Debt Capital Markets puzzles, solved step by step

Puzzles: 100
Traced to a firm: 16
Topics: 13
Hard: 30

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015A Rs 500 crore bond portfolio has 60% in bonds with a modified duration of 4 and 40% in bonds with a modified duration of 9. The central bank surprises with a 25 basis point hike and the whole curve moves up in parallel. Roughly what is the mark-to-market loss?Duration and convexityCorePIMCOSan Diego · 2026
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What is the portfolio's modified duration?
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About Rs 7.5 crore, 1.5% of the portfolio. Portfolio modified duration is the value-weighted average: 0.6 times 4 plus 0.4 times 9 is 6.0. A 25 basis point parallel rise costs about duration times the move, 6.0 times 0.25%, or 1.5%, and 1.5% of Rs 500 crore is Rs 7.5 crore. The duration 9 block is only 40% of the money but carries 60% of the loss.
What does modified duration convert?
Think of duration as a lever length. A seesaw with a long arm moves more at the end for the same push. Modified duration tells you the approximate percentage fall in a bond's price for a one percentage point rise in its yield, so a duration of 4 means about 4% per 1% move, or 1% for 25 basis points. Once you have that, a rate shock converts straight into rupees: duration times the move times the value held.
How do you combine two blocks of bonds?
Weight each duration by the money in it. Portfolio duration is the value-weighted average of the holdings' durations, because each bond's loss is its own value times its own duration times the move. Rs 300 crore at duration 4 loses Rs 3.0 crore; Rs 200 crore at duration 9 loses Rs 4.5 crore. Together that is Rs 7.5 crore, exactly what Rs 500 crore at duration 6.0 gives. The figure makes the point visually: area is the loss.
With width for rupees held and height for duration, the Rs 300 crore block at duration 4 loses Rs 3.0 crore and the Rs 200 crore block at duration 9 loses Rs 4.5 crore for a 25 basis point rise, together Rs 7.5 crore, the same area as Rs 500 crore at a portfolio duration of 6.0.
The relationship
$\Delta V \approx -D_{p} \times \Delta y \times V = -(0.6 \times 4 + 0.4 \times 9) \times 0.0025 \times 500 = -6.0 \times 0.0025 \times 500 = -7.5$
D_p portfolio modified duration, the value-weighted average
\Delta y the parallel rise in yields, 0.25%
V portfolio value, Rs 500 crore
What it says in wordsThe rupee change is roughly minus duration times the yield move times the money held.
What would make the true loss differ from Rs 7.5 crore?
Three things, and naming them is what separates a desk answer from a formula. Convexity makes the true loss slightly smaller than the duration estimate for a rise in yields, though for a 25 basis point move the difference is tiny. Curves rarely move in parallel after a surprise hike: short yields usually jump more, which would hurt the duration 4 block more than this sum assumes. And spreads on corporate bonds can move on top of the base rate. Say that Rs 7.5 crore is the first-order answer to a parallel shift, then name which of these you would check first.
Where candidates lose it
The common error is averaging 4 and 9 to get 6.5, giving Rs 8.12 crore. Durations combine by money weight, and the interviewer set 60 and 40 precisely to see whether you use them.
The second loss is getting the percentage right and the rupees wrong: 6 times 0.25 is 1.5%, and 1.5% of Rs 500 crore is Rs 7.5 crore, not Rs 75 crore. Say the percentage first, then convert.
What the interviewer asks next
How much of the duration 9 bonds would you sell into cash to cut the loss for the same shock to Rs 5 crore?
If the short end rises 40 basis points and the long end only 10, which block loses more?
How would you hedge this portfolio's duration with a bond future or an interest rate swap?
Asked at PIMCO, Debt Capital Markets, San Diego, 2026 (Wall Street Oasis): Which is cheaper us bonds or us equities How does duration affect interest rtes
026A callable bond is priced at 101.20. If yields fall 50 basis points it rises to 102.40; if they rise 50 basis points it falls to 99.10. What is its effective duration, and what does the asymmetry tell you about its convexity?Duration and convexityCoreAmundiLondon · 2018
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Before you divide anything: which way does this bond's convexity point?
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Effective duration is about 3.26, and convexity is negative. Take the price gap between the two shocked prices, 102.40 less 99.10, which is 3.30, and divide by twice the price times the 0.005 yield move: 3.30 over 1.012. A fall in yields adds only 1.20 while a rise costs 2.10, so the call is capping the upside: effective convexity works out near -356.
Why do you shock the yield both ways instead of using a formula?
