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Venture Capital puzzles, solved step by step

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  1. 011In your head, no calculator: a SaaS company has ARR of Rs 42 crore growing 65% a year, net burn of Rs 3.1 crore a month, net new ARR last quarter of Rs 6.2 crore and Rs 55 crore of cash. What are next year's ARR, the quarterly burn multiple and the runway?Mental maths and speed testsCoreVista Equity PartnersAustin · 2021

    Try it first

    What is the quarterly burn multiple?

    Show the worked solution

    About Rs 69.3 crore of ARR, a burn multiple of 1.5 and about 18 months of runway. 42 x 1.65 is 42 plus 21 plus 6.3. A quarter's burn is 9.3, and 9.3 over 6.2 is 1.5 because both are multiples of 3.1. Cash of 55 over 3.1 a month is a shade under 55 over 3, so about 17.7 months.

    How do you multiply by 1.65 without a calculator?

    Break the awkward multiplier into pieces you already know. A shopkeeper adding 65% to a Rs 42 cost does not multiply by 0.65; he adds half, then a bit more. 65% is 50% plus 15%, so 42 x 1.65 is 42 plus 21 plus 6.3, which is Rs 69.3 crore. Fifteen percent is itself 10% plus half of that again: 4.2 plus 2.1. Every step is a halving or a shift of the decimal point, which is fast and hard to get wrong out loud.

    Why does the burn multiple need care before any arithmetic?

    Because the two inputs come in different periods. Burn is quoted per month and net new ARR per quarter. A burn multiple divides the cash burned by the new annual recurring revenue added over the same stretch of time, so three months of burn, Rs 9.3 crore, goes over the quarter's Rs 6.2 crore. Then notice that 9.3 is 3 x 3.1 and 6.2 is 2 x 3.1, so the ratio is exactly 3 over 2, or 1.5. Interviewers choose numbers like these on purpose; spotting the common factor is part of the test.

    Round first, then correct: three answers in under a minuteNext year's ARR42 x 1.65= 42 + 21 + 6.3(the base, half, then 15%)Rs 69.3 crBurn multipleQuarterly burn 3 x 3.1 = 9.39.3 / 6.2 = (3 x 3.1) / (2 x 3.1)(match the periods first)1.5Runway55 / 3 = 18.33.1 is 3% more than 3,so shave 3%: about 17.7~18 monthsThe slip: monthly burn over quarterly net new ARR, 3.1 / 6.2 = 0.5, looks three times better than it is.Both halves of a burn multiple must cover the same period.
    Splitting 1.65 into 1 plus a half plus 15% gives Rs 69.3 crore of ARR, matching periods turns the burn multiple into 9.3 over 6.2, which is 1.5, and rounding 3.1 down to 3 then shaving 3% gives about 17.7 months of runway.
    The relationship
    BM=3×3.16.2=1.5Runway=553.1≈17.7 months\text{BM} = \frac{3 \times 3.1}{6.2} = 1.5 \qquad \text{Runway} = \frac{55}{3.1} \approx 17.7 \text{ months}
    3 x 3.1net burn over one quarter, Rs crore
    6.2net new ARR added in the quarter, Rs crore
    55cash in the bank, Rs crore
    What it says in wordsPut burn and new revenue on the same period before dividing, and divide cash by monthly burn for runway.

    What do you say once the three numbers are out?

    Check them against each other, because that is what a growth investor does next. Growing ARR by Rs 27.3 crore next year needs about Rs 6.8 crore of net new ARR a quarter, a little above the Rs 6.2 crore just achieved, so the 65% plan is plausible but not banked. At a 1.5 burn multiple that growth costs about Rs 41 crore of burn in the year, and with Rs 55 crore of cash and about 18 months of runway, the company will want to raise again within roughly a year, before the runway gets short. That one sentence turns arithmetic into a view on the company.

    Where candidates lose it

    The costly slip is dividing the monthly burn by the quarterly net new ARR and announcing a burn multiple of 0.5. It makes the company look three times more efficient than it is, and the interviewer chose mixed periods to see whether you notice.

    The second loss is going silent while you calculate. Say the shortcut as you use it: half, then fifteen percent; three parts over two parts; fifty five over three, then shave a little.

