Investment Banking puzzles, solved step by step

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004A company trades at 20x earnings and 10x EBITDA. Equity value is 200, interest expense is 20 at a 5% interest rate, and depreciation and amortisation is 20. What is the tax rate?Valuation riddlesHardEvercoreMenlo Park · 2025EvercoreSan Francisco · 2026
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Which two numbers do you need to find before the tax rate falls out?
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The tax rate is 50%. P/E of 20 on equity of 200 gives net income of 10. Interest of 20 at 5% means debt of 400, so enterprise value is 600 and EBITDA is 60. Take off depreciation of 20 and interest of 20 to reach pre-tax profit of 20. Tax is 20 minus 10, which is 10, so the rate is 50%.
Where do you start when every number looks equally useful?
Start from what the answer is made of. A tax rate is tax divided by pre-tax profit, so the job is to find the two profit lines either side of the tax charge. Everything in the question is a road to one of those two numbers. Say that out loud first: it tells the interviewer you have a plan before you touch the arithmetic.
Net income is one step: equity value over the P/E, 200 over 20, is 10. Pre-tax profit takes longer. The enterprise valueThe value of the whole business to all its funders: equity value plus debt, less cash. multiple is on EBITDA, so you need EV, which needs debt, which the interest line hands you: 20 of interest at 5% means 400 of debt.
Equity of 200 at 20x earnings gives net income of 10; interest of 20 at 5% gives debt of 400, so enterprise value is 600 and EBITDA at 10x is 60. EBITDA of 60 less depreciation of 20 and interest of 20 leaves pre-tax profit of 20, and a tax charge of 10 on that is a 50% rate.
What assumption are you making, and should you say it?
You are assuming the company holds no cash, so enterprise value is simply equity plus debt. Say the assumption before you use it, because with any cash on the balance sheet EV falls, EBITDA falls, and the tax rate changes. A 50% rate is also high for most countries, which is worth one sentence: the interviewer built round numbers, not a real company.
Where candidates lose it
Candidates grab EBITDA first and then stall, because EV/EBITDA looks like the obvious lever but EV is not given. The debt is hiding inside the interest line, and people who do not think of interest divided by rate never find it.
The second loss is silent assumptions. Saying no cash out loud costs two seconds and turns a lucky answer into a reasoned one.
What the interviewer asks next
Now the company holds 100 of cash. What is the tax rate?
What does a 50% effective tax rate tell you about this business?
If the P/E rises to 25x with everything else fixed, what happens to the implied tax rate?
Asked at Evercore, Investment Banking, Menlo Park, 2025 (Wall Street Oasis): P/E of 20x, Ev/EBITDa of 10x, 20 million interest expense, 5% IR, D/A of 20 million, EQ of 200 million -> find tax rate
Asked at Evercore, Mergers and Acquisitions, San Francisco, 2026 (Wall Street Oasis): Given the following, calculate the Tax Rate
010A company trades at 10x EV/EBITDA with a 20% EBITDA margin. What is its EV/Revenue multiple, and if net debt equals one year of EBITDA, what is its price-to-sales ratio?Valuation riddlesCoreHoulihan LokeyChicago · 2026
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What is the EV/Revenue multiple?
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EV/Revenue is 2.0x and price to sales is 1.8x. Take Rs 100 of revenue. A 20% margin gives EBITDA of Rs 20, and at 10x the enterprise value is Rs 200, two times revenue. Net debt equals one year of EBITDA, Rs 20, so equity value is Rs 200 minus Rs 20, which is Rs 180, or 1.8 times revenue.
How do multiples convert into one another?
Think of a corner shop priced at 10 years of profit, where profit is a fifth of takings. Priced against takings, it costs two years' worth: 10 times a fifth. An enterprise value multiple converts into another by the ratio of their denominators, so EV/Revenue equals EV/EBITDA times the EBITDA margin. Working per Rs 100 of revenue keeps every step visible: EBITDA Rs 20, enterprise value Rs 200.
Per Rs 100 of revenue, a 20% margin gives EBITDA of Rs 20 and a 10x multiple gives enterprise value of Rs 200, so EV/Revenue is 2.0x; taking off net debt of Rs 20 leaves equity of Rs 180 and price to sales of 1.8x.
