where candidates lose it
The common slip is discounting Rs 1,20,000 of milk sales instead of Rs 50,000 of net cash, which more than doubles the answer. Revenue is not what the owner keeps.
The second is forgetting the end value, or adding it undiscounted. Rs 20,000 in six years is worth about Rs 10,000 today at 12%, and saying so shows you treat every cash flow the same way.
What the interviewer asks next
Milk yield falls 10% a year from year 2. What is the cow worth now?
What discount rate would you use, and why might it be higher than for a bond?
How would you value a pet dog, which produces no cash?
Asked at Rothschild & Co, Generalist, New York, 2026 (Wall Street Oasis): How would you value your favorite animal? What is your personal beta?

Return on capital	Reinvestment rate	Free cash per Rs 100 of profit
30%	50%	50
20%	75%	25
15%	100%	0
10%	150%	(50)

006A product's price rises 25%, its volume falls 4% and the currency it is sold in adds 10% when translated back. Without paper, what is the combined change in revenue?Mental mathsCoreLeveraged financePrivate equity

Try it first

Say a number before you work it out properly.

Show the worked solution

Revenue rises 32%. Growth rates multiply, they do not add. Pair the price and volume factors first because they cancel neatly: 1.25 times 0.96 is exactly 1.20. Then 1.20 times 1.10 is 1.32. Adding 25, minus 4 and 10 gives 31%, which misses the cross terms, the growth earned on growth, worth one point here.

Why do the three changes multiply instead of add?

Think of a tea stall that sells 100 cups at Rs 10. Raise the price to Rs 12.50 and it now takes Rs 1,250 if it still sells 100 cups. If it then sells 4% fewer cups, those 4% are lost at the new, higher price, not the old one. Each change acts on revenue that the earlier changes have already moved, so the factors multiply. Revenue is price times volume times the exchange rate, and a product of three factors changes by the product of their changes.

The relationship

1+g = (1.25)(0.96)(1.10) = 1.20 \times 1.10 = 1.32

1.25	price factor, a 25% rise
0.96	volume factor, a 4% fall
1.10	currency factor, a 10% gain on translation
g	the combined revenue growth

What it says in wordsTurn every change into a factor, multiply the factors, and subtract one.

How do you do it in your head without fumbling?

Choose the order. Multiplication does not care about order, but your head does. 0.96 is 24 over 25 and 1.25 is 5 over 4, so their product is 120 over 100, exactly 1.20, and the hard step disappears. Ten per cent of 1.20 is 0.12, so the last step is 1.32. Pair the factors the other way and you are stuck with 1.25 times 1.10, then 1.375 times 0.96, which is the same answer by a much longer road.

Pair first	First product	Then multiply by	Ease in your head
Price x volume	1.2000	1.10	Easy: 24/25 x 5/4 is exactly 1.2
Price x currency	1.3750	0.96	Harder: 1.375 less 4% of it
Volume x currency	1.0560	1.25	Harder: 1.056 plus a quarter of it

All three routes give 1.32. The first is the one to say out loud, because every step is a round number.

Revenue of 100 moves to 125, then 120, then 132, so the combined change is 32%. Adding the rates gives 31%, because it leaves out the cross terms, which net to plus one point: 2.5 from price on the currency gain, less 1.0, 0.4 and 0.1 from the other pairings.

Why does the one-point gap matter on a real desk?

On a Rs 2,000 crore revenue line, one point is Rs 20 crore, which is a material miss in a budget bridge. The gap between adding and multiplying grows with the size of the changes, so it is small for 2% moves and large for 25% moves. When a board pack splits revenue growth into price, volume and currency, the cross terms have to sit somewhere, and an analyst should say where they put them rather than leave the bridge one point short.

Where candidates lose it

Saying 31% is the fast loss. It is close enough to sound right, and the interviewer asked precisely because the cross terms are what separates someone who knows growth compounds from someone who adds percentages.

The second loss is getting 32% by a slow route, multiplying 1.25 by 1.10 first and grinding through 1.375 times 0.96. Spend one second choosing the pairing that cancels; the interviewer is watching that choice as much as the answer.

What the interviewer asks next

Price falls 25% and volume rises 25%. Is revenue up, down or flat?
In local currency terms, how much did revenue grow?
How would you show the 32% split into price, volume and currency in a revenue bridge so it adds up?