    What the interviewer asks next

    • If net burn rises 20% next year while ARR grows 65%, what happens to the burn multiple if net new ARR grows in step with ARR?
    • How much cash should the company raise to have 24 months of runway at the current burn?
    • Is a burn multiple of 1.5 good for a company of this size, and what would change your view?

    Asked at Vista Equity Partners, Private Equity, Austin, 2021 (Wall Street Oasis): Mental math and tech/SaaS-specific sector insights

  2. 042A mental maths set from a first-round interview: work out 49 x 51, 998 x 1,002 and 12.5% of Rs 3,680 crore, each inside ten seconds.Mental maths and speed testsWarm upGeneral AtlanticNew York · 2026

    Try it first

    What is 998 x 1,002?

    Show the worked solution

    2,499, then 9,99,996, then Rs 460 crore. The first two use the same shortcut: numbers equally spaced either side of a round number multiply to its square minus the gap squared, so 49 x 51 is 2,500 minus 1, and 998 x 1,002 is 10,00,000 minus 4. The third is a fraction in disguise: 12.5% is one eighth, so halve Rs 3,680 crore three times, to 1,840, 920 and 460.

    Why does 49 x 51 come out one short of 2,500?

    Picture a square garden 50 metres a side. Take a one-metre strip off the bottom, 50 square metres, and lay it along the right-hand side. It only fits for 49 metres, so one square metre is left over. A rectangle 49 by 51 is a 50 by 50 square with one corner square missing, so the product is 2,500 minus 1, or 2,499. The same picture works for any pair spread evenly around a round number: the product is the middle number squared minus the gap squared.

    The relationship
    (a−b)(a+b)=a2−b249×51=502−12=2,499998×1,002=1,0002−22=9,99,996(a - b)(a + b) = a^2 - b^2 \qquad 49 \times 51 = 50^2 - 1^2 = 2{,}499 \qquad 998 \times 1{,}002 = 1{,}000^2 - 2^2 = 9{,}99{,}996
    athe round number in the middle, 50 or 1,000
    bhow far each factor sits from it, 1 or 2
    a squared minus b squaredthe product, always slightly below the square
    What it says in wordsTwo numbers spread evenly either side of a round number multiply to that number squared, less the gap squared.
    Two shortcuts: a difference of squares, and one eighth50 x 50= 2,5005050bottom strip of 50moved up asa 1 x 49 stripon the right:49 x 51 = 2,500 - 149 x 51 = 2,499998 x 1,002 = 9,99,99612.5% = 1/8 of Rs 3,680 crore460eight equal blocksHalve three times:3,680all1,840half920quarter460eighth12.5% of Rs 3,680 crore = Rs 460 crore
    49 x 51 is a 50 by 50 square with one unit square missing, so it equals 2,499, and 12.5% of Rs 3,680 crore is one of eight equal blocks, Rs 460 crore, found by halving three times.

    How do you take 12.5% of anything in a few seconds?

    Recognise the fraction first. 12.5% is one eighth, and dividing by eight is the same as halving three times, which is easier to do aloud than any long division. Rs 3,680 crore halves to 1,840, then 920, then 460. Keep a short list of these anchors ready: 12.5% is an eighth, 37.5% three eighths, 16.7% a sixth, 6.25% a sixteenth. Interviewers who give percentage questions usually pick one of them, because the speed of recognising the fraction is what they are testing.

    What is the interviewer actually checking?

    Speed sets are less about arithmetic than about whether you look for structure before you calculate. Saying the shortcut out loud, square minus one, or halve three times, shows a method that will also work on the next question. Two habits help. Check the size of your answer against an anchor: 49 x 51 must sit just under 2,500. And say the number back with its units, Rs 460 crore, not just 460. The limit of these tricks is that they only work on numbers chosen to suit them; for awkward numbers, round and say so.

    Where candidates lose it

    The common loss on the products is grinding through long multiplication and running out of time, or writing 10,00,004 because the sign of the correction is guessed. The product of numbers either side of a round number is always below its square.

    On the percentage, candidates multiply 3,680 by 0.125 digit by digit and fumble. Name the fraction, one eighth, and halve three times; the clock is part of the question.

    What the interviewer asks next

    • Work out 97 x 103 and 4.95 x 5.05 the same way.
    • What is 37.5% of Rs 2,400 crore?
    • Estimate 1,999 squared in your head.