The relationship
$\frac{EV}{Rev} = \frac{EV}{EBITDA}\times\frac{EBITDA}{Rev} = 10\times 0.20 = 2.0 \qquad \frac{P}{S} = \left(10 - 1\right)\times 0.20 = 1.8$
EV/EBITDA the enterprise multiple given, 10x
EBITDA/Rev the margin, 20%
10 - 1 the multiple less net debt measured in years of EBITDA
What it says in wordsMultiply by the margin to move from EBITDA to revenue, and subtract net debt in years of EBITDA to move from enterprise value to equity.
Why is price to sales lower than EV to revenue here?
Price to sales is an equity multiple: the market value of the shares over revenue. To reach it from enterprise value you cross the equity bridgeThe steps from enterprise value to equity value: subtract debt and similar claims, add cash.. Equity value is enterprise value less net debt, so an equity multiple sits below the enterprise multiple when a company has net debt, and above it when it holds net cash. Net debt of one year's EBITDA is Rs 20 per Rs 100 of revenue, which takes Rs 200 down to Rs 180, or 1.8x.
The limitation to state is why bankers prefer one family over the other. Revenue belongs to every funder of the business, so comparing it with enterprise value is consistent; comparing it with equity value alone mixes a whole-business line with one funder's slice. Two companies with identical operations but different debt will show the same EV/Revenue and different price to sales ratios.
Where candidates lose it
The classic slip is dividing by the margin instead of multiplying, which gives 50x. It should fail the smell test at once: fifty times revenue at a 20% margin is 250 times EBITDA. Check direction by asking whether the new multiple should be bigger or smaller than the old one.
The second slip is forgetting the bridge and answering 2.0x for price to sales too. Enterprise and equity multiples have different numerators, and net debt is what separates them.
What the interviewer asks next
If the company held net cash of one year's EBITDA instead, what would price to sales be?
If D&A is 5% of revenue, what is EV/EBIT?
Why do bankers rarely lean on price to sales for companies carrying heavy debt?
Asked at Houlihan Lokey, Private Funds Advisory, Chicago, 2026 (Wall Street Oasis): Valuation ratio questions like if EV/EBITDA is 10x, what is
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
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?
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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?
039A company earns Rs 10 a share, has a 10% cost of equity, does not grow and pays out everything. It decides to retain half its earnings and reinvest them at a 10% return. Does the share price change?Valuation riddlesCoreElite boutique IBBulge bracket IB
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Does the price move?
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No, the price stays at Rs 100. Paying out Rs 10 forever at a 10% cost of equity is worth 10 over 10%, Rs 100. Retaining half and reinvesting at 10% gives growth of 50% times 10%, which is 5%, on a Rs 5 dividend: 5 over (10% minus 5%) is also Rs 100. Reinvesting at exactly the cost of capital swaps cash today for cash later at a fair rate, so value does not change.
Why does growth not add value here?
Imagine lending your bonus to a friend at exactly the rate your bank pays. You will have more money later, but you are no richer today, because the bank would have paid you the same. Retained earnings create value only if the company reinvests them at more than shareholders could earn elsewhere at the same risk, which is the cost of equity. At exactly 10% the company is just the bank: the growth is real, but it is paid for rupee for rupee by the dividend given up.
Rs 10 a year forever and Rs 5 a year growing at 5% are both worth Rs 100 at a 10% cost of equity, even though the growing stream only overtakes after about 14 years; reinvesting at 15% would lift the price to Rs 200, at 6% it would cut it to Rs 71.
How do the two dividend streams compare?
The flat stream pays Rs 10 every year. The growing one starts at Rs 5 and rises 5% a year, so it overtakes Rs 10 only after about 14 years. Discounted at 10%, the early shortfall and the later surplus cancel exactly, and both streams are worth Rs 100. The tool is the Gordon growth modelA valuation of a stream that grows at a constant rate forever: the next payment divided by the discount rate minus the growth rate.: price equals next year's dividend over the cost of equity minus growth, and growth equals the share retained times the return on the money reinvested.