Think of a landlord who can ask the tenant to leave whenever a better tenant turns up. The tenant's lease is worth less when the market is hot, because that is exactly when it gets cut short. A callable bond works the same way: the issuer takes the bond back when rates fall. Because the cash flows change with the yield, no fixed schedule of payments exists to plug into the usual duration formula, so you move the yield up and down and watch what the price actually does. That is effective durationDuration measured by repricing the bond after a small yield shift each way, so that options that change the cash flows are captured.: the percentage price change per unit of yield, measured from the model rather than from a cash flow list.
The relationship
$D_{\text{eff}} = \frac{P_{-} - P_{+}}{2\,P_0\,\Delta y} = \frac{102.40 - 99.10}{2 \times 101.20 \times 0.005} \approx 3.26$
P_- price after yields fall 50 basis points, 102.40
P_+ price after yields rise 50 basis points, 99.10
P_0 today's price, 101.20
\Delta y the yield shock as a decimal, 0.005
What it says in wordsAverage the two price moves, express them as a share of today's price, and scale to a one-point yield change.
The callable bond rises only 1.20 when yields fall 50 basis points but loses 2.10 when they rise 50, because its price flattens as it approaches the call level, while the same bond without the call keeps climbing.
What does the lopsided move say about convexity?
For an ordinary bond the price curve bends upward, so a fall in yields adds more than an equal rise takes away. Here it is the reverse. A smaller gain than loss for the same shock means the price curve bends downward, which is negative convexity. The effective convexity formula makes it a number: 102.40 plus 99.10 less twice 101.20 is minus 0.90, divided by 101.20 times 0.005 squared, about -356. The sign is the point; the size depends on the shock you chose.
Say what it means for the holder. You are short an option to the issuer: you keep the losses when rates rise but hand back most of the gains when rates fall. The extra yield a callable bond pays over a straight bond is the premium for that option. In the illustrative model behind the picture, the same bond without the call has an effective duration of about 4.5, higher than 3.26, because the call shortens the bond's expected life when yields drop.
Where candidates lose it
The common slip is quoting a modified duration from the bond's final maturity, as if the call did not exist. That overstates the price gain from falling yields, which is exactly the move where the call bites.
The second loss is computing 3.26 and stopping. The interviewer gave you two different price moves on purpose: say the gain is smaller than the loss, name negative convexity, and say who owns the option.
What the interviewer asks next
Why would the effective duration shrink further if yields fell another 100 basis points?
Mortgage-backed securities show the same pattern. What plays the role of the issuer's call?
Would you use a 10 basis point or a 100 basis point shock to measure effective duration, and why?
Asked at Amundi, Rates, London, 2018 (Wall Street Oasis): What would your allocation be in today's market? What is effective duration?
041K investors each send a sorted list of n orders by limit yield. You need one sorted order book. How many comparisons does a naive merge take against a min-heap merge, and why is the heap the right tool as K grows?Logic and brainteasersCoreCitadelNew York · 2026Citadel SecuritiesNew York · 2026
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Merging 64 lists of 1,000 orders: roughly how many comparisons does scanning every list's front order each time take, against a heap?
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A naive scan takes about n K (K minus 1) comparisons; a min-heap takes about n K log2 K. For 64 investors with 1,000 orders each, that is about 4.03 million against 0.384 million, roughly 10 times fewer. The heap holds only each list's current best order, so finding the next order costs a few steps down one branch rather than a look at every list.
What is the naive way, and where does it waste effort?
Imagine 64 queues at a bank, each already in order of arrival, and you must call people one at a time in overall order. The naive clerk walks along all 64 queue fronts every time to find the earliest. Every time one order leaves the book, the naive merge re-compares all K front orders, even though only one of them changed. That is K minus 1 comparisons for each of n K orders: 64,000 orders times 63 is 4,032,000 comparisons.
The other naive route is to merge lists one at a time: merge list 1 and 2, then merge in list 3, and so on. Each merge re-reads everything merged so far, which costs about n times K squared over 2, here about 2.08 million. Better than scanning, but it still grows with the square of K.
A min-heap keeps each investor's best remaining order, with the lowest yield at the top, so each step costs about log2 K comparisons; merging 64 lists of 1,000 orders then takes about 0.384 million comparisons against 4.03 million for scanning every front order.
Why does a heap fix it?
