Venture Capital puzzles, solved step by step

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

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023A marketplace processes Rs 1,000 crore of GMV a year at a 12% take rate. Payment costs are 2% of GMV and refunds the platform absorbs are 1% of GMV. It is valued at 1x GMV. What is its contribution margin, and what multiples of revenue and of contribution is it valued at?SaaS and unit economics riddlesCoreConsumer internet VCIndia VC
Try it first
What multiple of contribution is the Rs 1,000 crore valuation?
Show the worked solution
Contribution is Rs 90 crore, a 75% margin on revenue, and the company is valued at 8.3x revenue and 11.1x contribution. A 12% take rate on Rs 1,000 crore of GMV is Rs 120 crore of revenue. Payment costs of Rs 20 crore and refunds of Rs 10 crore leave Rs 90 crore. The 1x GMV headline is the same price as 8.3x revenue.
Why is GMV not the company's revenue?
A property broker who helps sell a Rs 1 crore flat does not earn Rs 1 crore; she earns her commission. GMVGross merchandise value: the total value of goods or services sold through a marketplace, before the platform takes its cut. is the value flowing through the platform, and only the take rate, here 12%, is the platform's revenue. On Rs 1,000 crore of GMV that is Rs 120 crore. The other Rs 880 crore belongs to sellers, so a multiple of GMV prices something the company never keeps.
What is left after the costs that scale with every order?
Payment processing costs 2% of GMV, Rs 20 crore, and refunds the platform absorbs cost 1%, Rs 10 crore. Both are charged on GMV but paid out of revenue, so a 3% cost on GMV eats a quarter of a 12% take rate. Contribution is Rs 90 crore: 75% of revenue, but only 9% of GMV. This is the money available to pay for marketing, salaries and offices, and eventually profit.
The relationship
$C = 1{,}000 \times (0.12 - 0.02 - 0.01) = 90 \qquad \frac{1{,}000}{120} = 8.3\times \qquad \frac{1{,}000}{90} = 11.1\times$
C contribution, Rs crore
0.12 take rate on GMV
0.02, 0.01 payment costs and refunds as shares of GMV
What it says in wordsSubtract the per-order costs from the take rate, apply it to GMV, then divide the valuation by each line.
Of Rs 1,000 crore of GMV, only Rs 120 crore is revenue, and payment costs and refunds bring it down to Rs 90 crore of contribution, so a 1x GMV valuation is 8.3x revenue and 11.1x contribution.
What would you say about the valuation?
That the headline multiple flatters the price, and the real question is what the contribution can grow into. Paying 11.1x contribution is reasonable only if contribution grows fast or the take rate can rise without losing sellers. Two marketplaces at 1x GMV can be wildly different prices: one with a 25% take rate is valued at 4x revenue, one with a 5% take rate at 20x. Always convert GMV multiples into revenue and contribution before comparing companies.
Where candidates lose it
The trap is treating 1x GMV as cheap, as if GMV were revenue. The interviewer wants to hear you convert it before you judge it.
The second slip is taking the payment and refund costs as percentages of revenue rather than of GMV, which gives Rs 116.4 crore of contribution and a 8.6x multiple. Read which base each cost is quoted on.
What the interviewer asks next
If the take rate rises to 15% with no change in costs, what is the contribution multiple?
How would you compare this marketplace with one valued at 0.5x GMV and a 6% take rate?
Which costs below contribution matter most for a marketplace, and why?
046A software company offers a monthly plan at price p with 4% monthly churn, or an annual plan paid upfront at a 20% discount. Which brings in more revenue per customer in the first year?SaaS and unit economics riddlesCoreSaaS-focused VCSeed and early-stage VC
Try it first
Over the first year, how does expected revenue per customer compare?
Show the worked solution
They are almost equal: about 9.68p a year on the monthly plan against 9.6p on the annual plan. The monthly customer pays p in month one and is still paying with probability 0.96 to the k in month k plus one, so twelve months add to about 9.68p. The annual customer pays 12 x 0.8p, 9.6p, upfront. With revenue a near tie, the cash on day one and the lower churn of a committed customer decide it for annual.
How do you count revenue from a customer who might leave?
A gym that sells monthly memberships cannot count on twelve payments from every member who joins in January, because some stop coming in March. Expected revenue from a monthly customer is each month's price times the chance they are still a customer that month, added up. With 4% churn, the chance of still paying in month k plus one is 0.96 to the k: 1 in the first month, 0.96 in the second, and 0.61 by the twelfth. Twelve terms of a shrinking series add to about 9.68p, not 12p.
The relationship
$\sum_{k=0}^{11} 0.96^{k} \, p = \frac{1 - 0.96^{12}}{0.04}\, p \approx 9.68p \qquad 12 \times 0.8p = 9.6p$
p the monthly list price
0.96 the chance a customer stays from one month to the next
0.8p the discounted monthly price on the annual plan