The relationship
$P = \frac{D_1}{r - g} = \frac{5}{0.10 - 0.5 \times 0.10} = \frac{5}{0.05} = 100$
D1 next year's dividend, half of Rs 10
r the cost of equity, 10%
g growth: half retained, times a 10% return on it
What it says in wordsA smaller dividend that grows is worth exactly the same as the full dividend when the growth is bought at the cost of capital.
When would the decision change the price?
Change the return on the reinvested money. At 15%, growth is 7.5% and the price doubles to Rs 200; at 6%, growth is 3% and the price falls to about Rs 71. The same retention policy creates or destroys value depending only on whether the return beats 10%. That is the sentence the interviewer is waiting for: growth is not good in itself, profitable growth is.
Where candidates lose it
The usual answer is that the price rises because the company now grows. Growth sounds good, but it is bought with the dividend given up, and at a 10% return it costs exactly what it is worth.
The opposite slip is saying the price halves because the dividend halves. That ignores the growth the retained cash buys. Run both legs through the same formula and they cancel.
What the interviewer asks next
What if the retained earnings are reinvested at 15%?
Why might the market still cheer a company that announces growth at its cost of capital?
How does this connect to return on invested capital in a DCF?
049A bank trades at 2.0x book value, earns a 16% return on equity and has a 12% cost of equity. Using a dividend discount model, what long-run growth rate is the market pricing in?Valuation riddlesHardRothschild & CoRiyadh · 2026
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What growth is priced in?
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About 8% a year, forever. In a dividend discount model, a bank that earns its ROE on book and grows at g must retain g over ROE of its earnings and pays out the rest, which makes its fair price to book (ROE minus g) over (cost of equity minus g). Setting (16% minus g) over (12% minus g) equal to 2.0 gives g of 8%, with 50% of earnings paid out. Whether 8% forever is believable is the real question.
Where does the price-to-book formula come from?
Think of a fruit tree. The fruit you eat is the dividend; the fruit you replant grows the orchard. A bank earning its ROE on book value can grow only by retaining earnings, so growth equals ROE times the share retained, and the rest is paid out as dividends. Put that dividend into the dividend discount modelA valuation that prices a share as the present value of its future dividends; with constant growth it becomes the next dividend divided by the cost of equity minus growth. and divide by book value, and price to book becomes (ROE minus g) over (r minus g).
With a 16% return on equity and a 12% cost of equity, the justified price to book rises from 1.33x at zero growth to 2.0x at 8% growth and 3.0x at 10%, so a 2.0x price implies the market expects 8% growth forever.
How do you solve for the growth?
Set the formula equal to the price. (16% minus g) over (12% minus g) equals 2.0, so 16 minus g equals 24 minus 2g, and g is 8%. Check it with rupees: on book of Rs 100 the bank earns Rs 16, keeps Rs 8 to grow book by 8%, and pays Rs 8. Rs 8 over (12% minus 8%) is Rs 200, twice book.
The relationship
$\frac{P}{B} = \frac{ROE - g}{r - g} \;\Rightarrow\; 2.0 = \frac{0.16 - g}{0.12 - g} \;\Rightarrow\; g = 8\%$
ROE return on equity, 16%
r cost of equity, 12%
g the growth rate the price implies
What it says in wordsThe justified price to book depends on how far ROE and the cost of equity each sit above growth.
Is 8% growth forever reasonable?
That is the judgement the interviewer is waiting for. Look at the curve: near 8% the price is very sensitive to growth, so a small shortfall, 7% instead of 8%, would justify only 1.8x book. Compare 8% with the nominal growth the economy could sustain over decades, a figure to look up rather than assume. And note what the formula says about returns: if the bank earned only its 12% cost of equity, it would be worth exactly book value, whatever its growth.
Where candidates lose it
Candidates reach for P/B equals ROE over cost of equity, get 1.33x, and cannot reconcile it with 2.0x. That shortcut is the no-growth case; the gap between 1.33x and 2.0x is exactly the growth the market is paying for.
