Venture Capital puzzles, solved step by step

Puzzles: 100
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008You expect a company to exit at Rs 1,000 crore in six years and you need a 10x return on your cheque. Later rounds will dilute your stake by 40% before the exit. What is the highest post-money valuation you can pay today, and what ownership does a Rs 12 crore cheque need?Valuation riddlesCoreSeed and early-stage VCIndia VC
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What is the most you can pay, post-money?
Show the worked solution
A post-money of Rs 60 crore, and a Rs 12 crore cheque needs 20% of the company. Rs 1,000 crore divided by 10 is Rs 100 crore, but later rounds leave you with only 60% of your stake, so the price falls to Rs 60 crore. Rs 12 crore buys 20% at that price, which dilutes to 12% by the exit and is worth Rs 120 crore, exactly 10x.
Why work backwards from the exit?
A shop owner who knows a sari will sell for Rs 10,000 and needs to double her money can pay the weaver at most Rs 5,000. She starts at the selling price and divides. A venture investor does the same: start at the exit value, divide by the multiple you need, and what is left is the most the company can be worth when you buy in. Here that is Rs 1,000 crore over 10, Rs 100 crore, before you account for what later rounds do to your stake. This is often called the venture capital method.
Where does the dilution go in the chain?
Later rounds do not change the exit value; they shrink the share of it you own. If you hold 20% today and keep 60% of it, you own 12% at the exit. Because you only collect 60% of the stake you buy, the company must be priced at 60% of the undiluted figure for the maths to work, Rs 60 crore post-money rather than Rs 100 crore. Rs 12 crore at Rs 60 crore post is 20%, and the pre-money is Rs 48 crore.
The relationship
$\text{Post} = \frac{V_{exit} \times (1-d)}{M} = \frac{1{,}000 \times 0.60}{10} = 60 \qquad \text{own} = \frac{12}{60} = 20\%$
V_exit the expected exit value, Rs crore
d dilution from later rounds, 40%
M the return multiple you need
own the stake the cheque must buy today
What it says in wordsThe price you can pay today is the exit value you will actually own a share of, divided by the multiple you need.
Rs 1,000 crore at exit divided by 10x and multiplied by the 60% you keep gives a Rs 60 crore post-money, where Rs 12 crore buys 20%, dilutes to 12% and returns Rs 120 crore; paying Rs 100 crore instead buys 12%, dilutes to 7.2% and returns only Rs 72 crore, 6x.
What do you add to show judgement?
Translate the multiple into a yearly rate and question the inputs. 10x over six years is about 47% a year, and the whole answer leans on a single exit value that is far from certain. If only one company in three reaches that exit, the honest calculation uses an expected exit, and the price you can pay falls by the same factor. Saying that sentence turns a formula into an investment view.
Where candidates lose it
The trap is stopping at Rs 100 crore. It forgets that the investor's 20% will not still be 20% at the exit, and a candidate who pays that price earns 6x, not 10x.
The second slip is applying the dilution backwards, dividing by 0.60 to get Rs 166.7 crore. Ask yourself whether dilution should make you willing to pay more or less; the answer is less.
What the interviewer asks next
If the company reaches the Rs 1,000 crore exit only one time in three, what post-money can you pay?
You negotiate pro rata rights and keep your stake by investing in later rounds. How does that change the price today?
Why might a seed investor accept a lower target multiple than 10x?
020A company with no debt and no cash trades at 8x revenue and 40x earnings. Depreciation is 5% of revenue, there is no interest, and the tax rate is 25%. What are its net margin and its EBITDA margin?Valuation riddlesCoreGrowth equitySaaS-focused VC
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What is the net margin?
Show the worked solution
The net margin is 20% and the EBITDA margin is about 31.7%. With no debt or cash, enterprise and equity value are the same, so 8x revenue equals 40x earnings and earnings are 8/40 of revenue. Grossing up 20% for 25% tax gives a pre-tax and EBIT margin of 26.7%, and adding back 5% of depreciation gives 31.7%.
How can two multiples give a margin?
If a flat sells for 25 times its yearly rent and 5 times the owner's yearly income from all sources, rent must be one fifth of that income, without knowing the price. When two multiples price the same value, dividing one by the other gives the ratio of their denominators. Here 8x revenue and 40x earnings price the same equity, because a company with no debt and no cash has enterprise value equal to equity value. So earnings over revenue is 8 over 40, a 20% net margin.
The relationship
$\frac{E}{R} = \frac{8}{40} = 20\% \qquad \text{EBITDA} = \frac{20\%}{1 - 0.25} + 5\% = 31.7\%$
E/R earnings over revenue, the net margin
8, 40 value over revenue and value over earnings
0.25 the tax rate
5% depreciation as a share of revenue
What it says in wordsDivide the revenue multiple by the earnings multiple for the net margin, then gross up for tax and add back depreciation.