    Asked at General Atlantic, Generalist, New York, 2026 (Wall Street Oasis): The first round was behavioral with mental math at the end.

  3. 047A debt-free company has an enterprise value of Rs 1,000 crore and 10 crore shares at Rs 100. It borrows Rs 100 crore and buys back shares at Rs 125. Ignoring taxes, what happens to enterprise value, equity value and the price of the remaining shares, compared with a buyback at Rs 100?Valuation riddlesHardSilver LakeSan Francisco · 2022

    Try it first

    After the buyback at Rs 125, what is each remaining share worth?

    Show the worked solution

    Enterprise value stays at Rs 1,000 crore, equity value falls to Rs 900 crore, and the remaining shares fall to Rs 97.83, against Rs 100 for a buyback at Rs 100. Borrowing Rs 100 crore and paying it out swaps equity for debt without changing what the business is worth. At Rs 100 a share the company retires 1 crore shares and the price holds. At Rs 125 it retires only 0.8 crore, so the Rs 20 crore premium comes out of the holders who stay.

    Why does enterprise value not change?

    A house worth Rs 1 crore is still worth Rs 1 crore after the owner takes out a Rs 10 lakh loan against it and spends the cash; what changes is how much of the house the owner owns outright. Enterprise value is the value of the business, and borrowing to pay shareholders changes who has a claim on it, not what it is worth. The Rs 100 crore of new debt is matched by Rs 100 crore leaving the company, so net debt rises by Rs 100 crore and equity value falls by the same amount, to Rs 900 crore. That holds only while we ignore taxes and the costs of financial distress.

    Borrow Rs 100 crore, buy back shares: what moves and what does notEquity 1,000EV 1,000BeforeEquity 900Debt 100EV 1,000AfterRs crore; ignoring taxesPrice of each remaining shareBuyback priceRs 100Rs 125Shares retired, crore1.00.8Shares left, crore9.09.2Equity Rs 900 cr / sharesRs 100.00Rs 97.83Premium paid to sellers: Rs 20 crore= 9.2 crore shares x Rs 2.17 lost by holders who stay
    Enterprise value stays at Rs 1,000 crore while Rs 100 crore of it moves from equity to debt, and the price of each remaining share holds at Rs 100 for a buyback at Rs 100 but falls to Rs 97.83 for a buyback at Rs 125.

    Why does the buyback price change the price per share?

    Equity is Rs 900 crore after the buyback either way; what differs is how many shares it is split across. Buying at the fair price of Rs 100 retires 1 crore shares and leaves Rs 900 crore over 9 crore shares, Rs 100 a share, so nobody gains or loses. Paying Rs 125 retires only 0.8 crore shares, leaving Rs 900 crore over 9.2 crore, Rs 97.83. The sellers received Rs 100 crore for shares worth Rs 80 crore, a Rs 20 crore premium, and the holders who stay paid it: 9.2 crore shares times Rs 2.17 is Rs 20 crore.

    The relationship
    Pafter=EV−DN−D/Pbb=1,000−10010−100/125=9009.2=97.83P_{\text{after}} = \frac{EV - D}{N - D/P_{bb}} = \frac{1{,}000 - 100}{10 - 100/125} = \frac{900}{9.2} = 97.83
    EVenterprise value, Rs 1,000 crore, unchanged
    Dthe new debt, Rs 100 crore, all paid out
    Nshares before the buyback, 10 crore
    P bbthe buyback price per share
    What it says in wordsThe remaining equity is enterprise value less the new debt, spread over the shares not bought back.

    What changes once you stop ignoring taxes?

    Say the limits, because the interviewer will raise them next. Interest is usually tax-deductible, so the debt creates a tax saving that can lift enterprise value a little above Rs 1,000 crore; against that, more debt raises the risk and cost of distress. Signalling matters too: a buyback can tell the market that management thinks the shares are cheap, which may move the price on its own. None of that changes the core point. A buyback at a premium to fair value moves wealth from holders who stay to holders who sell.

    Where candidates lose it

    The common loss is saying the share price rises because there are fewer shares, or that enterprise value falls because cash left the company. The cash leaving is matched by debt arriving, so EV is unchanged, and fewer shares are matched by less equity.