The second loss is solving for 8% and stopping. The point of an implied number is to judge it: say whether 8% a year forever is plausible for a bank, and what happens to the price if it is not.
What the interviewer asks next
What payout ratio is consistent with this valuation?
If the market cut the bank to 1.5x book, what growth would that imply?
Why is a bank earning exactly its cost of equity worth book value whatever its growth?
Asked at Rothschild & Co, Generalist, Riyadh, 2026 (Wall Street Oasis): DDM model mechanics and A/P & A/R increase
058A company trades at 15x earnings and pays out 40% of its earnings as dividends. What is its dividend yield?Valuation riddlesWarm upJefferiesChicago · 2026
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Which is the dividend yield?
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About 2.67%. A P/E of 15 means each Rs 100 of share price buys Rs 6.67 of yearly earnings, an earnings yield of 1 over 15. The company pays out 40% of that, Rs 2.67, as dividend. Dividend yield is dividend over price, Rs 2.67 over Rs 100. In one line: the payout ratio divided by the P/E, 0.40 over 15.
How do you turn a P/E into something you can multiply?
Flip it. A P/E of 15 says you pay 15 rupees for every rupee of yearly profit, so every rupee of price buys one fifteenth of a rupee of profit. Inverting the P/E gives the earnings yieldEarnings per share divided by the share price: the inverse of the P/E., 1 over 15 or about 6.67%, and every other per-share ratio then falls out by multiplication. Picking a round share price of Rs 100 makes it concrete: earnings per share are Rs 6.67.
A Rs 100 share at 15x earnings carries Rs 6.67 of earnings; paying out 40% gives a Rs 2.67 dividend, a 2.67% yield, while the other Rs 4.00 stays in the business.
Why is the dividend only part of the shareholder's return?
Think of a shopkeeper who takes home 40% of each year's profit and leaves 60% in the shop to buy more stock. The retained Rs 4.00 is not lost to shareholders; it is reinvested, and if it earns a decent return it should lift future earnings and dividends. That is why a low dividend yield on its own says little about whether a share is cheap. A company paying out everything would show a 6.67% yield and little room to grow.
The relationship
$\text{Dividend yield} = \frac{\text{DPS}}{P} = \frac{\text{payout} \times \text{EPS}}{P} = \frac{\text{payout}}{P/E} = \frac{0.40}{15} = 2.67\%$
DPS dividend per share
EPS earnings per share
payout the share of earnings paid as dividend, 40%
P/E price over earnings per share, 15
What it says in wordsDividend yield is the payout ratio divided by the P/E, because both are measured against the same share price.
Say the general rule after the number, because the follow-up usually changes one input. If the P/E doubles to 30 with the same payout, the yield halves to 1.33%; if the payout doubles to 80% at the same P/E, the yield doubles to 5.33%. Having the one-line formula ready means you answer those in a breath.
Where candidates lose it
The trap is answering 6.67%, the earnings yield, because 1 over 15 is the first thing anyone computes. Dividends are the part of earnings paid in cash, not all of it.
The other slip is multiplying instead of dividing, 40% times 15, and saying 6.0. Pinning a share price of Rs 100 and walking down to earnings and then to the dividend keeps the direction right.
What the interviewer asks next
If dividends grow at 5% a year forever, what cost of equity does this price imply?
The payout rises to 60% and the share price does not move. What is the new yield, and what might the market be thinking?
Why might a fast-growing company pay no dividend at all?
Asked at Jefferies, Mergers and Acquisitions, Chicago, 2026 (Wall Street Oasis): what are specific line items in the BS, some very simple P/E calculations, etc.
069Two companies both trade at 8x EV/EBITDA. One spends 20% of its EBITDA on capex each year and the other spends 60%. Which is cheaper, and which multiple shows it?Valuation riddlesCoreElite boutique IBBulge bracket IB
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Before you work it: which company is cheaper?
Show the worked solution