On Rs 100 of revenue the company is worth Rs 800, so at 40x its earnings are Rs 20; grossing that up for 25% tax gives EBIT of Rs 26.7, and adding back Rs 5 of depreciation gives EBITDA of Rs 31.7, a 31.7% margin.
How do you climb from net profit back to EBITDA?
Undo each deduction in reverse order. Tax is 25% of pre-tax profit, so net profit is 75% of it, and pre-tax profit is 20% divided by 0.75, about 26.7% of revenue. With no interest, pre-tax profit equals EBIT. Adding back depreciation of 5% gives EBITDA of 31.7% of revenue. A common slip is grossing up by 1.25 instead of dividing by 0.75, which gives 25% instead of 26.7%.
Does the answer make sense for a company priced like this?
Check with a third multiple. The EV/EBITDA is 8 divided by 0.317, about 25.3x. A 20% net margin with a 40x earnings multiple describes a profitable business that the market expects to keep growing quickly, which is the profile of a mature software company rather than an early startup. Say the assumption that made the trick work, no debt and no cash; with net debt, EV and equity value differ and you need the balance sheet to link them.
Where candidates lose it
Candidates reach for a share price or revenue figure that the question never gave. The insight is that the two multiples share a numerator, so their ratio is the margin; say that first.
The second loss is the gross-up. Net profit is 75% of pre-tax profit, so divide by 0.75; multiplying by 1.25 understates EBIT and EBITDA.
What the interviewer asks next
If the company had net debt equal to 1x revenue, what would the net margin be?
What EV/EBITDA multiple does this company trade at?
If the P/E fell to 30x with the revenue multiple unchanged, what does that imply?
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
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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?
089You invest in a software company at 40x ARR. ARR triples in year one, doubles in year two and grows 50% in year three. By the end of year three the market pays only 10x ARR for companies like it. Ignoring dilution, what multiple of your money have you made?Valuation riddlesCoreSaaS-focused VCGrowth equity
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Pick the multiple of money before you calculate.
Show the worked solution
2.25x your money, about 31% a year over three years. ARR grew 3 x 2 x 1.5, nine times. The multiple fell from 40x to 10x, a quarter of where it started. Value is ARR times the multiple, so it grew 9 x 0.25 = 2.25 times. The company did nine times better as a business, and the price of that business fell by three quarters along the way.
Why do revenue growth and the multiple multiply?
A shopkeeper who sells three times as many mangoes at half the price takes in one and a half times the money, not three. Valuation is ARR times the multiple, so the change in value is the growth in ARR times the change in the multiple. Entry: ARR of 1 at 40x is a value of 40. Exit: ARR of 9 at 10x is 90. Ninety over forty is 2.25x. Compound the growth rates first: 3 x 2 x 1.5 is 9, not 3 + 2 + 1.5.
Indexed to 1, ARR rises to 9 over three years while the multiple falls from 40x to 10x, an index of 0.25, so value ends at 2.25; on a log scale the value line is the ARR line pulled down by the fall in the multiple.
The relationship
$\text{MOIC} = \frac{A_3 \times m_3}{A_0 \times m_0} = (3 \times 2 \times 1.5) \times \frac{10}{40} = 9 \times 0.25 = 2.25$
A ARR at entry and at the end of year three
m the valuation multiple of ARR, 40x then 10x
MOIC multiple of invested capital
What it says in wordsThe money made is revenue growth times the change in the multiple, with no dilution in between.
Is 2.25x in three years a good outcome?
It is about 31% a year, respectable, but look at where it came from. Nine times the business produced barely two and a quarter times the money, because the entry price assumed growth that the exit price no longer rewarded. The break-even exit multiple is 40 / 9, about 4.4x ARR: below that, a company that grew nine times would still lose money. That is the risk of paying a high multiple, and it is why growth investors ask what multiple they need at exit before they ask how fast the company will grow.
What did the puzzle leave out on purpose?
Dilution: any round in those three years shrinks the stake, so the real multiple is lower. Preferences: in a weak exit a preferred holder may be paid ahead of common, which can lift the investor's multiple above the common one. The path of the multiple: the figure draws an even decline, but only the two ends are given, and the multiple of money depends only on them. State these and the answer becomes an investor's view rather than an arithmetic result.
Where candidates lose it
The two fast wrong answers are opposite. One says 9x because revenue grew nine times; the other panics at the multiple falling to a quarter and says the investment lost money. Both look at one of the two moving parts.
The second slip is adding growth rates: tripling, doubling and 50% is not 6.5 times. Compound them, then multiply by the change in the multiple, and say the break-even exit multiple as a check.
