Private Equity puzzles, solved step by step

Puzzles: 100
Traced to a firm: 22
Topics: 12
Hard: 30

Showing 21–30 of 78 · filtered from 100Clear filters

028A sponsor invests 100. In year 2 it takes a dividend recap of 60, and in year 5 it exits for 180. What is the money multiple, and is the IRR higher or lower than a deal that simply turns 100 into 240 at year 5?Returns mathsCoreMid-market buyout fund
Try it first
Both deals return 2.4x. Which has the higher IRR, and by roughly how much?
Show the worked solution
The multiple is 2.4x in both cases, but the recap deal's IRR is about 24.1% against 19.1%. Money back is 60 plus 180, which is 240 on 100. The single exit's IRR is 2.4 to the power one fifth, less one. The recap returns part of the money in year 2, and cash that comes back sooner lifts the IRR even though the total is unchanged.
Why does the same multiple give a different IRR?
Lend a friend Rs 100 and get Rs 240 back. If Rs 60 of it comes back after two years, you have that money in hand for three years while waiting for the rest. The multiple counts how much money comes back; the IRR counts how fast it comes back, so pulling cash forward raises the IRR without touching the multiple. The two deals below differ only in timing.
Both deals turn 100 into 240 over five years, but the deal that returns 60 in year 2 earns an IRR of 24.1% while the single exit at year 5 earns 19.1%, because early cash shortens the average time the money is out.
How do you get the recap IRR without a spreadsheet?
The single exit is a one-line calculation: 2.4 to the power 0.2 is about 1.191, so 19.1%. The recap needs a guess and a check, because there are two inflows. Try 24%: 60 divided by 1.24 squared is about 39.0, and 180 divided by 1.24 to the fifth is about 61.4. Together that is 100.4, just above the 100 invested, so the true rate is a touch higher. Guess, discount each cash flow, and nudge the rate until the present values add back to the cheque. The answer is 24.1%.
The relationship
$100 = \frac{60}{(1+r)^2} + \frac{180}{(1+r)^5} \quad\Rightarrow\quad r \approx 24.1\%$
r the IRR, the rate that makes the discounted inflows equal the investment
60 the recap dividend in year 2
180 the exit proceeds in year 5
What it says in wordsThe IRR is the single rate at which the discounted cash coming back exactly repays the cash put in.
Say what the recap costs, because an interviewer will push. The dividend was paid with new debt, which is why the exit cheque is 180 and not 240. The company carried more leverage for three years, so the higher IRR came with higher risk of a covenant problem. That is the honest trade: an LP sees a better IRR and early cash back, and the business sees a thinner cushion.
Where candidates lose it
The fast wrong answer is that the IRRs are equal because the multiples are equal. Candidates who think of IRR as a multiple spread over years miss that IRR weights early cash more heavily.
The second loss is getting stuck on a two-cash-flow IRR. You do not need the exact figure in your head; bracket it with one trial rate, say it is a little above 24%, and explain why.
What the interviewer asks next
Why might a GP favour a dividend recap late in a fund's life?
If the recap had been 100 in year 2 and exit 140 in year 5, what happens to the IRR and to the multiple?
What does an LP look at besides IRR to judge whether the recap added value?
029A sponsor buys a platform at 11x EBITDA of 100, then adds three bolt-ons with EBITDA of 10, 15 and 25, bought at 6x, 7x and 5x. What is the blended entry multiple for the whole group?Valuation riddlesCoreMid-market buyout fundIndian mid-market PE
Try it first
Which is closest to the blended multiple?
Show the worked solution
About 9.27x: total price of 1,390 over total EBITDA of 150. The platform costs 1,100. The bolt-ons cost 60, 105 and 125, which is 290 for 50 of EBITDA, a 5.8x average of their own. Add prices, add EBITDA, divide. The simple average of the four multiples, 7.25x, is wrong because it weights a 10 of EBITDA deal the same as a 100.
Why can you not average the multiples?
Buy 10 kg of rice at Rs 60 a kg and 1 kg of saffron rice at Rs 600 a kg. The average price per kg is not Rs 330; it is Rs 1,200 over 11 kg, about Rs 109. A multiple is a price per unit of EBITDA, so blending multiples means total price over total EBITDA, which weights each deal by its size. The platform holds two thirds of the group's EBITDA, so it pulls the blend towards 11x.