The company spending 20% is cheaper, and EV over EBITDA less capex shows it. Give both Rs 100 crore of EBITDA, so each is worth Rs 800 crore. The first keeps Rs 80 crore after capex and trades at 10x that cash figure; the second keeps Rs 40 crore and trades at 20x. EV/EBITDA cannot see capital intensity, so when capex differs this much, compare value against cash earnings instead.
Why does the same 8x mean different things?
Two taxi drivers each earn Rs 1 lakh a month before costs. One drives a new car that needs a service a year; the other drives an old one that eats Rs 60,000 a month in repairs. You would not pay the same for both businesses. EBITDA is earnings before the spending needed to keep the assets working, so two companies with equal EBITDA can hand their owners very different amounts of cash. At 8x, both are valued at Rs 800 crore on Rs 100 crore of EBITDA. The first spends Rs 20 crore of that on capex, the second Rs 60 crore, and that difference never appears in the headline multiple.
Both companies carry Rs 100 crore of EBITDA and an Rs 800 crore enterprise value, but after capex the first keeps Rs 80 crore and the second Rs 40 crore, so on EV over EBITDA less capex they trade at 10x and 20x and the first is the cheaper company.
Which multiple fixes it?
Take the capex off before dividing. EV over EBITDA less capex puts the two companies on cash they can actually keep, and the gap opens up to 10x against 20x. EV over EBIT does a rougher version of the same job, because depreciation is yesterday's capex spread over time, but it lags when a company is spending more than it depreciates. The cleanest version is EV over unlevered free cash flow, which also takes tax and working capital off. Name the limitation too: capex can be lumpy, so use a normal year or an average, and growth capex that adds capacity deserves a different reading from maintenance capex that merely keeps the lights on.
Rs crore a year Company A Company B
EBITDA 100 100
Capex 20 60
EBITDA less capex 80 40
Enterprise value 800 800
EV / EBITDA 8.0x 8.0x
EV / (EBITDA less capex) 10.0x 20.0x
On identical EBITDA and value, company A keeps Rs 80 crore after capex and company B Rs 40 crore, so company B costs twice as much per rupee of cash earnings.
The relationship
$\frac{EV}{EBITDA - capex} = \frac{800}{100 - 20} = 10x \qquad \frac{800}{100 - 60} = 20x$
EV enterprise value, Rs 800 crore for both
EBITDA Rs 100 crore for both
capex capital spending, Rs 20 crore and Rs 60 crore
What it says in wordsDivide value by the cash left after capex, and the capital-hungry company looks twice as expensive.
When would the market be right to pay 8x for both?
Say the case against your own answer. If company B's Rs 60 crore of capex is building capacity that will lift EBITDA sharply, the market may be paying for growth that company A will never deliver. The question has no growth figures, so the honest answer is that on today's cash the 20% company is cheaper, and that the interviewer would need to tell you about growth and the split between maintenance and growth capex before you could defend an equal multiple.
Where candidates lose it
The common loss is answering that neither is cheaper because the multiples match. The interviewer has deliberately picked a multiple that is blind to capex to see whether you know what EBITDA leaves out.
The second loss is naming the fix without the limitation. Capex is lumpy and some of it is growth, so say which capex you would use and why.
What the interviewer asks next
Both companies also have the same EV/EBIT. What would that tell you about their depreciation?
How would you separate maintenance capex from growth capex if the company does not disclose the split?
Which industries tend to show the biggest gap between EV/EBITDA and EV/(EBITDA less capex)?
076An office building earns net operating income of Rs 10 crore a year and trades at an 8% cap rate. If cap rates fall to 7%, what happens to its value?Valuation riddlesCoreElite boutique IBBulge bracket IB
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Before you compute: how much does the value move?
Show the worked solution
The value rises about 14%, from Rs 125 crore to Rs 142.9 crore. A cap rate is the income yield a buyer demands, so value is net operating income divided by the cap rate. Rs 10 crore over 8% is Rs 125 crore; the same Rs 10 crore over 7% is Rs 142.9 crore. The ratio of the two values is 8 over 7, a rise of 14.3%. Nothing happened to the building; the market now pays more for each rupee of its rent.
Why does a lower cap rate mean a higher value?
