Venture Capital puzzles, solved step by step

Puzzles: 100
Traced to a firm: 7
Topics: 12
Hard: 30

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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.
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
$\text{BM} = \frac{3 \times 3.1}{6.2} = 1.5 \qquad \text{Runway} = \frac{55}{3.1} \approx 17.7 \text{ months}$
3 x 3.1 net burn over one quarter, Rs crore
6.2 net new ARR added in the quarter, Rs crore
55 cash 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
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.
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
$M = (1+g)^{10} \times \frac{P/E_{\text{exit}}}{P/E_{\text{entry}}}: \quad A = 1.05^{10} \times \tfrac{10}{10} = 1.63, \quad B = 1.2^{10} \times \tfrac{15}{25} = 3.72$
g annual earnings growth
P/E entry, exit the price-to-earnings multiple paid and received
M money 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?
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.
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
$c^{*} = \frac{F}{p(1-f)\,d} = \frac{8{,}00{,}000}{600 \times 0.65 \times 30} \approx 68.4$
c* covers a day needed to break even
F fixed costs a month, Rs 8 lakh
p average bill, Rs 600
f food cost as a share of the bill, 35%
d trading 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?

3 x 3.1	net burn over one quarter, Rs crore
6.2	net new ARR added in the quarter, Rs crore
55	cash in the bank, Rs crore

g	annual earnings growth
P/E entry, exit	the price-to-earnings multiple paid and received
M	money multiple over ten years

c*	covers a day needed to break even
F	fixed costs a month, Rs 8 lakh
p	average bill, Rs 600
f	food cost as a share of the bill, 35%
d	trading days a month, 30

Try it first

How do you multiply by 1.65 without a calculator?

Why does the burn multiple need care before any arithmetic?

What do you say once the three numbers are out?

Where candidates lose it

What the interviewer asks next

Try it first

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

When does the cheap business win instead?

Where candidates lose it

What the interviewer asks next

Try it first

What does each cover actually contribute?

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

What else would an investor ask about?

Where candidates lose it

What the interviewer asks next