Drawn with width equal to EBITDA and height equal to the multiple, each deal's area is its price; the four blocks hold 1,390 of price over 150 of EBITDA, a blended multiple of 9.27x, well above the 7.25x simple average.
What does the blend tell you about the buy-and-build story?
The sponsor has bought 150 of EBITDA for 9.27x. If the larger group is worth the platform's 11x at exit, the same EBITDA is worth 1,650, against 1,390 paid. That gap of 260 is the multiple arbitrage that buy-and-build plans are built on, and it exists only if the market values the combined group at the platform's multiple.
Block EBITDA Multiple Price
Platform 100 11x 1,100
Bolt-on 1 10 6x 60
Bolt-on 2 15 7x 105
Bolt-on 3 25 5x 125
Group 150 9.27x 1,390
Adding prices and EBITDA separately gives 1,390 over 150, a blended 9.27x for the group.
Say the limitation. Bolt-on EBITDA is often bought on the seller's figures, before integration costs, lost customers and the management time each deal eats. Small businesses sell for lower multiples partly because they are riskier. The blend is a fair measure of what was paid; whether the group deserves 11x at exit is a separate judgement.
Where candidates lose it
The average of the four multiples, 7.25x, is the trap, and it is tempting because the question lists four multiples side by side. The interviewer is checking whether you treat a multiple as a price per unit and weight it by size.
The second loss is stopping at the number. A buyout interviewer wants the next sentence: the blend is below the platform multiple, and that gap is the paper value the strategy is counting on.
What the interviewer asks next
What exit multiple on the group would leave the sponsor no better off than the entry blend?
Why do smaller businesses trade at lower multiples, and is that gap sure to close once they are inside a platform?
How would integration costs change the blended multiple you report to the investment committee?
030A sponsor funds a buyout with 400 of preference shares compounding at 12% a year and 45 of ordinary shares for 90% of the ordinary. Management pays 5, at the same price per share, for the other 10%. After 5 years the equity is sold for 1,000. What does management receive?Fund economics numeracyHardMid-market buyout fundIndian mid-market PE
Try it first
Roughly what multiple does management make on its 5?
Show the worked solution
Management receives about 29.5, roughly 5.9x its money. The preference compounds to 400 x 1.12^5 = 704.9 and is paid first. That leaves 295.1 for the ordinary shares, and management's 10% is 29.5. The sponsor gets 970.5 on 445, about 2.18x. The structure gears management's small cheque on the ordinary hard.
Why does management do so much better than the sponsor on the same deal?
Imagine two friends buy a flat for Rs 50 lakh. One lends Rs 45 lakh at a fixed rate; both put a little cash in for the ownership. When the flat sells, the loan and its interest are repaid first and whatever is left belongs to the owners. If the price rises, the owners' small stake multiplies; the lender just gets the fixed rate. The preference share is the lender here: it takes a fixed 12% a year first, so all of the upside above that sits on the thin layer of ordinary equity where management's 10% lives. This is called sweet equityOrdinary shares sold to management at the same price as the sponsor, made valuable because most of the sponsor money sits in a senior preference instrument..
The relationship
$\text{Mgmt} = 10\% \times \big(1000 - 400 \times 1.12^5\big) = 10\% \times 295.1 = 29.5$
400 x 1.12^5 the preference with five years of compounding, 704.9
1000 exit equity
10% management's share of the ordinary equity
What it says in wordsManagement gets its share of whatever exit equity is left after the compounded preference.
Of 1,000 of exit equity the compounded preference takes 704.9 and the ordinary shares split 295.1, so management's 10% is 29.5, about 5.9x its 5; below 705 of exit equity management gets nothing.
What happens to management if the deal goes less well?
Run it at different exits. Because the preference keeps compounding whether the business grows or not, management's payout swings from nothing to many times its money over a narrow range of exit values. The table shows management's cheque and multiple at four exit values.
Exit equity Left for ordinary Management gets Multiple on 5