A min-heapA tree in which every parent is smaller than its children, so the smallest item is always at the top and can be removed and replaced in a number of steps equal to the tree height. keeps the K front orders only partly sorted: the best is always at the top, and the rest are arranged so that fixing the tree after a change touches one path from top to bottom. Taking the best order and inserting that investor's next one costs about log2 K comparisons instead of K, which is 6 instead of 63 at K of 64. Total work becomes n K log2 K, about 384,000 comparisons.
The relationship
$\text{scan: } nK(K-1) \approx 4.03\text{m} \qquad \text{heap: } nK\log_2 K = 64{,}000 \times 6 = 384{,}000$
n orders per investor list, 1,000
K number of investor lists, 64
\log_2 K height of the heap, 6 for 64 lists
What it says in wordsBoth methods output every order once; the heap makes each output cost the height of a small tree instead of a scan of every list.
Say where the heap does not matter. With four or five lists, scanning is about as fast and simpler to code, and the orders arrive as fast as a person can read them anyway. The heap earns its place when K is large or the lists do not fit in memory, which is the version in the reported question: arrays read from disk, where only the front of each list is held at once. A careful heap counts about two comparisons per level on the way down, so treat log2 K as the order of the cost, not an exact count.
Where candidates lose it
The common miss is proposing to concatenate all the lists and sort them. It works, but costs about n K log2 of n K and throws away the fact that each list is already sorted, which is the whole hint in the question.
The second loss is naming a heap without saying what sits in it. Say clearly: one entry per list, the current front order, plus which list it came from so you know where to fetch the next one.
What the interviewer asks next
What else does each heap entry need to store besides the yield?
How would you merge the lists if they were too large to fit in memory at once?
Two orders have the same yield. How do you keep allocation fair in the merged book?
Asked at Citadel, Equity Capital Markets, New York, 2026 (Wall Street Oasis): I was asked to implement K-way merge of K sorted arrays
Asked at Citadel Securities, Equity Capital Markets, New York, 2026 (Wall Street Oasis): and the cadidate was expected to use a min heap
048A plane has 100 seats and 100 passengers with assigned seats. The first passenger is drunk and sits in a random seat; every later passenger takes their own seat if it is free, otherwise a random free seat. What is the probability the last passenger gets their own seat, and the probability for the Nth passenger?Probability and expected valueCoreBelvedere TradingChicago · 2022
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The chance that passenger 100 gets their own seat is:
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The last passenger gets their own seat with probability exactly 1/2. Every random choice picks seat 1, seat 100, or another seat that just passes the problem on. Seat 1 and seat 100 are always equally likely, and whichever goes first decides it. For passenger k, the same argument over the seats that still matter gives (n minus k plus 1) over (n minus k plus 2): 99 in 100 for passenger 2, falling to 1/2 for the last.
Which seats actually matter to the last passenger?
Think of a game of musical chairs where every displaced person grabs a random empty chair. It looks like a mess, but most grabs only move the mess along to someone else. For the last passenger, only two seats matter: seat 1, the drunk's own, and seat 100, their own. If a displaced passenger takes seat 1, the chain stops and everyone after sits correctly. If someone takes seat 100, the last passenger loses. Any other seat hands the same situation to a later passenger.
Every random pick lands on seat 1, which ends the chain and saves the last passenger, on seat 100, which dooms them, or on another seat, which just passes the choice along, and since seats 1 and 100 are always equally likely the last passenger's chance is exactly one half.
How do you get the answer for any passenger?
Apply the same logic to passenger k. For them, the deciding seats are seat 1 and the seats of passengers k to n, which are still unclaimed by their owners when the chain reaches them. Passenger k loses only if their own seat is picked before seat 1, and among the n minus k plus 2 seats that matter, only one of them is theirs. The chance of the chain ending well for them is therefore n minus k plus 1 over n minus k plus 2.
The relationship
$P(k \text{ gets own seat}) = \frac{n - k + 1}{n - k + 2} \qquad k = 100: \frac{1}{2} \qquad k = 2: \frac{99}{100}$
n number of seats and passengers, 100
k the passenger's boarding position, from 2 to n
What it says in wordsPassenger k is safe unless their own seat is the one picked first among the seats that still matter to them.
Check the ends of the formula, which is what an interviewer will do. Passenger 2 loses only if the drunk sits in seat 2, a 1 in 100 chance, so 99 in 100 is right. Passenger 99 has a 2 in 3 chance, and passenger 100 has 1 in 2. The answer does not depend on the size of the plane for the last passenger: with 10 seats or 1,000 it is still one half, which is the fact worth saying out loud.