007You have a biased coin that lands heads one third of the time. How can you use it to produce a fair 50:50 result, and how many flips of the biased coin does each fair result take on average?Probability and expected valueHardD.E. ShawNew York · 2026
Try it first
Flip in pairs, keep heads-tails and tails-heads, discard the rest. On average, how many single flips does one fair result take?
Show the worked solution
Flip twice: heads then tails counts as heads, tails then heads counts as tails, and anything else is thrown away and flipped again. The two mixed orders each have probability 2/9, so they are equally likely whatever the bias. A pair succeeds 4/9 of the time, so each fair result takes 9/4 pairs, or 4.5 flips. Knowing the bias is exactly 1/3 lets you cut that to 2.25.
Why are heads-tails and tails-heads always equally likely?
Picture two friends flipping the same lopsided coin, one after the other. The chance the first gets heads and the second tails is the heads chance times the tails chance. The chance of the reverse is the tails chance times the heads chance. Multiplication does not care about order, so the two mixed outcomes are exactly equally likely, whatever the bias. That symmetry is the whole trick, known as the von Neumann method. Here each mixed pair has probability 1/3 times 2/3, which is 2/9.
Flipping the biased coin twice gives heads-tails and tails-heads with probability 2/9 each, so calling one heads and the other tails is fair. Discarding the matching pairs means a pair works 4/9 of the time, which costs 4.5 flips per fair result on average.
How do you get the average of 4.5 flips?
Each pair either works or does not, independently of the last. Waiting for a success that happens with probability q takes 1/q tries on average, the same reason a die takes six rolls on average to show a six. A pair works with probability 4/9, so you need 9/4 pairs, and two flips a pair makes 4.5 flips. The method pays for its fairness with waste: 5 pairs in 9 are thrown away.
The relationship
$E[\text{flips}] = \frac{2}{P(HT)+P(TH)} = \frac{2}{2p(1-p)} = \frac{2}{4/9} = 4.5$
p the chance of heads on one flip, 1/3
2p(1-p) the chance a pair is mixed, 4/9
2 flips used by each pair
What it says in wordsDivide the flips per attempt by the chance an attempt succeeds.
Can you do better if you know the bias exactly?
Yes, and this is usually the follow-up. With p exactly 1/3, tails-tails has probability 4/9, the same as the two mixed pairs together. Call tails-tails one side and either mixed pair the other, and only heads-heads, 1/9 of pairs, is wasted, so each fair result costs 2 times 9/8, or 2.25 flips. The von Neumann method is still the better answer when nobody tells you the bias, because it works for any p. The limit for any scheme is set by how much randomness one flip carries: about 0.92 of a fair bit here, so no method can beat roughly 1.09 flips per fair result on average.
Where candidates lose it
The common loss is trying to build fairness from single flips, for example calling heads on one flip and tails on two in a row. Those schemes depend on the exact bias and usually fail the moment you write out the probabilities.
The second loss is giving the method and not the cost. The interviewer reported here went straight on to efficiency, so have 4.5 flips ready, then say why the known-bias grouping halves it and why the order trick is still the safe answer.
What the interviewer asks next
Your fair-result method uses 4.5 flips. How could you reuse the discarded heads-heads and tails-tails pairs to get more fair results from the same flips?
How would you simulate a fair six-sided die with this coin?
If the coin's bias is unknown and drifts slowly over time, does the pair method still work?
Asked at D.E. Shaw, Research, New York, 2026 (Wall Street Oasis): How can I make an effective fair coin given a biased coin with p_heads = 1/3?
008A company's D&A is Rs 80 crore and its capex Rs 200 crore. Revenue is Rs 1,600 crore and growing 10% a year, and fixed asset turnover is 2.0x. Estimate how much of the capex is growth capex and how much is maintenance capex.Working capital and cash riddlesHardEquity researchCorporate FP&A
Try it first
How much of the Rs 200 crore is maintenance capex?
Show the worked solution
Growth capex is about Rs 80 crore and maintenance capex about Rs 120 crore. Revenue grows by Rs 160 crore, and at a fixed asset turnover of 2.0x each rupee of new revenue needs 50 paise of new assets, so growth capex is Rs 80 crore. The rest, Rs 120 crore, replaces worn assets. That is Rs 40 crore more than D&A, because D&A records assets at the older prices paid for them.
Why not just say maintenance capex equals D&A?
Think of a taxi owner who bought a car eight years ago for Rs 6 lakh and has been setting aside Rs 75,000 a year as depreciation. When the car dies, the same model costs Rs 9 lakh, not Rs 6 lakh. D&A spreads the price paid for old assets, while maintenance capex pays today's price to replace them, so with any inflation the two drift apart. D&A is a reasonable floor for maintenance spending, not an estimate of it.