    The second loss is answering only the Rs 100 case. The question's Rs 125 is there to test whether you see that overpaying for shares hands the Rs 20 crore premium to sellers, and the remaining shares fall to Rs 97.83.

    What the interviewer asks next

    • At what buyback price would the remaining shares rise above Rs 100?
    • With a 25% tax rate and permanent debt, roughly how much does the tax shield add to enterprise value?
    • How would the answer change if the company paid for the buyback from Rs 100 crore of existing cash instead of new debt?

    Asked at Silver Lake, Technology, Media and Telecom, San Francisco, 2022 (Wall Street Oasis): If you raise $100 debt to buy back $100 of shares, how does that affect EV and equity value?

  4. 059A company's assets will be worth either Rs 200 crore or Rs 1,400 crore next year, with equal odds. It owes Rs 1,000 crore of debt, all due then, so the expected asset value of Rs 800 crore is below the debt. Why is the equity still worth something, and how much? Ignore discounting.Valuation riddlesHardSilver LakeSan Francisco · 2022

    Try it first

    What is the equity worth?

    Show the worked solution

    About Rs 200 crore, because equity is a call option on the assets. Shareholders get whatever is left after the debt, but never less than zero. In the bad case the assets of Rs 200 crore all go to lenders and equity gets nothing; in the good case equity keeps Rs 1,400 crore less Rs 1,000 crore, or Rs 400 crore. Half of Rs 400 crore is Rs 200 crore. Lenders, expecting Rs 600 crore on Rs 1,000 crore owed, carry the downside.

    If expected assets are below the debt, where does the equity value come from?

    Think of a lottery ticket bought with borrowed money where the lender can only take the ticket back. If it loses you owe nothing more; if it wins you keep the winnings above the loan. Limited liability makes equity a call optionThe right, not the obligation, to buy an asset at a fixed price. Its payoff is zero below that price and rises one for one above it. on the company's assets with a strike equal to the debt, so equity is worth the average of its payoffs, not the payoff at the average assets. The payoff at Rs 800 crore of assets is zero. The average of the payoffs, 0 and Rs 400 crore, is Rs {ev_eq59:.0f} crore.

    Equity is a call option on the assets, struck at the debt04008001,2001,6000200400600Asset value next year, Rs croreEquity, Rs croreDebt Rs 1,000 crthe strike priceBad: equity 0Good: equity 400Expected equity Rs 200 crpayoff at 800 is 0
    The equity payoff is flat at zero below the Rs 1,000 crore debt and rises above it, so the chord joining the two outcomes passes above the curve: at expected assets of Rs 800 crore the payoff is zero, but expected equity is Rs 200 crore.
    The relationship
    E[max⁡(A−D,0)]=12max⁡(200−1000,0)+12max⁡(1400−1000,0)=0+200=200E[\max(A - D, 0)] = \tfrac{1}{2}\max(200-1000,0) + \tfrac{1}{2}\max(1400-1000,0) = 0 + 200 = 200
    Aasset value next year, Rs 200 or Rs 1,400 crore
    Ddebt due, Rs 1,000 crore
    max(A - D, 0)what shareholders receive; never negative
    What it says in wordsTake what equity gets in each outcome, floored at zero, and average those, rather than averaging the assets first.

    Who pays for the equity's value, and why does it matter in practice?

    Assets are worth Rs 800 crore on average, and equity takes Rs 200 crore of that, so the debt is worth Rs 600 crore against Rs 1,000 crore owed. Equity's option value is paid for by the lenders, which is why shareholders of a distressed company prefer riskier bets: more spread raises the option's value and pushes more of the downside onto the debt. If the outcomes were Rs 0 or Rs 1,600 crore, the same Rs 800 crore average would give equity Rs 300 crore. That is the answer to why a distressed company's stock can trade well above zero, and why lenders write covenants to stop management gambling.

    State the limits. Ignoring discounting, and treating the odds as known, keeps the arithmetic clean; a real valuation would use risk-neutral probabilities and a time value, which is what an option pricing model does. And the debt is assumed to be one bullet due next year; covenants that let lenders take control earlier would cut the equity's option short.

    Where candidates lose it

    The fast wrong answer is zero, or a negative number, from netting Rs 1,000 crore of debt against Rs 800 crore of average assets. It forgets that shareholders cannot owe more than they put in, and that floor is the entire source of value.