Where candidates lose it
Candidates try to track the chain of displaced passengers and drown in cases. The interviewer is waiting to see if you spot that only two seats matter; say that first and the answer follows in one line.
The second loss is answering 1/2 for the last passenger and then guessing 1/2 for everyone. The reported question asked for the Nth passenger, so have the general formula and its two sanity checks ready.
What the interviewer asks next
What is the expected number of passengers who end up in the wrong seat?
What if the first two passengers are both drunk?
Why is the answer for the last passenger independent of the number of seats?
Asked at Belvedere Trading, Equity Capital Markets, Chicago, 2022 (Wall Street Oasis): Drunk passenger on a plane, what's the probability the Nth passenger gets his assigned seat
062A company has an enterprise value of Rs 1,000 crore against senior secured debt of Rs 500 crore, senior unsecured debt of Rs 300 crore and subordinated debt of Rs 150 crore. Enterprise value then falls 30%. What does each layer recover, which layer is the fulcrum, and at what enterprise value would the equity start to be worth something?Capital structure and recoveryCoreKKRNew York · 2025
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After the fall, which layer is the fulcrum?
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At Rs 700 crore, senior secured recovers 100%, senior unsecured 66.7% and the subordinated debt nothing, so the senior unsecured layer is the fulcrum. Value is paid down the stack in order: Rs 500 crore to the secured lenders leaves Rs 200 crore for Rs 300 crore of unsecured claims, and nothing below. The equity is worth something only once enterprise value exceeds total debt of Rs 950 crore.
How is value shared out when it falls short of the debt?
Picture water poured into a stack of glasses, each filling completely before any spills into the next. In a recovery, value pays each layer of the capital structure in full, in order of priority, before anything reaches the next layer down. The senior secured lenders' glass holds Rs 500 crore, the senior unsecured Rs 300 crore, the subordinated Rs 150 crore, and the equity takes whatever is left. Pour in Rs 700 crore and watch where it stops.
At Rs 700 crore of enterprise value, the Rs 500 crore senior secured layer is covered in full, the senior unsecured layer receives Rs 200 crore of its Rs 300 crore, 66.7%, and the subordinated debt and equity receive nothing, which makes senior unsecured the fulcrum.
Layer Claim At EV Rs 1,000 crore At EV Rs 700 crore
Senior secured 500 500 (100%) 500 (100%)
Senior unsecured 300 300 (100%) 200 (66.7%)
Subordinated 150 150 (100%) 0 (0%)
Equity 50 0
Total 950 1,000 700
Rs crore, recovery in brackets. At Rs 1,000 crore every debt layer is paid in full and the equity is worth Rs 50 crore; at Rs 700 crore the senior unsecured layer recovers 66.7% and everything below it is wiped out.
Why does the fulcrum matter to a credit investor?
The fulcrum securityThe most senior layer of the capital structure that the company value does not cover in full, so it is likely to receive the equity in a restructuring. is the layer where the value runs out. It usually ends up owning the business in a restructuring, because the layers above are paid in full and the layers below are wiped out. Here the senior unsecured lenders would likely exchange their Rs 300 crore of claims for most of the new equity. Distressed investors buy the fulcrum because its value moves most with the enterprise value: between Rs 500 and Rs 800 crore, every extra Rs 1 crore goes straight to it.
At what value does the equity come back to life?
The equity is out of the money until enterprise value covers every debt claim, Rs 500 plus 300 plus 150 crore, which is Rs 950 crore. At the original Rs 1,000 crore it was worth only Rs 50 crore, 5% of enterprise value, which is why a 30% fall wiped it out and went on through the subordinated layer too. The limit: this is a strict priority waterfall; in real restructurings junior classes often receive a small share to win their votes, and claims include accrued interest and fees, so treat these recoveries as the starting point of a negotiation.
Where candidates lose it
The common slip is sharing the loss pro rata: Rs 700 crore over Rs 950 crore of debt is 73.7% for everyone. That ignores priority, which is the whole point of a capital structure question.
The second is naming the subordinated debt as the fulcrum because it is the first layer to lose everything. The fulcrum is the layer where the value line lands, the one that is only partly covered: here the senior unsecured.
What the interviewer asks next
Enterprise value falls to Rs 450 crore. What does each layer recover now?
The senior secured lenders are also owed Rs 30 crore of accrued interest. Does the fulcrum move?
Where would the senior unsecured bonds trade if the market expects Rs 700 crore of value in a restructuring a year from now?
Asked at KKR, Distressed Debt, New York, 2025 (Wall Street Oasis): What are your weaknesses? A capital structure question with enterprise value.

