Private Equity puzzles, solved step by step

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

Showing 31–40 of 100

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
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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?
034Roughly how many cinema tickets are sold in India in a year? Build it from the demand side, then check it from the supply side.Market sizing and estimationHardAdvent InternationalBoston · 2022
Try it first
Before building anything: which order of magnitude feels right?
Show the worked solution
Roughly 0.8 to 0.9 billion tickets a year, on round assumptions. Demand: 1,400 million people, a quarter of whom go in a year, about 2.5 times each, gives about 875 million. Supply: about 9,000 screens, 4 shows a day, 200 seats, 30% full, gives about 788 million. Two routes agreeing within about 11% is the check; every input should be tested against an industry report.
Why build it twice?
If you want to know how many people eat at a canteen each day, you can count students and guess how often they eat there, or count tables, sittings and how full they look at lunch. Either guess on its own could be badly off; if both land near the same number you can trust it. A sizing built from demand and checked from supply catches the assumption that is wildly off, which a single chain never reveals. Interviewers care more about the check than about the final digit.
Demand of 1,400 million people times 25% who go times 2.5 visits gives 875 million tickets, and supply of 9,000 screens times 1,460 shows times 200 seats times 30% occupancy gives 788 million, so two independent routes agree on roughly 0.8 to 0.9 billion.
How do you defend each assumption out loud?
Segment before you guess. A quarter of the population going at least once a year is an average of very different groups: urban young adults may go many times, while much of rural India has no screen nearby. Say which segment drives the answer and why your share and frequency are reasonable for it, then give one number. On supply, the interviewer will push on occupancy: 30% is plausible because weekday afternoon shows run thin while weekend evenings fill. The screen count is an assumption to confirm, not a fact to recite.
Input Assumption If you halve it
People who go in a year 25% 438m demand
Visits per goer 2.5 438m demand
Occupancy 30% 394m supply
Screens 9,000 394m supply
Every input moves the answer one for one, so the honest range is wide and worth saying out loud.
A growth investor would go one step further: tickets times an average price gives box office revenue, and food and drink add a second stream on the same visits. Say the limitation: streaming changes how often people go, so a figure built on old habits may overstate tomorrow's market.
Where candidates lose it
The common loss is a single long chain with one unrealistic link, usually that most Indians go to the cinema several times a year, giving a number in the billions with no check. The interviewer then asks how many screens that implies, and the answer falls apart.
The second loss is reciting a screen count or a ticket figure from memory as fact. Present every input as an assumption, explain why it is reasonable, and offer the second route as the check.
What the interviewer asks next
What average ticket price would you assume, and what does that make the box office?
How would you split the answer between multiplex and single-screen cinemas?
Which single assumption would you research first, and where?
Asked at Advent International, Private Equity, Boston, 2022 (Wall Street Oasis): Market sizing questions, e.g.: how many books were sold this year in the US?
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?
036A target company faces a lawsuit: a 30% chance it must pay Rs 200 crore in damages in 2 years, otherwise nothing. At a 10% discount rate, how much should the price come down? What would you negotiate instead of a price cut?Probability and expected value in dealsCoreAres ManagementLondon · 2025
Try it first
What is the lawsuit worth in today's money?
Show the worked solution
About Rs 49.6 crore off the price, but a cut is the weaker fix. Expected damages are 30% x 200 = Rs 60 crore, payable in two years, so 60 / 1.1^2 is Rs 49.6 crore today. A price cut is fair on average yet leaves you Rs 200 crore exposed if the case is lost. A specific indemnity from the seller backed by an escrow moves the bad branch to the seller instead.
How do you put a number on something that may never happen?
A shopkeeper who knows that 3 in 10 customers return a gadget within the warranty sets aside money for returns before counting profit. A contingent liability is priced as chance times cost, then discounted for time: here 0.3 x 200 = Rs 60 crore, and two years at 10% brings it to Rs 49.6 crore. That is the average cost across all the ways the case could end, in today's money.
A 30% chance of paying Rs 200 crore in two years is worth Rs 60 crore on average and Rs 49.6 crore today at 10%, which is the fair price cut, yet on the losing branch the buyer still owes Rs 165.3 crore in today's money.
The relationship
$PV = \frac{p \times D}{(1+r)^t} = \frac{0.3 \times 200}{1.1^2} \approx 49.6$
p the chance of losing, 30%
D damages if lost, Rs 200 crore
r the discount rate, 10%
t years until payment, 2
What it says in wordsThe value of a possible future payment is its chance times its size, discounted back to today.
Why is a price cut not the best answer?