A fixed deposit paying Rs 10,000 a year is worth Rs 1.25 lakh if savers demand 8%, and Rs 1.43 lakh if they will accept 7%. The cheque has not changed; the price people pay for it has. A cap rate is the yield a buyer requires on a building's income, so value is income divided by the cap rate, and a fall in the required yield raises the price of the same income. Rs 10 crore over 0.08 is Rs 125 crore; over 0.07 it is Rs 142.9 crore. The cap rateCapitalisation rate: net operating income divided by the property value, the income yield a buyer requires. works exactly like a bond yield, and value moves the other way.
With net operating income fixed at Rs 10 crore, a fall in the cap rate from 8% to 7% lifts the building's value from Rs 125 crore to Rs 142.9 crore, a rise of 14.3%, because value is income divided by the cap rate and 8 over 7 is 1.143.
How do you get the percentage without computing either value?
The income cancels. The ratio of new to old value is the old cap rate over the new cap rate, 8 over 7, so the rise is one seventh, 14.3%. The move is not symmetric: the same one point rise, from 8% to 9%, would cut value by 8 over 9 minus 1, about 11.1%. Small cap rates make the swings bigger: from 5% to 4% is a 25% jump in value, from 10% to 9% only 11.1%. Say that pattern after the number, because the follow-up is usually about a different starting rate.
The relationship
$V = \frac{NOI}{c} \qquad \frac{V_{7\%}}{V_{8\%}} = \frac{0.08}{0.07} = 1.143 \Rightarrow +14.3\%$
V the building's value
NOI net operating income, Rs 10 crore a year
c the cap rate, 8% falling to 7%
What it says in wordsValue is income over the cap rate, so the value changes by the ratio of the old cap rate to the new one.
Cap rate Value of Rs 10 crore of NOI, Rs crore Change from the 8% case
6% 166.7 +33.3%
7% 142.9 +14.3%
8% 125.0 +0.0%
9% 111.1 -11.1%
10% 100.0 -20.0%
Each one point step in the cap rate moves the value by a different percentage, larger as the cap rate gets lower, because the value is a fixed income divided by a shrinking rate.
What would a banker add about why cap rates move?
Cap rates track the cost of money and the perceived risk of the rent. A fall from 8% to 7% usually means lower interest rates, more buyers chasing the asset, or more confidence in the tenant, and none of those is something the owner did. That is why a real estate team separates value created by raising income from value handed over by the market, and why an owner who bought at 8% and sells at 7% has earned a 14% gain on cap rate compression alone. Mention the limit: the formula assumes a stable income, so a building with leases about to expire does not deserve the same cap rate as one with ten years of rent locked in.
Where candidates lose it
The common loss is reading a falling cap rate as bad news for the value, because falling sounds like a fall. A cap rate is a yield, and a lower required yield means a higher price for the same income.
The second loss is saying 12.5%, from 1 over 8, or 1%, from the one point move. The value scales by the ratio of the rates, 8 over 7, and saying that ratio aloud is the answer.
What the interviewer asks next
NOI also rises 5% as the cap rate falls to 7%. What is the value now?
Why is a one point move in the cap rate a bigger deal at 5% than at 10%?
If the building was bought with 60% debt at the 8% cap rate, what did the cap rate move do to the equity?
087A DCF sets its terminal value at 10x final-year EBITDA. Free cash flow runs at half of EBITDA and the WACC is 10%. What perpetual growth rate is that exit multiple quietly assuming?Valuation riddlesHardElite boutique IBBulge bracket IB
Try it first
Roughly what growth rate does 10x EBITDA imply here?
Show the worked solution
About 4.8% a year, forever. Write the terminal value both ways. The multiple says 10 x EBITDA. The Gordon formula says 0.5 x EBITDA x (1 + g) / (0.10 - g). Setting them equal, EBITDA cancels: 1.0 - 10g = 0.5 + 0.5g, so g = 0.5 / 10.5 = 4.76%. Every exit multiple implies a growth rate, and the check is whether that rate is believable for this business.
Why does a multiple contain a growth rate at all?
If a buyer wants a 5% return and pays 25 times this year's rent for a flat, they are counting on the rent rising: with flat rent, a 5% return supports a price of only 20 times. A multiple is a shorthand price for a stream of future cash flows, so every multiple implies some combination of growth and discount rate. In a DCF the exit multiple sits beside an explicit WACC, which means the growth assumption can be solved for exactly.