Layer	Claim	At EV Rs 1,000 crore	At EV Rs 700 crore
Senior secured	500	500 (100%)	500 (100%)
Senior unsecured	300	300 (100%)	200 (66.7%)
Subordinated	150	150 (100%)	0 (0%)
Equity		50	0
Total	950	1,000	700

075Revenue is Rs 800 crore, up 10% on last year's Rs 727.3 crore. The EBITDA margin is 18%, depreciation is Rs 30 crore, the tax rate is 25%, capex is Rs 45 crore, and the net working capital build is 12% of the change in revenue. Walk from revenue to unlevered free cash flow.Leverage, coverage and cash flowCoreRBC Capital MarketsLondon · 2026

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Roughly what is unlevered free cash flow?

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Unlevered free cash flow is about Rs 61.8 crore. EBITDA is 18% of Rs 800 crore, Rs 144 crore. Less Rs 30 crore of depreciation gives EBIT of Rs 114 crore, and tax at 25% leaves NOPAT of Rs 85.5 crore. Add back depreciation, which is not cash, to reach Rs 115.5 crore, then take off capex of Rs 45 crore and the working capital build of 12% of the Rs 72.7 crore revenue increase, Rs 8.7 crore.

What order do you walk the lines in?

Think of a shopkeeper's year: sales come in, stock and staff are paid, the taxman takes a share, some money goes on a new fridge, and more stock sits on the shelves because the shop is busier. What is left is what the owner could take out. Unlevered free cash flow follows the same order: operating profit, less tax on that profit, plus non-cash charges, less investment in fixed assets and in working capital. It is unlevered because interest is left out: the cash belongs to lenders and shareholders together.

EBITDA of Rs 144 crore loses Rs 30 crore of depreciation and Rs 28.5 crore of tax to reach NOPAT of Rs 85.5 crore, gets the depreciation back, then loses Rs 45 crore of capex and Rs 8.7 crore of working capital, leaving Rs 61.8 crore of unlevered free cash flow.

Line	Rs crore
Revenue	800.0
EBITDA at 18%	144.0
Less depreciation	(30.0)
EBIT	114.0
Less tax at 25% of EBIT	(28.5)
NOPAT	85.5
Add back depreciation	30.0
Less capex	(45.0)
Less working capital build, 12% x 72.7	(8.7)
Unlevered free cash flow	61.8

Unlevered free cash flow is Rs 61.8 crore, 43% of EBITDA, after tax on operating profit, capex of 1.5 times depreciation and a working capital build on the Rs 72.7 crore rise in revenue.

Why tax EBIT rather than profit after interest?

Unlevered cash flow is the cash the business makes before any financing choice, so tax is charged as if there were no debt: 25% of EBIT, Rs 28.5 crore. Real tax is lower when there is interest to deduct, and that saving is counted elsewhere, in the discount rate or in a separate tax shield line. Taxing profit after interest and then discounting at a rate that already includes the shield counts the same benefit twice.

Where does the cash go between EBITDA and free cash flow?