700 0.0 0.0 0.0x
800 95.1 9.5 1.9x
1,000 295.1 29.5 5.9x
1,200 495.1 49.5 9.9x
A 30% fall in exit equity, from 1,000 to 700, takes management from 5.9x its money to nothing, while the sponsor still recovers most of its cheque.
Sponsors measure this with the envy ratioThe price per 1% of ordinary equity paid by the sponsor, counting all its money, divided by the price per 1% paid by management.. The sponsor pays 445 for 90%, about 4.94 per point; management pays 5 for 10%, 0.5 per point, an envy ratio of about 9.9x. The limitation: the sums assume no leaver clauses, ratchets or management loan notes, all of which change who gets what in a real deal.
Where candidates lose it
The common loss is giving management 10% of the whole 1,000, which is 100, or 20x its money. That forgets that the preference sits ahead of the ordinary and has been compounding for five years.
The second loss is compounding the preference with simple interest: 400 plus 5 years of 48 is 640, not 704.9. That error hands management an extra 6.5 and makes the structure look safer than it is.
What the interviewer asks next
At what exit equity does management make 3x its money?
If the preference rate were 8% instead of 12%, how much would management get at 1,000?
Why do sponsors want the envy ratio high, and what stops them pushing it further?
031On a 5-year hold, how much more exit equity do you need to lift the IRR from 20% to 25%?Returns mathsCoreLarge-cap buyout fund
Try it first
Pick the closest answer.
Show the worked solution
About 22.6% more exit equity: from 2.49x the cheque to 3.05x. 1.2 to the fifth is 2.49 and 1.25 to the fifth is 3.05. Their ratio is (1.25 / 1.2) to the fifth, about 1.226. Five points of IRR compound every year, so over five years they add up to almost a quarter more money at exit, and more again over longer holds.
Why is the answer not five per cent?
Two runners leave together, one about 4% faster. After one lap the gap is small. After five laps it is five small gaps stacked, each measured on a longer distance. An extra five points of IRR is an extra growth factor of 1.25 / 1.20, about 1.042, applied every year, so over five years the exit has to be 1.042 to the fifth, about 1.226 times larger. That is a 22.6% increase in exit equity.
The relationship
$\frac{(1.25)^5}{(1.20)^5} = \left(\frac{1.25}{1.20}\right)^5 = 1.0417^5 \approx 1.226$
1.25^5 the exit multiple at 25% a year for five years, 3.05x
1.20^5 the exit multiple at 20% a year, 2.49x
What it says in wordsThe extra exit value needed is the ratio of the two yearly growth factors, raised to the number of years.
Lifting the IRR from 20% to 25% over five years needs exit equity of 3.05x the cheque instead of 2.49x, 22.6% more, and the same five points need 33.1% more over a seven-year hold.
How much more enterprise value does that take?
Less than 22.6%, if the deal carries debt at exit. Say exit EV is 1,000 with 400 of debt, so equity of 600 earns 20%. Equity needs to rise to about 736, and with debt unchanged that needs EV of about 1136. Leverage works in your favour here: a 13.6% rise in enterprise value delivers the 22.6% rise in equity. That is also why sponsors stress-test exit multiples so carefully, since small EV moves swing equity hard either way.
Say the limitation: the sums assume a single cheque in and a single exit. With interim dividends or staged investments, the required change in exit value differs, and the IRR needs a full cash flow schedule.
Where candidates lose it
The common loss is thinking linearly: five more points sounds like a small tweak, so candidates say exit value needs to rise by 5% or so. Compounding turns five points a year into about 23% over five years.
The second loss is dividing 25 by 20 and answering 25%. That compares the rates, not the money multiples. Raise the ratio of the growth factors, 1.25 over 1.20, to the number of years.
What the interviewer asks next
What exit multiple of the cheque does 30% over five years need?
Over a three-year hold, how much more exit equity does the same move need?
If exit equity can only rise 10%, how much shorter must the hold be to reach 25%?
032A portfolio company has a loan of 300 at 9% with three years left. It can repay early at a 2% call premium and refinance at 7.5%. How much does refinancing save, net of the premium?Credit and PIK mathsCorePrivate creditMid-market buyout fund
Try it first
Ignoring discounting, what is the net saving?