How does fixed asset turnover split the capex?
Fixed asset turnoverRevenue divided by net fixed assets. At 2.0x, each rupee of plant and equipment supports two rupees of yearly revenue. tells you how much plant each rupee of revenue needs. At 2.0x, the company's Rs 1,600 crore of revenue sits on about Rs 800 crore of net fixed assets. If the new revenue needs assets at the same ratio, the Rs 160 crore of growth needs Rs 80 crore of new capacity, and that is growth capex. Whatever is left of the Rs 200 crore went on keeping the existing Rs 1,600 crore of revenue alive.
The relationship
$\text{growth capex} = \frac{\Delta \text{revenue}}{\text{FAT}} = \frac{160}{2.0} = 80 \qquad \text{maintenance} = 200 - 80 = 120$
Δ revenue next year's extra revenue, 10% of 1,600
FAT fixed asset turnover, revenue over net fixed assets
What it says in wordsNew capacity is the new revenue divided by how much revenue each rupee of assets supports; the rest of capex is upkeep.
Treating D&A as maintenance splits the Rs 200 crore into 80 of maintenance and 120 of growth. The turnover method gives the opposite split, 120 of maintenance and 80 of growth, so maintenance runs Rs 40 crore above D&A.
Is Rs 120 crore believable, and what is the catch?
Check it against inflation. If the average asset was bought about eight years ago and equipment prices rose 5% a year, replacing it costs 1.05 to the power 8, about 1.48 times its original price. Rs 80 crore of D&A at today's prices is about Rs 118 crore, close to the Rs 120 crore estimate, so the split hangs together. The catch is that turnover is measured on net book value, which is itself at old prices. New capacity bought at today's prices may need more than 50 paise per rupee of revenue, which would make growth capex larger and maintenance smaller. Give the estimate as a range, and say why it matters: free cash flow before growth spending is Rs 40 crore lower than the D&A shortcut suggests.
Where candidates lose it
The common loss is the shortcut: maintenance equals D&A, so growth capex is 200 less 80, which is 120. It gives exactly the reverse of the turnover answer and overstates how much cash the business could release if it stopped growing.
The second loss is giving 120 and stopping. Say why D&A understates replacement cost, then name the weakness in your own method, the book-value turnover, before the interviewer does.
What the interviewer asks next
If growth stopped tomorrow, how much free cash flow would the business release each year?
How would you estimate maintenance capex from five years of the company's own history?
Why might a company with ageing assets report rising margins while its true earnings power falls?
009A company's EBITDA margin moves from 8% to 10%. Is that up 2% or up 25%? And a bank's gross NPA ratio falls from 4% to 3%: how would you describe that change in a results note?Percentages and averagesWarm upCorporate FP&ARating agencies
Try it first
Which phrase belongs in a results note about the margin moving from 8% to 10%?
Show the worked solution
Both are true, but say 2 percentage points first. A margin is already a percentage, so a change in it is measured in points: 8% to 10% is up 2 points, or 200 basis points, and up 25% relative to where it started. The NPA ratio fell 1 percentage point, or 100 basis points, which is a 25% relative fall. Use points for a rate and per cent for an amount.
Why can one change honestly be called both 2 and 25?
Think of a student whose exam score goes from 40% to 50%. She scored 10 more marks out of 100, so she is up 10 points. Her score is also a quarter higher than before, up 25%. A percentage point measures the gap between two rates; a per cent measures that gap against the starting rate. Neither is wrong. The confusion comes from writing the same % sign for both, so the reader cannot tell which one you meant.
The margin moving from 8% to 10% is a rise of 2 percentage points, or 200 basis points, and 25% in relative terms. The NPA ratio falling from 4% to 3% is a fall of 1 percentage point, or 100 basis points, and a 25% relative fall.
Which label should lead, and when does the relative one matter?
Lead with points, because that is the convention in results notes, credit reports and board packs. A basis pointOne hundredth of a percentage point. 100 basis points equal 1 percentage point. is one hundredth of a point, which helps when moves are small: margin up 200 bps. The relative change matters when the rate drives an amount. On flat revenue of Rs 1,000 crore, EBITDA goes from Rs 80 crore to Rs 100 crore, which is a 25% rise in profit. So the 2 points and the 25% are describing two different things: the margin, and the profit it produces.
The relationship
$\Delta_{\text{pp}} = 10\% - 8\% = 2 \text{ pp} \qquad \Delta_{\text{rel}} = \frac{10\% - 8\%}{8\%} = 25\%$
pp percentage points, the plain gap between two rates
rel the relative change, the gap divided by the starting rate
What it says in wordsSubtract for the change in points; divide that by the start for the change in per cent.