Of Rs 144 crore of EBITDA, only Rs 61.8 crore, about 43%, becomes unlevered free cash flow: tax takes 28.5, capex 45 and working capital 8.7. Capex is 1.5 times depreciation, so the company is investing to grow, and working capital rises with sales because more revenue means more receivables and stock. A lender sizing debt on EBITDA should look at this conversion, because interest and repayments are paid from the Rs 61.8 crore, not the Rs 144 crore. The limit: one year of cash conversion can mislead when capex is lumpy.

Where candidates lose it

The common slip is stopping at EBITDA less capex and calling it free cash flow, forgetting tax and working capital; that gives Rs 99 crore, well above the true Rs 61.8 crore.

The second is charging working capital on the whole revenue, 12% of Rs 800 crore, instead of on the change. Working capital is a balance; only the increase uses cash this year.

What the interviewer asks next

Revenue falls 10% next year instead. What happens to the working capital line?
How would you get from unlevered to levered free cash flow?
Capex falls to the level of depreciation. What is free cash flow now, and is that sustainable?

Asked at RBC Capital Markets, Leveraged Finance, London, 2026 (Wall Street Oasis): Walk me through Revenue to unleveraged FCF

076A conglomerate owns three businesses worth Rs 1,200 crore, Rs 800 crore and Rs 500 crore of enterprise value. The market applies a 15% holding company discount to the sum of the parts. Net debt is Rs 600 crore and there are 50 crore shares. What is the value per share, and what would it be with no discount?Cost of capital and valuation riddlesCoreDeutsche BankMumbai · 2024
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Before you calculate: the discount is 15% of enterprise value. How much does the value per share fall?
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Rs 30.5 per share with the discount and Rs 38.0 without it. The parts add to Rs 2,500 crore. A 15% discount takes off Rs 375 crore, leaving Rs 2,125 crore of enterprise value. Less Rs 600 crore of net debt gives equity of Rs 1,525 crore over 50 crore shares. With no discount equity is Rs 1,900 crore, or Rs 38.0. A 15% discount costs shareholders 19.7%.
Why does the discount come off before the debt?
Think of a house worth Rs 1 crore with a Rs 60 lakh home loan on it. If buyers suddenly pay 15% less for houses on that street, the house is worth Rs 85 lakh, the bank is still owed Rs 60 lakh, and the owner's share drops from Rs 40 lakh to Rs 25 lakh. A conglomerate works the same way. The holding company discount is a haircut on what the whole group is worth, and the lenders' claim is a fixed number that sits ahead of the shareholders, so the haircut is taken from enterprise value and passes through to equity untouched.
So the order is: value each business, add them to get the sum of the partsValuing each business on its own, usually against its own peers, and adding the values together., apply the holding company discountThe gap between what a group trades at and what its businesses would be worth separately, often blamed on head office costs, capital allocation or tax leakage. to the total, subtract net debt, and divide by shares. Rs 2,500 crore less Rs 375 crore is Rs 2,125 crore; less Rs 600 crore is Rs 1,525 crore; over 50 crore shares is Rs 30.5.
The three businesses add to Rs 2,500 crore; the 15% discount removes Rs 375 crore and net debt removes Rs 600 crore, leaving equity of Rs 1,525 crore, or Rs 30.5 a share against Rs 38.0 with no discount.
The relationship
$\text{Value per share} = \frac{(1-d)\sum EV_i - ND}{N} = \frac{0.85 \times 2{,}500 - 600}{50} = 30.5$
d the holding company discount, 15%
EV_i the enterprise value of each business
ND net debt, Rs 600 crore
N shares outstanding, 50 crore
What it says in wordsDiscount the sum of the businesses, take off what the lenders are owed, and share what is left.
Why does a 15% discount cost the shareholders more than 15%?
Equity is the thin slice left after debt, so any fall in enterprise value is a bigger fall as a share of equity. The Rs 375 crore haircut is 15% of Rs 2,500 crore but 19.7% of Rs 1,900 crore. Push net debt to Rs 1,500 crore and the same haircut takes 37.5% of the equity. This is why a credit analyst reading a holding company cares about the discount even though no lender ever sees it on a statement: it is a measure of how much equity cushion the market will actually pay for.
What should you say about where the discount is applied?