Because a buyer does not live the average; it lives one branch. Cut the price by 49.6 and lose the case, and you have paid for a Rs 200 crore liability with a Rs 49.6 crore discount. A specific indemnityA promise by the seller to reimburse the buyer for one named liability, here the lawsuit, if it costs money after completion. puts the bad branch back with the seller, who knows the case best. Backing it with an escrow, part of the price held back until the case ends, makes sure the money is there to collect.
Say the trade-offs. Sellers dislike escrows because cash is locked up, so expect to give something back, perhaps a smaller cut or a cap on the indemnity. Warranty and indemnity insurance usually excludes known issues like this one, so check the policy before relying on it. And the 30% is itself an estimate: ask the legal team how they reached it, because the answer moves one for one with it.
Where candidates lose it
The common loss is taking the full Rs 200 crore off the price, which overpays for caution and usually kills the deal, or taking Rs 60 crore off and forgetting the two years of time value.
The second loss is stopping at the number. The question asks what you would negotiate, and a buyout interviewer wants structure: an indemnity, an escrow or a holdback, so the risk sits with the party that knows it best.
What the interviewer asks next
The seller refuses an escrow. What else could you ask for?
How would you treat the lawsuit in the enterprise value to equity value bridge?
If your lawyers say the chance of losing is between 20% and 50%, how does that change your approach?
Asked at Ares Management, Infrastructure, London, 2025 (Wall Street Oasis): How would you itemise a potential lawsuit?
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?
040A company has floating-rate debt of 500 priced at a 5% base rate plus a 4% margin, and EBITDA of 110. The base rate rises by 200 basis points. What happens to interest cover?Credit and PIK mathsWarm upPrivate creditIndian mid-market PE
Try it first
Where does EBITDA interest cover go?
Show the worked solution
Interest cover falls from 2.44x to 2.0x. The all-in rate is 5% plus 4%, so 9% on 500 is 45 of interest, and 110 / 45 is 2.44x. After a 200 basis point rise the rate is 11%, interest is 55, and 110 / 55 is 2.0x. A two-point rise in the base rate lifts the interest bill by 22% and cuts cash left after interest from 65 to 55.
Why does a two-point rate rise do so much damage?
A household with a floating-rate home loan feels every rate rise in the next EMI, while one with a fixed rate does not. On floating-rate debt the borrower carries the rate risk, so a rise in the base rate goes straight into the interest bill. Two points on 500 is 10 more a year, which is 22% more than the 45 being paid today, with no change in how the business is running.
With EBITDA fixed at 110, a 200 basis point rise in the base rate lifts interest on 500 of floating debt from 45 to 55, so cover falls from 2.44x to 2.0x and the cash left after interest falls from 65 to 55.
The relationship
$\text{Cover} = \frac{EBITDA}{D \times (b + m)} = \frac{110}{500 \times 11\%} = 2.0x$
D floating debt, 500
b the base rate, now 7%
m the lender's margin, 4%
What it says in wordsInterest cover is EBITDA over the interest bill, and on floating debt the bill moves with the base rate.
What does a sponsor do about it?
Most leveraged loans are floating, so sponsors usually hedge part of the debt. An interest rate swap fixes the rate on a portion of the loan, and a cap limits how high it can go in return for an upfront premium. Lenders often require a minimum hedged share in the loan agreement. The trade-off is cost and lost upside: a swap set before rates fall locks the borrower into the higher rate.
Say what a credit analyst would look at next. EBITDA interest cover ignores capital spending and tax, so cash cover is tighter than 2.0x. A cover covenant set at, say, 2.0x would now be right at its limit, which turns a market move into a negotiation with lenders.
Where candidates lose it
The common loss is saying cover is unchanged because EBITDA is unchanged. Candidates forget that the coupon on floating debt resets with the base rate.
The second loss is adding the 200 basis points to the margin and calling it a 2% rise in interest. The rate goes from 9% to 11%, which is a 22% rise in the bill. Say the percentage change in the bill, not in the rate.
What the interviewer asks next
How much EBITDA growth would restore 2.44x cover after the rate rise?
If 60% of the debt is swapped to a fixed 7.5%, what is cover after the rise?
Why do lenders often insist on hedging, and who benefits when rates fall?

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

L	the loan, 300
r_old - r_new	the rate cut, 1.5 points
n	years remaining, 3
p	the call premium, 2%

c	the percentage cut to the cost base
Costs / EBITDA	how many times larger the cost base is than profit

Input	Assumption	If you halve it
People who go in a year	25%	438m demand
Visits per goer	2.5	438m demand
Occupancy	30%	394m supply
Screens	9,000	394m supply

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Why is the answer not five per cent?

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

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How do you put a number on something that may never happen?

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Why can you not divide the cheque by EBITDA?

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

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How can margin fall when nothing got worse?

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Why does a two-point rate rise do so much damage?

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