Show the worked solution
About 7.5 before discounting, about 5.7 after. The rate falls 1.5 points on 300, saving 4.5 a year, or 13.5 over three years. The call premium is 2% of 300, which is 6, paid up front. Net, 13.5 less 6 is 7.5. Discount the savings at 7.5% and they are worth 11.7 today, so the net gain is about 5.7.
How should you think about a call premium?
Switching to a cheaper phone plan midway through a contract usually costs an exit fee. You switch only if the monthly saving, times the months left, beats the fee. A call premium is the lender's exit fee: it compensates the lender for losing a loan that pays above today's rate, so the borrower refinances only when the saving over the remaining term beats it. Here the fee is 6 and each year saves 4.5, so the fee is earned back in 1.33 years.
The borrower pays a premium of 6 at the refinancing date and saves 4.5 a year for three years, so the cumulative saving turns positive during year two and ends at 7.5, or about 5.7 discounted at 7.5%.
When would refinancing not be worth it?
Work out the breakeven rate gap. Spread the premium over the years left: 6 over 3 years is 2 a year, which is 0.67% of 300. Refinancing pays only if the rate falls by more than the premium divided by the years remaining, about 67 basis points here. With one year left the breakeven gap would be the full 2 points, and refinancing at 7.5% would lose money.
The relationship
$\text{Net} = L\,(r_{old}-r_{new})\,n - pL = 300 \times 1.5\% \times 3 - 2\% \times 300 = 7.5$
L the loan, 300
r_old - r_new the rate cut, 1.5 points
n years remaining, 3
p the call premium, 2%
What it says in wordsThe saving is the rate cut times the loan times the years left, less the premium paid to get out.
Say what the sums leave out. A new loan carries its own arrangement fee and legal costs, often a point or more, which would eat most of the 7.5. Lenders also build call protection to step down over time, so waiting a year can cut the premium. And if the business improves, a lender may simply reprice the existing loan, which avoids the premium altogether.
Where candidates lose it
The common loss is quoting the gross saving of 13.5 and forgetting the premium, or quoting one year's saving of 4.5. The interviewer wants the full trade: saving over the remaining term against the one-off cost.
The second loss is ignoring the fees on the new loan. Mentioning them, even without a number, shows you know refinancing has a cost on both sides.
What the interviewer asks next
With one year left, does refinancing at 7.5% still make sense?
The new lender charges a 1% arrangement fee. What is the net saving now?
Why do lenders insist on call protection in leveraged loans, and why does it usually step down?
033A business has revenue of 800 and a 12% EBITDA margin. The new owner cuts the cost base by 3% with revenue unchanged. What are the new EBITDA, the new margin and the EBITDA growth?Operating levers and margin mathsCorePortfolio operations teamIndian mid-market PE
Try it first
By how much does EBITDA grow?
Show the worked solution
EBITDA rises from 96 to 117.1, a 22% increase, and the margin from 12% to 14.6%. Costs are 800 less 96, which is 704. A 3% cut saves 21.1, and with revenue fixed every rupee of it reaches EBITDA. Because costs are about 7.3 times EBITDA, a small cost change is a large profit change: 3% times 7.33 is 22%.
Why does a 3% cost cut grow EBITDA by 22%?
A family earning Rs 1 lakh a month and spending Rs 88,000 saves Rs 12,000. Trim spending by 3%, about Rs 2,640, and savings jump to about Rs 14,640, up 22%. Profit is the thin slice left after costs, so any change to the large cost base is magnified when measured against the small profit. The magnifier is the ratio of costs to EBITDA, here 704 over 96, about 7.3.
Cutting a cost base of 704 by 3% saves 21.1, which lifts EBITDA from 96 to 117.1 and the margin from 12% to 14.6%, a 22% rise in profit from a small change in costs.
How does an operating partner use this, and where does it break?
Multiply by the exit multiple to see what it is worth. At 8x EBITDA, 21.1 of lasting savings adds about 169 of enterprise value, which is why cost programmes sit at the centre of so many buyout plans. The thinner the margin, the bigger the magnifier: at a 5% margin costs are 19 times EBITDA and a 3% cut lifts EBITDA by 57%.
The relationship
$g_{EBITDA} = c \times \frac{\text{Costs}}{\text{EBITDA}} = 3\% \times \frac{704}{96} = 22\%$