Some desks apply the discount to equity value instead of enterprise value. On equity of Rs 1,900 crore, 15% gives Rs 1,615 crore and Rs 32.3 a share. The two conventions differ by Rs 1.8 a share here, so name your convention in the first sentence rather than let the interviewer find it. The enterprise value version is the more common reading when the discount is described as a discount to the sum of the parts, and it is the one that treats the lenders' claim as fixed.
Where candidates lose it
The frequent slip is subtracting the net debt first and then taking 15% off what is left. That gives Rs 32.3 a share and quietly assumes the lenders share the discount, which they do not when the discount is on the sum of the parts. Interviewers accept either convention only if you name it.
The second slip is telling the interviewer that shareholders lose 15%. Say 19.7%, and give the reason in one line: the debt does not shrink, so the whole haircut falls on equity.
What the interviewer asks next
With net debt of Rs 1,500 crore, what discount would halve the equity value?
The group sells unit C for Rs 500 crore of cash and repays debt. If the discount stays at 15% on what remains, what happens to value per share?
Why would a lender to the holding company watch the discount at all?
Asked at Deutsche Bank, Equity Capital Markets, Mumbai, 2024 (Wall Street Oasis): working capital, leases and SOTP with conglomerate discount question
077You have two bowls, 60 white balls and 40 black balls. Split all 100 balls between the bowls any way you like. One bowl is then chosen at random and one ball drawn from it. How do you maximise the chance of drawing white, and what is that chance?Probability and expected valueCoreDeutsche BankMumbai · 2024
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Pick the best chance you think a clever split can reach.
Show the worked solution
Put one white ball alone in bowl A and the other 99 balls, 59 white and 40 black, in bowl B. Bowl A gives white every time and bowl B gives white 59 times in 99. Each bowl is chosen half the time, so the chance is 0.5 x 1 + 0.5 x 59/99, about 79.8%, against 60% for an even split.
Why does a bowl with one ball count as much as a bowl with 99?
Picture two teams tossing a coin to bat first: the coin does not care that one side has eleven players and the other has one. The bowls are chosen the same way. The coin picks a bowl, not a ball, so a bowl holding a single white ball gets the same half of the draws as a bowl holding ninety nine. That makes one lone white ball the cheapest way to buy certainty for half of all outcomes, and it costs bowl B only one white ball out of sixty.
Bowl A with one white ball gives white every time; bowl B with 59 white and 40 black gives white 59.6% of the time, so the average is 79.8%, well above the 60% an even split gives.
How do you show that nothing beats it?
Bowl A cannot do better than 100%, and one white ball is the least that gets it there. Every further white ball moved into bowl A is wasted there and missed in bowl B, and every black ball moved into bowl A drags it below 100%. So bowl A is one white ball and bowl B takes what is left. Checking all 2,499 possible splits by computer agrees: the best is 79.80%, and only the one-ball split reaches it.
The relationship
$P(\text{white}) = \tfrac{1}{2}\cdot 1 + \tfrac{1}{2}\cdot\frac{W-1}{W+B-1} = \tfrac{1}{2} + \tfrac{1}{2}\cdot\frac{59}{99} \approx 0.798$
W white balls, 60
B black balls, 40
1/2 the chance each bowl is chosen
(W-1)/(W+B-1) the white share in bowl B once one white ball is set aside
What it says in wordsHalf the time you get the certain bowl, half the time you get everything else.
The formula also shows how the answer moves. With 50 white and 50 black, the version a candidate reported from an interview, it gives 74.7%. More white in the pool lifts bowl B and the total; bowl A is already at its ceiling. Here the split adds about 20 percentage points because one ball is turned into half of the probability.
Where candidates lose it
Most people answer 60% because the pool is 60% white and they assume a split cannot change the pool. It cannot change the pool, but it changes the weights, because the bowl is chosen before the ball.
The second loss is stopping at the number. Give the one-line reason no other split does better, then generalise: one half plus one half of (W minus 1) over (W plus B minus 1).
What the interviewer asks next
What if the bowl is chosen with probability proportional to how many balls it holds?
With three bowls and the same 100 balls, what is the best split and the best chance?
You are paid Rs 100 for a white ball and nothing for black. What is the most you would pay to play once?
Asked at Deutsche Bank, Equity Capital Markets, Mumbai, 2024 (Wall Street Oasis): After the distribution, one bowl will be selected at random, and then one ball will be randomly drawn from that bowl