What it says in wordsA year of monthly revenue is a shrinking series of payments; the annual plan is twelve discounted payments collected at once.
A monthly customer's expected payments shrink from p to 0.64p over the year and add to 9.68p, almost the same as the 9.6p an annual customer pays upfront, so the revenue difference is under 1%.
If revenue is a near tie, what decides it?
Everything the revenue sum leaves out. The annual plan collects 9.6p on day one, which funds growth without new equity, while the monthly plan collects its 9.68p over twelve months. Annual customers also cannot churn mid-year, and at renewal they tend to churn less than monthly customers, so year two favours annual too. The break-even is close: at monthly churn of 4.16% the two plans give the same first-year revenue, so at any churn above that the annual plan wins on revenue as well.
What could make the comparison misleading?
The sum assumes the same customer would choose either plan. In practice the customers who pick annual plans are already the more committed ones, so their lower churn is partly selection, not a result of the plan. A founder who shows that annual customers churn less is showing a correlation; the useful question is what happens to churn when the company pushes hesitant customers onto annual terms. The other limit is the discount itself: at 20% it is roughly break-even, but a deeper discount gives revenue away for cash that may be cheaper to raise elsewhere.
Where candidates lose it
The common loss is comparing 12p with 9.6p and declaring the monthly plan 25% better, as if no one churned. The question gave you the churn rate so that you would weight each month's payment by the chance the customer is still there.
The second loss is getting the near tie and stopping. The interviewer wants the tie-breakers: cash upfront, no mid-year churn, and the selection effect that flatters annual customers.
What the interviewer asks next
At what discount would the annual plan bring in exactly the same first-year revenue at 4% churn?
How would you compare the two plans over three years rather than one?
Why might a company report annual contracts as better retention when it is partly selection?
078A customer pays Rs 10,000 a month at an 80% gross margin, churns at 2% a month, and costs Rs 1.2 lakh to acquire. What are lifetime value and LTV to CAC, first undiscounted and then discounting at 2% a month?SaaS and unit economics riddlesCoreSaaS-focused VCSeries A to C VC
Try it first
Before working it: what does discounting at 2% a month do to the LTV here?
Show the worked solution
Undiscounted, LTV is Rs 4 lakh and LTV to CAC is 3.3; discounted at 2% a month, LTV is Rs 2 lakh and the ratio is 1.7. Gross profit is Rs 8,000 a month and 2% churn means an average life of 50 months, so 8,000 x 50 is Rs 4 lakh. Discounting adds the 2% rate to the 2% churn, so LTV becomes 8,000 over 0.04, which is Rs 2 lakh.
Why is the average customer life one over the churn rate?
A gym that loses 2 of every 100 members each month, month after month, keeps the average member for 50 months: some leave in the first month, some stay ten years, and the steady 2% leak averages out to one over 0.02. With a constant monthly churn c, the expected customer life is 1 / c months, and lifetime value is the monthly gross profit times that life. Use gross profit, not revenue: Rs 10,000 at 80% margin is Rs 8,000 a month, and 8,000 x 50 is Rs 4 lakh, against a Rs 1.2 lakh acquisition cost, a ratio of 3.3.
Monthly gross profit per customer starts at Rs 8,000 and decays by 2% a month, an area of Rs 4.0 lakh; discounting each month at 2% as well makes the stream decay twice as fast, halving the area to Rs 2.0 lakh and taking LTV to CAC from 3.3 to 1.7.
What does discounting do to a stream that already decays?
A rupee of gross profit in month 40 is worth about 0.45 today at 2% a month. When churn and the discount rate are both monthly rates, discounted LTV is monthly gross profit divided by churn plus the discount rate, because each month the stream shrinks by survival and by time together. Here that is 8,000 / (0.02 + 0.02), exactly Rs 2 lakh if each month's profit arrives at the month end.
The relationship
$\text{LTV} = \frac{m}{c + r} = \frac{8{,}000}{0.02 + 0.02} = 2{,}00{,}000$
m monthly gross profit per customer, Rs 8,000
c monthly churn, 2%
r monthly discount rate, 2%
What it says in wordsDivide monthly gross profit by the total rate at which it leaks away, through customers leaving and through time.
Is 2% a month a fair rate? It compounds to about 27% a year, a venture-style hurdle rather than a bank rate, so the halving here is at the harsh end. The point survives a gentler rate: a ratio that looks comfortable at 3.3 can sit much closer to 1 once time is priced, and the 15-month payback on gross profit is often the more honest single number to quote alongside it.
Where candidates lose it
The first loss is using revenue: Rs 10,000 x 50 gives Rs 5 lakh and a ratio of 4.2, which flatters the business by a quarter. A customer's value to the company is the gross profit they leave behind, not the invoice.
The second is saying churn already handles time. Churn counts customers who leave; discounting prices the wait for the ones who stay. Leave either out and the ratio looks healthier than the cash.