c the percentage cut to the cost base
Costs / EBITDA how many times larger the cost base is than profit
What it says in wordsEBITDA growth from a cost cut equals the cut times the ratio of costs to EBITDA.
Say the limitations. Not all of 704 can be cut: raw materials may be fixed by contract and wages by law, so the 3% often has to come from a much smaller part of the base. Cuts that hurt service can cost revenue later. And the same magnifier works in reverse: a 3% cost overrun would take 22% off EBITDA.
Where candidates lose it
The common loss is answering 3%, applying the cut to EBITDA instead of to costs. The interviewer is testing whether you see that costs are many times larger than profit.
The second loss is computing a 15% margin by adding 3 points to 12%. The new margin is 117.1 over 800, which is 14.6%; it rises by 2.6 points, not 3.
What the interviewer asks next
What revenue growth, with costs growing at the same rate, would deliver the same EBITDA as the 3% cut?
Which costs in a manufacturing business are hardest to cut, and why?
If half of the cost base is fixed, what does a 10% revenue fall do to EBITDA?
035Without a calculator, estimate the square root of 2.5. Then use it: an investment returns 2.5x in 2 years. What is the annual return?Mental mathsCoreGrowth equity
Try it first
What annual return turns 1 into 2.5 over two years?
Show the worked solution
The square root of 2.5 is about 1.58, so 2.5x over two years is about 58% a year. 1.5 squared is 2.25 and 1.6 squared is 2.56, so the root lies between them and much nearer 1.6: 2.5 is 25 of the 31 hundredths along, giving about 1.581. One Newton step from 1.6 gives 1.5813, against a true 1.5811.
How do you find a square root you have not memorised?
A train leaves one station at 6:00 and reaches the next at 9:00. A signal four fifths of the way along is passed at about 8:24: you slide between the two times you know. Find the two squares you know that bracket the number, then slide between them in proportion: the root sits about as far along as the number sits between the squares. 1.5 squared is 2.25 and 1.6 squared is 2.56. The target 2.5 is 0.25 above the lower square out of a gap of 0.31, about 0.81 of the way, so the root is about 1.5 plus 0.081, or 1.581.
Since 1.5 squared is 2.25 and 1.6 squared is 2.56, the root of 2.5 sits about 25/31 of the way from 1.5 to 1.6, close to 1.581, which makes 2.5x over two years about 58.1% a year rather than 75%.
How do you sharpen the estimate and check it?
Use one Newton step: take a guess, divide the number by it, and average the two. From 1.6, 2.5 divided by 1.6 is 1.5625, and the average of 1.6 and 1.5625 is 1.58125. One averaging step from a good guess gets you to three decimals, close enough for any interview. Check by squaring: 1.58 squared is 2.4964, just under 2.5, so the root is a hair above 1.58.
The relationship
$x_{1} = \tfrac{1}{2}\left(x_0 + \frac{N}{x_0}\right) = \tfrac{1}{2}\left(1.6 + \frac{2.5}{1.6}\right) = 1.58125$
x_0 the starting guess, 1.6
N the number whose root you want, 2.5
x_1 the improved guess
What it says in wordsAverage your guess with the number divided by your guess, and you land much closer to the root.
Now the investing use. A growth deal returning 2.5x in two years earns the square root of 2.5, less one, each year: about 58%. The fast answer, 150% over two years so 75% a year, ignores compounding: 1.75 squared is 3.06, not 2.5. Say the limitation: short holds produce eye-catching IRRs on modest money, so investors read the multiple alongside it.
Where candidates lose it
The common loss is splitting the gain evenly: 150% over two years, 75% a year. That treats the return as simple interest. Over two years the factor is squared, so you need a square root, about 1.581.
The second loss is freezing on the root itself. Interviewers are not testing whether you have 1.5811 memorised. They want to see you bracket it with 1.5 and 1.6 and slide.
What the interviewer asks next
Estimate the cube root of 3, and use it for 3x over three years.
What annual return turns 1 into 2 over two years?
A deal returns 2.5x in two years and another 3x in four. Which would an LP prefer, and why might they disagree?
037You buy 30% of a company from its existing shareholders for 300. The company has net debt of 500 and EBITDA of 160. What EV/EBITDA multiple did you pay?Valuation riddlesCoreGrowth equityMid-market buyout fund
