Venture Capital puzzles, solved step by step

Puzzles
100
Traced to a firm
7
Topics
12
Hard
30
Topic
All topicsPower law and portfolio maths10SaaS and unit economics riddles10Probability and expected value10Dilution and ownership riddles9Fund economics riddles8Market sizing and estimation9Growth and compounding8Valuation riddles9Preferences, payouts and protections8Logic and brainteasers6Mental maths and speed tests7Decision and game theory6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–3 of 3 · filtered from 100Clear filters
  1. 014It costs Rs 1.2 lakh in sales and marketing to acquire a customer who pays Rs 10,000 a month, at a 75% gross margin. What is the CAC payback period?SaaS and unit economics riddlesWarm upSaaS-focused VCSeries A to C VC

    Try it first

    Pick the payback period.

    Show the worked solution

    16 months. The customer pays Rs 10,000 a month, but at a 75% gross margin only Rs 7,500 of that is left after the cost of serving them. That gross profit is what repays the Rs 1.2 lakh spent to win the customer, and 1,20,000 divided by 7,500 is 16 months. Dividing by revenue instead gives 12 months, which flatters the business by a third.

    Why does payback use gross profit and not revenue?

    A tea stall that spends Rs 1,200 on a signboard has not earned it back when it has sold Rs 1,200 of tea, because the milk, sugar and gas cost money too. CAC is repaid only by what the customer leaves behind after the cost of serving them, which is gross profit, not revenue. Here the cost of hosting, support and payment processing takes a quarter of each month's Rs 10,000, leaving Rs 7,500 to pay back the Rs 1.2 lakh.

    The relationship
    Payback=CACMRR×GM=1,20,00010,000×0.75=16 months\text{Payback} = \frac{\text{CAC}}{\text{MRR} \times \text{GM}} = \frac{1{,}20{,}000}{10{,}000 \times 0.75} = 16 \text{ months}
    CACsales and marketing cost to win one customer
    MRRmonthly recurring revenue from that customer
    GMgross margin, the share of revenue left after the cost of serving
    What it says in wordsDivide what it cost to win the customer by the gross profit the customer leaves each month.
    Payback is measured in gross profit, so it lands at month 16, not 120.5 lakh1.0 lakh1.5 lakh2.0 lakhCAC Rs 1.2 lakhRevenue: month 12 (wrong)Gross profit: month 16revenue, Rs 10,000 a monthgross profit, Rs 7,500 a month048121620Months since the customer signed
    Cumulative revenue of Rs 10,000 a month reaches the Rs 1.2 lakh acquisition cost at month 12, but cumulative gross profit of Rs 7,500 a month only reaches it at month 16, which is the real payback period.

    What does 16 months tell an investor?

    It says how long the company's cash is tied up in each new customer. A company that grows fast with a 16-month payback consumes cash for well over a year on every customer it adds, so faster growth means a bigger cash need, not a smaller one. Many SaaS investors treat payback under about 12 to 18 months as healthy for mid-market customers, though the benchmark moves with customer size and churn. If this customer stays four years, it leaves Rs 3.6 lakh of gross profit, three times its acquisition cost.

    Name the limitation as well. The simple payback assumes the customer never leaves. If 2% of customers churn each month, the average customer takes about 19 months to repay its CAC, because some leave before they have paid back.

    Where candidates lose it

    Dividing Rs 1.2 lakh by Rs 10,000 and saying 12 months is the whole trap. It ignores the cost of serving the customer, and the interviewer included the margin precisely to see whether you use it.

    The quieter loss is giving 16 and stopping. Add one line on what it means for cash and one on churn, and the answer sounds like an investor rather than a calculator.

    What the interviewer asks next

    • With 2% monthly churn, how long does the average customer take to pay back?
    • The company raises prices 10% with no change in costs. What is the new payback?
    • Why might a company with a 30-month payback still be a good investment?
  2. 057A software company grows revenue 70% a year with a free cash flow margin of minus 45%. What is its Rule of 40 score, and what margin would it need to reach 40 if growth falls to 50%?SaaS and unit economics riddlesWarm upSaaS-focused VCGrowth equity

    Try it first

    If growth falls to 50%, what free cash flow margin reaches 40?

    Show the worked solution

    A score of 25 today, and a margin of minus 10% to reach 40 at 50% growth. The Rule of 40 adds revenue growth and free cash flow margin: 70 plus minus 45 is 25. If growth slows to 50 and the burn stays at minus 45, the score falls to 5. To get back to 40 the margin must rise to minus 10, a 35 point improvement in a year when growth is also slowing.

    What does adding growth to margin actually measure?

    A cricket team can win on runs scored or on runs saved; a selector looks at the margin of victory, not either number alone. The Rule of 40A rough test for software companies: revenue growth % plus free cash flow margin % should reach at least 40. treats growth and cash generation as substitutes, so a company may burn cash only to the extent that its growth pays for the burn. Today this company grows 70 and burns 45, for a score of 25: it is spending more than its growth justifies. A company growing 20 with a 20% margin also scores 40 and passes, which is the point: the test does not care which mix you choose.