What the interviewer asks next
What monthly churn gives an undiscounted LTV to CAC of exactly 3?
Price rises 10% a year for customers who stay. How does that change the formula?
Why might a seed investor care more about payback months than LTV to CAC?
100A software company's quarterly revenue rose from Rs 25 crore to Rs 30 crore. Its sales and marketing spend in the previous quarter was Rs 16 crore. What is its magic number, and what does it become if Rs 2 crore of the increase was one-off implementation services?SaaS and unit economics riddlesCoreSaaS-focused VCSeries A to C VC
Try it first
With the one-off services taken out, what is the magic number?
Show the worked solution
1.25 on the headline numbers, and 0.75 once the one-off services are removed. The magic number is the quarter's revenue increase, annualised, divided by the previous quarter's sales and marketing spend. Headline: Rs 5 crore x 4 = Rs 20 crore over Rs 16 crore is 1.25. But only Rs 3 crore will recur; Rs 12 crore over Rs 16 crore is 0.75. Two crore of services flattered the efficiency by two thirds.
What is the magic number measuring?
A coaching centre that spends Rs 1.6 lakh on advertising one month and signs students paying an extra Rs 50,000 a month in fees has bought Rs 6 lakh a year of fees for Rs 1.6 lakh. The magic number is the annualised increase in recurring revenue divided by the sales and marketing spend that produced it, usually the previous quarter's. It is a quick read on how efficiently a company turns sales spend into new revenue. Annualise because the spend buys a full year of revenue from each new customer, not just one quarter.
Quarterly revenue rose by Rs 5 crore, of which Rs 3 crore recurs and Rs 2 crore was one-off services, so against Rs 16 crore of prior-quarter sales and marketing the magic number is 1.25 on the headline but 0.75 on recurring revenue alone.
The relationship
$\text{MN} = \frac{4\,(R_t - R_{t-1})}{S_{t-1}} = \frac{4 \times 5}{16} = 1.25 \qquad \frac{4 \times 3}{16} = 0.75$
R_t recurring revenue in the quarter, Rs crore
S_{t-1} sales and marketing spend in the previous quarter
4 annualises a quarterly increase
What it says in wordsAnnualise the new recurring revenue and divide by the sales spend that bought it.
Why does the one-off revenue matter so much?
Because the measure is built on a small difference. A Rs 2 crore swing in a Rs 5 crore increase is 40% of the numerator, so a one-off item moves the magic number far more than it moves revenue. Read as recurring revenue, a magic number of 1 means a year of the new revenue repays the quarter's sales spend; 1.25 suggests about 9.6 months, but the true 0.75 means about 16 months, and that is before the cost of serving the customers. Some investors multiply by gross margin for that reason: at a 75% margin the recurring figure becomes 0.56.
Ask three things before trusting the number: is the revenue recurring, is the spend fully counted, including sales salaries and commissions, and is one quarter representative. A single strong quarter can follow a deal that slipped from the quarter before, so investors look at a rolling average across several quarters.
Where candidates lose it
The first slip is forgetting to annualise: 5 over 16 gives 0.31 and makes a healthy sales engine look broken. The second is counting services revenue, which inflates the numerator with money that will not recur next quarter.
The interviewer included the Rs 2 crore precisely to see whether you ask what kind of revenue moved. Give both numbers, then say which one you would use and why.
What the interviewer asks next
If sales and marketing spend rises to Rs 20 crore and the recurring increase stays Rs 3 crore, what is the magic number?
How would you adjust the magic number for gross margin, and why?
Why might a company's magic number fall as it grows, even with a good sales team?

C	contribution, Rs crore
0.12	take rate on GMV
0.02, 0.01	payment costs and refunds as shares of GMV

p	the monthly list price
0.96	the chance a customer stays from one month to the next
0.8p	the discounted monthly price on the annual plan

m	monthly gross profit per customer, Rs 8,000
c	monthly churn, 2%
r	monthly discount rate, 2%

R_t	recurring revenue in the quarter, Rs crore
S_{t-1}	sales and marketing spend in the previous quarter
4	annualises a quarterly increase

Try it first

Why is GMV not the company's revenue?

What is left after the costs that scale with every order?

What would you say about the valuation?

Where candidates lose it

What the interviewer asks next

Try it first

How do you count revenue from a customer who might leave?

If revenue is a near tie, what decides it?

What could make the comparison misleading?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the average customer life one over the churn rate?

What does discounting do to a stream that already decays?

Where candidates lose it

What the interviewer asks next

Try it first

What is the magic number measuring?

Why does the one-off revenue matter so much?

Where candidates lose it

What the interviewer asks next