Try it first
Which multiple did you pay?
Show the worked solution
About 9.4x EV/EBITDA. Paying 300 for 30% values all the equity at 300 / 0.3 = 1,000. Enterprise value is equity plus net debt, 1,000 + 500 = 1,500. Divided by EBITDA of 160, that is 9.38x. Two steps turn a minority cheque into a whole-company multiple: gross up to 100%, then add back the debt.
Why can you not divide the cheque by EBITDA?
Buying a 30% share of a flat for Rs 30 lakh tells you the owners think the whole flat's equity is worth Rs 1 crore. If the flat also carries a Rs 50 lakh home loan, the flat itself is worth Rs 1.5 crore. EBITDA is earned by the whole company for all its funders, so it has to be compared with the whole company's value, which is all the equity plus the net debt. The cheque is a fraction of only one of those two pieces.
Paying 300 for 30% implies equity of 1,000, and adding net debt of 500 gives an enterprise value of 1,500, which is 9.38x EBITDA of 160; had the 300 gone into the company as new money, the multiple would have been 7.5x.
The relationship
$\frac{EV}{EBITDA} = \frac{\text{Cheque}/\text{stake} + \text{Net debt}}{EBITDA} = \frac{300/0.3 + 500}{160} = 9.375$
Cheque / stake the value of 100% of the equity implied by the price paid
Net debt borrowings less cash, 500
EBITDA 160
What it says in wordsGross the cheque up to the whole equity, add net debt, and divide by EBITDA.
Does it matter whether the money goes to the sellers or into the company?
Yes, and growth investors are asked this often. If the 300 is new money paid into the company, the company's cash rises by 300, net debt falls to 200, and the same price buys a business valued at only 1,200, or 7.5x. Buying existing shares sends the cash to the sellers, so the company's debt is unchanged and the multiple is 9.38x. Ask which it is before you answer.
Say the limitation. A minority price can carry a discount for lack of control, or a premium if the investor gets preference shares with downside protection. So the implied multiple is a starting point, not a clean comparison with what a buyer of 100% would pay.
Where candidates lose it
The common loss is forgetting the debt: grossing the cheque up to 1,000 and reporting 6.25x. That mixes an equity value with an enterprise-level profit.
The second loss is not asking whether the investment is primary or secondary. New money changes net debt, and the multiple moves from 9.4x to 7.5x on the same cheque.
What the interviewer asks next
What P/E did you pay if net income is 80?
The 300 is new money. What is the post-money equity value and your stake?
Why might a minority investor accept a higher implied multiple than a buyer of the whole company?
038A fund draws 1,000 at once and returns 1,500 in a single distribution after 5 years. The waterfall has an 8% compounding preferred return, a full GP catch-up and 20% carry. How much does the GP receive, and what share of the fund's profit is that?Fund economics numeracyHardSecondaries and fund of funds
Try it first
Profit is 500. How much carry does the GP get?
Show the worked solution
The GP receives about 30.7, all of it from the catch-up, which is 6.1% of the profit. LPs first get their 1,000 back, then the 8% compounding preferred return: 1,000 x (1.08^5 - 1) = 469.3. That leaves 30.7. A full catch-up sends 100% of the next distributions to the GP until it holds 20% of profit, which would take 117.3, so the money runs out inside that tier.
What order does the money flow in?
Think of a restaurant partnership where the investor gets her money back first, then an 8% a year return on it, and only then does the chef share in the profit. A waterfall pays in tiers: capital back, then the preferred returnThe minimum return LPs receive before the GP shares in profit, often 8% a year, here compounding., then the GP's catch-up, then the 80/20 split, and each tier must fill before the next one starts. Here capital takes 1,000, the preferred return takes 469.3, and only 30.7 is left to flow further.
The relationship
$\text{Pref} = 1000\,(1.08^5 - 1) = 469.3 \qquad \text{Full catch-up} = \frac{0.2}{0.8}\times 469.3 = 117.3$
1.08^5 - 1 five years of 8% compounding, 46.9%
0.2 / 0.8 the catch-up needed for the GP to hold 20% of the profit paid so far
What it says in wordsThe catch-up tier is a quarter of the preferred return, because the GP must end with one part to the LPs' four.