What the interviewer asks next
What exit multiple of ARR gives you 3x your money?
If you were diluted 20% in a round during the three years, what is your multiple now?
Why do growth investors focus on the exit multiple they need rather than the entry multiple they pay?
099A company's last round valued it at Rs 1,200 crore post-money, for preferred shares. A secondary buyer now offers to buy some of the founders' common shares at a 40% discount to that round's price per share. What valuation does that price imply if you apply it to every share, and why is it not a markdown of the company?Valuation riddlesCoreSecondariesMulti-stage VC
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Does the offer mean the company is now worth Rs 720 crore?
Show the worked solution
Applied to every share, the offer implies Rs 720 crore, but it prices common shares, not the company. The Rs 1,200 crore figure was a price for preferred shares, which are paid back first in a sale and carry protections. Common is paid last, is illiquid and usually needs company consent to sell. A buyer discounts for all of that. Neither Rs 1,200 crore nor Rs 720 crore is the company's value.
Why do the two prices differ for the same company?
A first-class and a general ticket on the same train cost different amounts, but the fare gap says nothing about the train's speed. Preferred and common are different securities in the same company: preferred is paid back before common in a sale, so a rupee of preferred is worth more than a rupee of common whenever a weak exit is possible. Multiplying the preferred price by every share gives the headline Rs 1,200 crore; multiplying the common offer, 60% of that price, by every share gives Rs 720 crore. Both are prices of a security scaled up, not a measure of what the business is worth.
Rs 1,200 crore is the preferred price times every share and Rs 720 crore the common price times every share; in an illustrative sale at Rs 400 crore the preferred holders' Rs 400 crore preference takes everything and common gets nothing, while at Rs 2,000 crore both share pro rata, which is why common trades below preferred.
Where does the discount come from?
Take an illustration: preferred holders own 40% and are owed Rs 400 crore first in any sale. In a Rs 400 crore sale they take everything and common gets nothing; only above Rs 1,000 crore, where 40% of the sale beats Rs 400 crore, do the two classes share pro rata. Common holds the first loss in the bad outcomes. On top of that come illiquidity, the company's right to block or match a sale, and the lack of information rights. Each adds to the discount, and none says the company is worth less than at the last round.
When would a secondary price be a real markdown signal?
When the discount is to the same security, or much larger than the structure explains. A buyer offering a deep discount for preferred shares from the latest round is a stronger signal, because the security is identical to the one that set the headline. Ask which class is being sold, how big the preference stack is relative to the likely exit range, and how much stock is on offer; a small, forced sale tells you about the seller's need for cash as much as the company.
Where candidates lose it
The common slip is announcing that the company has been marked down 40% to Rs 720 crore. The offer is for common shares, a junior and illiquid claim, so a lower price is expected even if nothing about the business has changed.
The opposite slip is dismissing secondary prices altogether. Say what the discount does reflect, the preference stack and illiquidity, and what would make it a genuine warning.
What the interviewer asks next
How would a 1x participating preference change the common discount?
Why might a company want to limit or approve secondary sales by founders?
An auditor must value the fund's preferred stake. Should it use Rs 1,200 crore, Rs 720 crore or something else?

V_exit	the expected exit value, Rs crore
d	dilution from later rounds, 40%
M	the return multiple you need
own	the stake the cheque must buy today

E/R	earnings over revenue, the net margin
8, 40	value over revenue and value over earnings
0.25	the tax rate
5%	depreciation as a share of revenue

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

A	ARR at entry and at the end of year three
m	the valuation multiple of ARR, 40x then 10x
MOIC	multiple of invested capital

Try it first

Why work backwards from the exit?

Where does the dilution go in the chain?

What do you add to show judgement?

Where candidates lose it

What the interviewer asks next

Try it first

How can two multiples give a margin?

How do you climb from net profit back to EBITDA?

Does the answer make sense for a company priced like this?

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

Why do revenue growth and the multiple multiply?

Is 2.25x in three years a good outcome?

What did the puzzle leave out on purpose?

Where candidates lose it

What the interviewer asks next

Try it first

Why do the two prices differ for the same company?

Where does the discount come from?

When would a secondary price be a real markdown signal?

Where candidates lose it

What the interviewer asks next