    The second trap is getting Rs 200 crore but not naming the mechanism. Say the words call option, struck at the debt, and add who pays for it: the lenders. That is the sentence the interviewer is listening for.

    What the interviewer asks next

    • If the outcomes were Rs 0 or Rs 1,600 crore, what would the equity be worth?
    • Why might management of this company take on a riskier project with a lower expected value?
    • What covenant would you write into the debt to protect against that?

    Asked at Silver Lake, Technology, Media and Telecom, San Francisco, 2022 (Wall Street Oasis): Why would a distressed company have a high equity value?

  5. 065An online aptitude test has 50 questions in 12 minutes, five options each, and no penalty for wrong answers. You can answer about 30 questions carefully in the time, at 85% accuracy. Should you guess the other 20, and what is your expected score?Mental maths and speed testsWarm upVista Equity PartnersAustin · 2022

    Try it first

    What is your expected score if you guess the last 20?

    Show the worked solution

    Yes, guess every remaining question; the expected score rises from 25.5 to 29.5. Your 30 careful answers at 85% are worth 25.5 points. A blind guess on a five-option question is right one time in five, and a wrong answer costs nothing, so 20 guesses add 20 x 0.2, or 4 expected points. A blank is a sure zero. The only real decision is leaving yourself the last 30 seconds to fill them in.

    Why is a blind guess worth anything at all?

    A free raffle ticket is worth taking even if the odds are poor, because it costs nothing. When wrong answers carry no penalty, every guess has a positive expected value, one point times the chance of being right, and a blank has an expected value of exactly zero. With five options that chance is 1 in 5, so each guess is worth 0.2 points and twenty are worth 4. On a 50-question test, 4 points is often the gap between two scoring bands.

    Blind guesses add 4 points for free when wrong answers cost nothingLeave 20 blank25.5 careful25.5Guess the last 2025.5 careful+429.501020304050Expected correct answers out of 50Time budget: 12 minutes / 50 questions = 14.4 seconds each. Save the last 30 seconds to fill blanks.
    Thirty careful answers at 85% give 25.5 expected points, and filling the remaining 20 with blind guesses adds 20 x 0.2 = 4 more, lifting the expected score to 29.5 at no cost because wrong answers are not penalised.
    The relationship
    E[score]=30×0.85+20×15=25.5+4=29.5E[\text{score}] = 30 \times 0.85 + 20 \times \tfrac{1}{5} = 25.5 + 4 = 29.5
    30 x 0.85careful answers times your accuracy
    20 x 1/5blind guesses times the chance a random pick is right
    What it says in wordsAdd what the careful answers are worth to what the guesses are worth; blanks add nothing.

    What changes if wrong answers are penalised, and how do you manage the clock?

    Suppose a wrong answer cost a quarter of a point. A blind guess would then be worth 0.2 minus 0.8 x 0.25, which is exactly zero. The rule is to guess whenever the chance of being right times the reward beats the chance of being wrong times the penalty, and eliminating even one option tips a penalised guess back into positive value. On the clock: 12 minutes for 50 questions is 14.4 seconds each. Skip any question that will take more than about 30 seconds, come back if time allows, and stop answering carefully with half a minute left to fill every blank.

    Two honest notes. The 4 points are an average: 20 guesses have a standard deviation of about 1.8 points, and there is roughly a 1% chance none of them land. And the no-penalty rule is the premise of this question; tests differ, so check the instructions of the one you are sitting before deciding.

    Where candidates lose it

    The trap is leaving blanks out of a sense that guessing is unserious. On a no-penalty test that throws away free expected points, and the people who score well on these tests always fill every answer.

    The second loss is spending too long on hard questions early. At 14.4 seconds a question, one stubborn item can cost you three easy ones; skip, mark and return.

    What the interviewer asks next

    • If a wrong answer cost a quarter point, would you still guess?
    • You can eliminate one option on each of the 20. What is the guess value now?
    • Would you rather answer 35 at 75% accuracy or 30 at 85%?

    Asked at Vista Equity Partners, Technology, Media and Telecom, Austin, 2022 (Wall Street Oasis): Application requires a CCAT, 50 questions in 12 minutes.