    Growth climbs the bar, the cash burn pulls it back down020406080Rule of 40+70-45TodayScore 25+50-45Growth slows, burn unchangedScore 5+50-10Growth slows, burn cutScore 40Green: revenue growth %. Red: free cash flow margin %. Black line: growth plus margin, the score.
    Growth of 70 less a burn of 45 scores 25; if growth slows to 50 with the burn unchanged the score sinks to 5, and only cutting the margin to minus 10 lifts it back to exactly 40.
    The relationship
    g+m≥40  ⇒  m≥40−50=−10%g + m \ge 40 \;\Rightarrow\; m \ge 40 - 50 = -10\%%
    grevenue growth, % a year
    mfree cash flow margin, % of revenue
    What it says in wordsSubtract the growth you have from 40 and what remains is the worst margin you can run.

    Why is the slowdown the dangerous part of this question?

    Growth rarely falls while the cost base shrinks on its own. When growth drops 20 points with the burn unchanged, the score falls from 25 to 5, and the company has to find 35 points of margin to make up for it. Those points come from cutting sales hiring and marketing, which is often what was producing the growth, so the cut can slow growth further. Say this in the room: the score is easy to compute, the hard part is whether the company can move margin that far without breaking the growth engine.

    State the limits too. The rule is a rule of thumb from listed software companies; applied to an early company growing 200% it says little, because small numbers make growth rates swing. Which margin you use matters as well, free cash flow or EBITDA, and companies quote whichever flatters them, so ask which one is in the deck.

    Where candidates lose it

    The common error is answering plus 10%, as if the company must turn profitable. The margin is negative and can stay negative: 50 plus minus 10 is 40. Getting the sign wrong tells the interviewer you computed without looking at the setup.

    The second loss is stopping at the number. The real point is that a 35 point margin swing in a slowing year is a large ask; say whether it looks achievable and what it would cost in growth.

    What the interviewer asks next

    • Which margin would you use, free cash flow or EBITDA, and why does it matter here?
    • Is the Rule of 40 useful for a company growing 200% from a small base?
    • What spending would you cut first to move the margin from minus 45 to minus 10?
  3. 090A subscription business loses 3% of its customers every month. What is its annual churn? And what monthly churn would give an annual churn of 10%?SaaS and unit economics riddlesWarm upSaaS-focused VCConsumer internet VC

    Try it first

    Answer quickly: 3% monthly churn is how much a year?

    Show the worked solution

    About 30.6% a year, not 36%; and 10% a year needs monthly churn of about 0.87%. Each month keeps 97% of the customers still there, so a year keeps 0.97 to the power 12, which is 69.4%. Going the other way, 90% retention a year means a monthly retention of 0.9 to the power one twelfth, about 99.13%, so monthly churn of 0.87%. This counts one starting group of customers and ignores new sign-ups.

    Why is it not simply twelve times 3%?

    A water tank that loses 3% of what is in it every hour loses less each hour, because there is less water to lose. Monthly churn is a share of the customers still there, so it compounds on a shrinking base: the yearly survival rate is the monthly survival rate raised to the twelfth power. After six months 0.97 to the sixth leaves 83.3%, and after twelve 69.4%. Twelve times 3% would be right only if each month lost 3% of the original group, which nobody measures.

    Churn compounds on a shrinking base, so 3% a month is 30.6% a year60708090100036912MonthsCustomers left, out of 1000.87% a month: 90 left3% a month: 69.4 leftannual churn 30.6%Naive 3% x 12: 64 left
    Out of 100 customers, 3% monthly churn leaves 69.4 after a year, an annual churn of 30.6%, above the 64 a straight-line reading gives, while 0.87% monthly churn leaves 90, which is what a 10% annual churn means.
    The relationship
    cyr=1−(1−cmo)12cmo=1−(1−cyr)1/12c_{yr} = 1 - (1 - c_{mo})^{12} \qquad c_{mo} = 1 - (1 - c_{yr})^{1/12}
    c_momonthly churn, a share of the customers present at the start of the month
    c_yrannual churn of the starting group
    What it says in wordsConvert churn by compounding the survival rate, never by multiplying or dividing the churn rate.

    How do you get the monthly rate for 10% a year without a calculator?

    Dividing 10% by 12 gives 0.83%, and it is close because small rates compound gently. The exact figure is slightly higher, 0.87%, because the monthly losses come out of a shrinking base and so each month must lose a touch more to reach 10% in total. Say the division as a first estimate, then the correction. For large rates the gap grows: 3% a month gives 30.6% a year, against 36% by multiplication.

    Why does an investor care which convention a company used?

    Because companies quote whichever looks better. A business that reports 3% monthly churn and 30.6% annual churn is internally consistent; one that reports 3% monthly and 25% annual is either measuring different customers or counting new sign-ups against losses. Ask what base the churn is measured on and whether it counts logos or revenue, since revenue churn can be much lower when the customers who leave are the small ones.

    Where candidates lose it

    Saying 36% is the whole trap. It treats churn as a fixed number of customers lost each month, when it is a share of a shrinking base. The overstatement is more than five points here and grows with the rate.

    The reverse slip is dividing 10% by 12 and stating 0.83% as exact. It is a fine first estimate, but say that the true figure is a little higher and why.

    What the interviewer asks next

    • What annual churn does 5% a month give?
    • A company reports 2% monthly logo churn and 0.5% monthly revenue churn. What could explain the gap?
    • How long does a customer stay on average at 3% monthly churn?