Of 1,500 returned, 1,000 repays capital and 469.3 pays the preferred return, so only 30.7 reaches the GP catch-up, which needs 117.3 to fill; the GP's share of profit is 6.1% here and reaches the full 20% only at 1,587.
Why does the GP's share jump so fast just above the hurdle?
Because inside the catch-up tier every extra unit goes to the GP. Between 1,469 and 1,587 of proceeds, each additional 1 of exit value adds 1 to carry, so the GP's share climbs from zero to 20% across a band of only 117. Above 1,587 the split settles at 80/20 and stays there.
This is why secondaries buyers and LPs model carry near the hurdle so carefully. A fund sitting just above its hurdle has a GP with a strong incentive to push value up through that band, and a buyer of the LP interest must remember that much of the next gain goes to the GP. The limitation: real waterfalls run on dated cash flows, often deal by deal, with clawbacks; a single drawdown and exit is the clean case.
Where candidates lose it
The common loss is answering 100, 20% of the 500 profit, as if carry were a flat share. Near the hurdle the catch-up tier decides the answer, and here it is barely filled.
The second loss is using a simple 8% a year, 400 over five years, instead of compounding. That leaves 100 for the catch-up, and the GP's share comes out at 20%, not 6.1%. Ask whether the hurdle compounds before you start.
What the interviewer asks next
What would the GP receive with a 50% catch-up instead of a full one?
At what total proceeds does the GP first receive anything?
How does a deal-by-deal waterfall change the GP's carry on the same fund?
039A company sells two products with gross margins of 60% and 20%. Sales shift from 50/50 to 40/60, towards the low-margin product. What happens to the blended gross margin?Operating levers and margin mathsWarm upPortfolio operations team
Try it first
Where does the blended margin go?
Show the worked solution
The blended margin falls from 40% to 36%, with no change in either product's economics. Before, 0.5 x 60% + 0.5 x 20% = 40%. After, 0.4 x 60% + 0.6 x 20% = 24% + 12% = 36%. Moving 10 points of the mix from a 60% product to a 20% product costs 10% of the 40-point gap between them, which is 4 points of blended margin.
How can margin fall when nothing got worse?
A cafe earns 70% on coffee and 25% on sandwiches. If more customers come at lunch and order sandwiches, the cafe's overall margin drops even though neither the coffee nor the sandwich got less profitable. A blended margin is a sales-weighted average, so shifting weight towards the lower-margin product pulls the average down by itself. Each 1 point of mix moved costs 1% of the margin gap, here 0.4 points.
With product margins fixed at 60% and 20%, a 50/50 mix earns 30 plus 10 on revenue of 100, a 40% blend, while a 40/60 mix earns 24 plus 12, a 36% blend, so mix alone takes 4 points off the margin.
The relationship
$m = w_A m_A + w_B m_B = 0.4 \times 60\% + 0.6 \times 20\% = 36\%$
w_A, w_B each product's share of sales
m_A, m_B each product's gross margin
What it says in wordsThe blended margin is each product's margin weighted by its share of sales.
Why does a buyout team care, and what should it check next?
When a target's margin falls, the first question is whether the products got worse or the mix moved. A mix-driven margin fall is a different problem from a pricing or cost problem, and it can come with rising profit. If the low-margin product is growing fast, total gross profit may still rise even as the percentage falls: a business at a 36% margin on revenue of 150 earns more than one at 40% on 100.
Say the limitation. Gross margin ignores the overheads each product uses. A low-margin product that needs little selling effort can be more attractive after overheads than it looks here, so ask for contribution by product before judging the mix.
Where candidates lose it
The common loss is saying the margin stays at 40% because neither product changed. The interviewer is checking whether you know that a blend is a weighted average and moves with its weights.
The second loss is reading a falling margin as bad news without asking about volume. Margin percentage and profit in rupees can move in opposite directions.
What the interviewer asks next
What mix would bring the blended margin down to 30%?
If revenue grows from 100 to 130 with the new mix, does gross profit rise or fall?
How would you separate price, cost and mix effects in a margin bridge?