  6. 071Business A costs 10x earnings, grows earnings 5% a year, and still trades at 10x in ten years. Business B costs 25x earnings, grows earnings 20% a year, and trades at only 15x in ten years. Ignoring dividends, which makes you more money over the ten years, and at what annual rate?Valuation riddlesCoreCoatue ManagementNew York · 2023

    Try it first

    Which business returns more over ten years?

    Show the worked solution

    B, about 3.72x or 14% a year, against 1.63x or 5% a year for A. Your return is earnings growth times the change in multiple. A's earnings grow 1.05 to the tenth, 1.63x, and its multiple stays at 10x, so you make 1.63x. B's earnings grow 1.2 to the tenth, 6.19x, and its multiple falls from 25x to 15x, a factor of 0.6, so you make 3.72x. B's multiple could fall to 6.6x and still match A.

    How do you split a ten-year return into its parts?

    A flat bought cheap in a stagnant town can earn less than one bought dear in a fast-growing suburb, even if the suburb's prices later cool. Ignoring dividends, the return on a business is the growth in its earnings times the change in the multiple the market pays for them, so a high starting multiple only hurts if earnings growth cannot outrun the fall in that multiple. A gets 1.63 x 1.0. B gets 6.19 x 0.6. Ten years of 20% growth multiplies earnings by over six, which swamps the 40% multiple compression.

    Paying up for growth beats a bargain that barely grows0x1x2x3x4xYr 0Yr 2Yr 4Yr 6Yr 8Yr 10B: 3.72x, 14% a yearA: 1.63x, 5% a yearA: cheap, slowearnings x 1.63multiple 10x to 10x: x 1.0= 1.63xB: dear, fastearnings x 6.19multiple 25x to 15x: x 0.6= 3.72xbreak-even exit: 6.6xValue of Rs 1 invested, before dividends.
    Rs 1 in the 10x business growing 5% becomes 1.63x in ten years, while Rs 1 in the 25x business growing 20% becomes 3.72x even after its multiple falls to 15x, because earnings growth of 6.19x outruns the 0.6 multiple factor.
    The relationship
    M=(1+g)10×P/EexitP/Eentry:A=1.0510×1010=1.63,B=1.210×1525=3.72M = (1+g)^{10} \times \frac{P/E_{\text{exit}}}{P/E_{\text{entry}}}: \quad A = 1.05^{10} \times \tfrac{10}{10} = 1.63, \quad B = 1.2^{10} \times \tfrac{15}{25} = 3.72
    gannual earnings growth
    P/E entry, exitthe price-to-earnings multiple paid and received
    Mmoney multiple over ten years
    What it says in wordsMultiply how much earnings grew by how much the multiple changed; the annual rate is the tenth root of the result.

    When does the cheap business win instead?

    Three cases. If B's growth fades early, the answer flips: at 10% a year, B's earnings grow only 2.6x and 2.6 x 0.6 is about 1.55x, below A. If A pays out its earnings as dividends, a 10x multiple means a 10% earnings yield, and reinvesting that cash adds a lot that this sum leaves out; B, growing at 20%, likely reinvests everything. And if the growth never arrives, B's price has nothing to fall back on. The honest answer to a 'great price or great business' question is that it turns on how long and how surely the better business keeps growing.

    Give the interviewer a number that frames the judgement: B's exit multiple could fall all the way to 6.6x and still match A's return. That margin, not the entry multiple, is the measure of how much you are overpaying.

    Where candidates lose it

    The common error is choosing A because 10x feels safe and the 40% multiple drop on B sounds painful. Candidates react to the entry price and never multiply out the earnings growth.

    The second trap is the opposite: declaring that quality always wins. Say the condition, growth that lasts, and give the break-even multiple, so the answer reads as a judgement rather than a slogan.

    What the interviewer asks next

    • If A pays out all its earnings as dividends and you reinvest them at 10%, does the answer change?
    • At what growth rate does B only match A?
    • Which of B's numbers would you test hardest in diligence?

    Asked at Coatue Management, Technology, Media and Telecom, New York, 2023 (Wall Street Oasis): Would you rather buy a low quality business at a great price or a high quality business at an ok price?