For the NPA ratio, a falling ratio is good news, so say it plainly: gross NPA down 1 percentage point to 3%, or down 100 basis points. You can add that the ratio is a quarter lower. Say the limit too: a lower ratio can also come from loans growing faster than bad loans, so check the rupee amount of NPAs before calling it an improvement in asset quality.
Where candidates lose it
The loss is writing margin up 2% in a results note or saying it in an interview. A reader who takes you literally hears a move from 8% to 8.16%, and a credit reader will mark it as sloppy at once.
The second loss is choosing the bigger number to sound better: up 25% sounds stronger than up 2 points. Interviewers listen for whether you pick the label that fits, then offer the other as context.
What the interviewer asks next
Interest rates rise from 6.50% to 6.75%. How many basis points is that, and what is the relative change?
A bank's gross NPA ratio falls but its NPAs in rupees rise. How is that possible?
Margin is flat at 10% while revenue grows 20%. What happened to EBITDA?
010Estimate the number of coffee shops in Bengaluru.Estimation and market sizingCoreVista Equity PartnersAustin · 2023
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Before any number, what do you need to settle first?
Show the worked solution
About 2,000 sit-down cafés, as a range of roughly 1,000 to 4,000. Take about 1.3 crore people, 70% of them aged 15 to 64, and assume 20% of those visit a café twice a week. That is about 5.2 lakh cups a day; at 250 cups a café a day, about 2,080 cafés. A supply check, 150 commercial clusters with 10 cafés each plus 500 neighbourhood ones, gives about 2,000.
What exactly are you counting?
Say the definition before any number. In Bengaluru the answer changes several times over depending on whether small standing filter coffee counters count, so define a coffee shop as a sit-down café selling espresso-style coffee and say you are leaving the counters out. Then state the population as an assumption, about 1.3 crore for the metro area, and tell the interviewer you would confirm it. In a market sizing nobody is marking the population figure; they are marking whether your chain of reasoning holds.
How do you build it from demand?
Think of a single café first: how many cups does it need to sell to pay its rent? Then ask how many cups the city drinks. Of 1.3 crore people, about 70% are aged 15 to 64, so 91 lakh. Assume 20% of them use cafés, 18.2 lakh people, at two cups a week each: 36.4 lakh cups a week, or about 5.2 lakh a day. A café open 12 hours selling around 20 cups an hour serves about 250 cups a day, so the city supports about 2,080 cafés.
The relationship
$N = \frac{1.3\text{ cr} \times 0.70 \times 0.20 \times 2/7}{250} \approx 2{,}080$
0.70 share of people aged 15 to 64
0.20 share of those who use cafés
2/7 cups a day per café user, two a week
250 cups one café serves in a day
What it says in wordsDaily cups demanded by the city, divided by daily cups one café can serve.
Demand of about 5.2 lakh cups a day, at 250 cups a café, needs about 2,080 cafés, and counting from supply, 150 commercial clusters with 10 cafés each plus 500 neighbourhood cafés, gives about 2,000, so the two routes agree.
How do you check it, and which assumption matters most?
Count from the other side: supply. Picture the tech parks, malls and busy high streets, say 150 of them, with about 10 cafés each, plus about 500 standalone neighbourhood cafés. That is about 2,000, close to the demand answer. Then name the swing factor. The 20% share of café users is the softest input: halve it and the answer falls to about 1,040. Say the range out loud, roughly 1,000 to 4,000, because a single precise number from soft inputs sounds less credible, not more.
Where candidates lose it
The common loss is starting to multiply before defining the thing. Ten minutes later the candidate realises filter coffee counters are in or out of the count, and the answer jumps by a factor of five.
The second loss is giving one number with no check. Interviewers who ask market sizing want two routes that meet, and a sentence on which input you trust least.
What the interviewer asks next
The reported version of this question asked about the United States. How would your structure change?
How many cups a day does a café need to sell to cover its rent, staff and coffee?
If a café chain wants 300 outlets in the city, what share of the market is that?
Asked at Vista Equity Partners, Healthcare, Austin, 2023 (Wall Street Oasis): market sizing - how many coffee shops in US

12	yearly rent, Rs crore
0.09	the discount rate applied to the lease
10	years left on the lease

β_U	unlevered beta, the business risk alone, 0.8
t	tax rate, 25%
D/E	your target debt to equity, 0.5
β_L	levered beta your shareholders bear

50,000	net cash each year, Rs
4.111	the six-year annuity factor at 12%
20,000	sale value at the end of year 6, Rs

p	the chance of heads on one flip, 1/3
2p(1-p)	the chance a pair is mixed, 4/9
2	flips used by each pair

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