Investment Banking puzzles, solved step by step

Puzzles
100
Traced to a firm
36
Topics
12
Hard
29
Topic
All topicsProbability7Mental maths and counting11Growth and compounding9Valuation riddles11Logic and brainteasers11Rates, risk and options9Estimation and market sizing7Accounting riddles9Expected value and games7Enterprise value and dilution6Deal maths6DCF and cost of capital7
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–2 of 2 · filtered from 100Clear filters
  1. 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

    Try it first

    What is the EV/Revenue multiple?

    Show the worked solution

    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: margin, then multiple, then the bridge100Revenuethe starting point20EBITDAx 20% margin200Enterprise valuex 10 EBITDA-20Net debt1 year of EBITDA180Equity valueEV less net debtEV / Revenue2.0x200 / 100Price / Sales1.8x180 / 100
    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
    EVRev=EVEBITDA×EBITDARev=10×0.20=2.0PS=(10−1)×0.20=1.8\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/EBITDAthe enterprise multiple given, 10x
    EBITDA/Revthe margin, 20%
    10 - 1the 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

  2. 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

    Try it first

    Before you discount anything: what is the gift worth?

    Show the worked solution

    About Rs 27.3 lakh, the value of selling it. Keeping the elephant forever costs Rs 20 lakh a year, minus Rs 2 crore in today's money at 10%. Selling means one more year of upkeep and Rs 50 lakh at the end, a net Rs 30 lakh worth Rs 27.3 lakh today. Donating is worth zero. A gift is worth its best use, and the free exit means it can never be worth less than zero.

    Why does the elephant not have one value?

    Think of being handed an old car that needs Rs 30,000 of repairs before anyone will buy it. The car is not worth its sticker price; it is worth what you can do with it, net of what doing that costs. An asset with a carrying cost has no value of its own: each option for it has a value, and the asset is worth the best of them. So the first move is to list the options out loud, keep it, sell it or give it away, and then price each one at the same 10% rate.

    The elephant has no single value: each option does, at 10%Keep it foreverPay Rs 20 lakh every yearNo sale, no end datePV = -20 / 10%-200Rs lakh, todaySell after a yearYear 1: pay 20, receive 50Net Rs 30 lakh at year endPV = 30 / 1.10+27.3Rs lakh, todayDonate todaySanctuary takes it freeNo cost, no cashPV = 00Rs lakh, todayThe three options on one scale, Rs lakh todayKeep: -200Sell: +27.3Donate: 0-200-1000+50The gift is worth its best option: Rs 27.3 lakh
    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⁡(−200.10,  50−201.10,  0)=max⁡(−200, 27.3, 0)=27.3V = \max\left(-\frac{20}{0.10},\; \frac{50-20}{1.10},\; 0\right) = \max(-200,\ 27.3,\ 0) = 27.3
    20/0.10keeping it: Rs 20 lakh of upkeep a year, forever, at 10%
    (50 - 20)/1.10selling it: the sale price less one year of upkeep, received a year from now
    0donating 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?