Set the two terminal values equal. The multiple gives 10 x EBITDA. The perpetuity growth method gives next year's free cash flow over (r minus g), and next year's cash flow is 0.5 x EBITDA x (1 + g). EBITDA cancels from both sides, leaving one equation in g, which solves to 4.76%.
With free cash flow at half of EBITDA and a 10% WACC, a 10x exit multiple implies perpetual growth of 4.8%, and implied growth rises with the multiple while bending toward the 10% WACC, which it can never reach.
The relationship
$m = \frac{f(1+g)}{r-g} \;\Rightarrow\; g = \frac{mr - f}{m + f} = \frac{1.0 - 0.5}{10 + 0.5} \approx 4.76\%$
m exit multiple of EBITDA, 10x
f free cash flow as a share of EBITDA, 0.5
r WACC, 10%
g implied perpetual growth
What it says in wordsRearranging the perpetuity formula turns any exit multiple into the growth rate it assumes.
How do you judge whether 4.8% is believable?
Perpetual growth means growth forever, so it should not exceed the long-run nominal growth of the economy whose currency the cash flows are in, or the business eventually becomes larger than that economy. Whether 4.8% passes depends on that currency's inflation and real growth, so state the benchmark you are using rather than a number from memory. The useful habit is running the check both ways: an exit multiple that implies an unbelievable growth rate is a sign the multiple came from a peer set that does not match this business.
Say the convention too. If you apply the multiple to final-year EBITDA but take next year's cash flow without the (1 + g) uplift, the answer becomes 10% minus 0.5/10, which is 5.0%. A small difference, but naming the convention shows you know where it comes from.
Where candidates lose it
The common answer is that an exit multiple has no growth assumption, which is exactly backwards. Candidates who have only used the multiple method never think to translate it, and the interviewer is testing that translation.
The second loss is solving the algebra but not commenting on the result. Say the number, then say what you would compare it against and why.
What the interviewer asks next
What exit multiple implies zero growth here?
If free cash flow conversion rises to 70% of EBITDA, what growth does 10x imply?
Which method would you lead with in a fairness opinion, and why show both?

EV/EBITDA	the enterprise multiple given, 10x
EBITDA/Rev	the margin, 20%
10 - 1	the multiple less net debt measured in years of EBITDA

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

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

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

Try it first

Where do you start when every number looks equally useful?

What assumption are you making, and should you say it?

Where candidates lose it

What the interviewer asks next

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How do multiples convert into one another?

Why is price to sales lower than EV to revenue here?

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

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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

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Why does growth not add value here?

How do the two dividend streams compare?

When would the decision change the price?

Where candidates lose it

What the interviewer asks next

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Where does the price-to-book formula come from?

How do you solve for the growth?

Is 8% growth forever reasonable?

Where candidates lose it

What the interviewer asks next

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How do you turn a P/E into something you can multiply?

Why is the dividend only part of the shareholder's return?

Where candidates lose it

What the interviewer asks next

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Why does the same 8x mean different things?

Which multiple fixes it?

When would the market be right to pay 8x for both?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a lower cap rate mean a higher value?

How do you get the percentage without computing either value?

What would a banker add about why cap rates move?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a multiple contain a growth rate at all?

How do you judge whether 4.8% is believable?

Where candidates lose it

What the interviewer asks next