r	the IRR, the rate that makes the discounted inflows equal the investment
60	the recap dividend in year 2
180	the exit proceeds in year 5

Block	EBITDA	Multiple	Price
Platform	100	11x	1,100
Bolt-on 1	10	6x	60
Bolt-on 2	15	7x	105
Bolt-on 3	25	5x	125
Group	150	9.27x	1,390

400 x 1.12^5	the preference with five years of compounding, 704.9
1000	exit equity
10%	management's share of the ordinary equity

Exit equity	Left for ordinary	Management gets	Multiple on 5
700	0.0	0.0	0.0x
800	95.1	9.5	1.9x
1,000	295.1	29.5	5.9x
1,200	495.1	49.5	9.9x

Try it first

Why does the same multiple give a different IRR?

How do you get the recap IRR without a spreadsheet?

Where candidates lose it

What the interviewer asks next

Try it first

Why can you not average the multiples?

What does the blend tell you about the buy-and-build story?

Where candidates lose it

What the interviewer asks next

Try it first

Why does management do so much better than the sponsor on the same deal?

What happens to management if the deal goes less well?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the answer not five per cent?

How much more enterprise value does that take?

Where candidates lose it

What the interviewer asks next

Try it first

How should you think about a call premium?

When would refinancing not be worth it?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a 3% cost cut grow EBITDA by 22%?

How does an operating partner use this, and where does it break?

Where candidates lose it

What the interviewer asks next

Try it first

How do you find a square root you have not memorised?

How do you sharpen the estimate and check it?

Where candidates lose it

What the interviewer asks next

Try it first

Why can you not divide the cheque by EBITDA?

Does it matter whether the money goes to the sellers or into the company?

Where candidates lose it

What the interviewer asks next

Try it first

What order does the money flow in?

Why does the GP's share jump so fast just above the hurdle?

Where candidates lose it

What the interviewer asks next

Try it first

How can margin fall when nothing got worse?

Why does a buyout team care, and what should it check next?

Where candidates lose it

What the interviewer asks next