  7. 091If you were to open a restaurant, the first concern is whether it can cover its costs. A 60-seat restaurant pays rent of Rs 3 lakh, staff costs of Rs 4 lakh and other fixed costs of Rs 1 lakh a month. The average bill is Rs 600 a cover and food costs 35% of the bill. How many covers a day does it need to break even, and how many table turns is that?Market sizing and estimationCoreGeneral AtlanticBeijing · 2014

    Try it first

    Roughly how many covers a day does it need?

    Show the worked solution

    About 68 covers a day, a little over one turn of its 60 seats. Each cover leaves Rs 390 once food is paid for. Fixed costs are Rs 8 lakh a month, so the restaurant needs 8,00,000 / 390 = 2,051 covers a month, or 68.4 a day over 30 days. That is 1.14 turns. Open 26 days a month and the bar rises to about 79 a day.

    What does each cover actually contribute?

    A tea stall that sells a cup for Rs 15 and spends Rs 5 on milk, leaves and sugar has Rs 10 a cup to pay its rent and wages. Break-even is fixed costs divided by contribution per unit, the price less the cost that rises with each unit, never fixed costs divided by the full price. Here a Rs 600 bill with 35% food cost leaves Rs 390 a cover. The rent, the staff and the other Rs 1 lakh do not change with covers, so they add to Rs 8 lakh a month that the Rs 390s must clear.

    Break-even comes at about 68 covers a day, a little over one turn4812160306090120Covers a dayRs lakh a month1 turn = 60 coversFixed costs: Rs 8 lakh a monthContribution, Rs 390 a coverBreak-even: 68.4 a daylossprofitPer cover600 x (1 - 35%) = Rs 390Covers a month8,00,000 / 390 = 2,051Covers a day, 30 days2,051 / 30 = 68.4Turns of 60 seats68.4 / 60 = 1.14
    Contribution of Rs 390 a cover over 30 days crosses Rs 8 lakh of monthly fixed costs at 68.4 covers a day, so the 60-seat restaurant loses money until it fills every seat a little more than once a day, 1.14 turns.
    The relationship
    c∗=Fp(1−f) d=8,00,000600×0.65×30≈68.4c^{*} = \frac{F}{p(1-f)\,d} = \frac{8{,}00{,}000}{600 \times 0.65 \times 30} \approx 68.4
    c*covers a day needed to break even
    Ffixed costs a month, Rs 8 lakh
    paverage bill, Rs 600
    ffood cost as a share of the bill, 35%
    dtrading days a month, 30
    What it says in wordsDivide the month's fixed costs by what each cover leaves after food, then by the days the restaurant is open.

    Is one turn a day an easy bar or a hard one?

    It depends on the meals the restaurant serves. A place open for lunch and dinner gets two chances to fill the room; at 1.14 turns it needs each seat filled a little over once across both services. The sensitivity matters more than the point estimate: if the average bill falls to Rs 500, the bar rises to 82 covers a day, and if it closes four days a month it rises to about 79. At 90 covers a day it earns about Rs 2.5 lakh a month before tax, which shows how much of each extra cover falls to profit once fixed costs are covered.

    What else would an investor ask about?

    This puzzle leaves out costs that scale with sales besides food: delivery platform commissions, card fees and electricity on busy nights. Each one lowers the Rs 390 and raises the break-even. Then there is the opening cost, the fit-out and deposit, which break-even ignores but payback does not. A growth investor asks the same three questions of a chain: what each outlet contributes per cover, how many covers a mature outlet does, and how long a new one takes to get there.

    Where candidates lose it

    The common slip is dividing fixed costs by the full Rs 600 bill, which gives about 44 covers a day. Food is paid out of every bill before anything is left for rent, so the right divisor is Rs 390, and the answer is half as large again.

    The second loss is giving 68 covers and stopping. The interviewer asked about turns because covers alone mean nothing without the seat count: say 1.14 turns and whether that looks achievable for a lunch and dinner restaurant.

    What the interviewer asks next

    • Delivery is 30% of covers and the platform takes 25% of those bills. What is the new break-even?
    • How many covers a day would pay back a Rs 60 lakh fit-out in two years?
    • What would you want to know before backing a chain of these restaurants?

    Asked at General Atlantic, Generalist, Beijing, 2014 (Wall Street Oasis): If you were to open a restaurant, what are some key concerns?

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