093A Rs 1,000 crore fund charges a 2% management fee and a 20% performance fee on returns above fees, and earns a 10% gross return. Investors push the management fee down to 1.5%. What performance fee rate keeps the manager's revenue the same?Compounding, PIK and feesCoreTwo SigmaNew York · 2026
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Roughly what performance fee replaces the lost 0.5%?
Show the worked solution
A performance fee of about 24.7%. Today the manager earns Rs 20 crore of management fee plus 20% of the Rs 80 crore return after fees, Rs 16 crore, for Rs 36 crore. At 1.5% the fixed fee is Rs 15 crore and the return after fees rises to Rs 85 crore, so the performance fee must bring Rs 21 crore: 21 / 85 = 24.7%. The swap is exact only at a 10% gross return.
Why does the performance fee base change?
Think of a salesperson paid a fixed salary plus a share of profit after salary. Cut the salary and the profit after salary goes up, so the share needed to make up the difference is smaller than a straight swap would suggest. The performance fee is charged on the return left after the management fee, so lowering the management fee enlarges the base the performance fee is charged on. That is why the answer is 24.7%, not 25%.
At a 10% gross return both fee terms pay the manager Rs 36 crore, but at 5% the old terms pay 26.0 against 23.6 and at 15% the new terms pay 48.4 against 46.0, so the trade shifts revenue from weak years to strong ones.
The relationship
$15 + x\,(100 - 15) = 20 + 0.20\,(100 - 20) \;\Rightarrow\; x = \frac{36 - 15}{85} = 24.7\%$
100 the 10% gross return on Rs 1,000 crore, in Rs crore
15, 20 the new and old management fees, Rs crore
x the new performance fee rate
What it says in wordsSet the new fixed fee plus the new share of the bigger base equal to today's total.
Is the manager really indifferent?
Only at a 10% gross return. At 5% gross, the old terms pay Rs 26.0 crore and the new pay Rs 23.6 crore; at 15%, the old pay Rs 46.0 crore and the new Rs 48.4 crore. Swapping fixed fee for performance fee moves the manager's revenue out of weak years and into strong ones, so the trade depends on the return you assume. Investors who push for it pay less when things go badly and more when they go well, which is often exactly what they want. A real fund would also have a hurdle rate, a high-water mark and fees charged on average rather than opening assets; each changes the arithmetic, not the logic.
Where candidates lose it
The common answer is 25% or 22.5%, from treating the two fees as if they sat on the same base. The management fee is on assets and the performance fee is on return after fees, so moving one changes the base of the other.
The second loss is saying the new terms are equivalent. They are equal at one assumed return only; say so, and give the 5% and 15% cases to show which way the risk moved.
What the interviewer asks next
What performance fee keeps revenue the same if the assumed gross return is 15%?
The fund adds a 5% hurdle, with performance fee only on returns above it. How does that change the answer at 10%?
From the investor's side, which fee terms would you prefer in a year you expect to be weak, and why?
Asked at Two Sigma, Equity Capital Markets, New York, 2026 (Wall Street Oasis): the 2/20 rule, and if one part of this equation changed, how would the other variable make up for it
096Two Rs 1,000 crore loans are sold in the broadly syndicated market. A term loan A amortises 20% a year over 5 years. A term loan B amortises 1% a year and repays the rest as a bullet at year 7. What is the weighted average life of each?Leverage, coverage and cash flowCoreScotiabankNew York · 2026
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Before calculating: roughly what is term loan B's weighted average life?
Show the worked solution
Term loan A has a weighted average life of 3.0 years and term loan B about 6.8 years. Term loan A repays 200 in each of years 1 to 5, so its average is (1 + 2 + 3 + 4 + 5) x 200 / 1,000 = 3.0. Term loan B repays 10 in each of years 1 to 6 and 940 in year 7: (210 + 6,580) / 1,000 = 6.79. Amortisation, not maturity, sets how long the lender's money is out.
What are the two loans, and why do they amortise so differently?
That is the question a candidate reported being asked, and the arithmetic is the best way to answer it. A term loan A is built for banks: it amortises steadily, so the lender's exposure shrinks every year. A term loan B is built for institutional investors such as loan funds: it amortises only nominally and returns almost everything at maturity, which suits investors who want to stay invested. The difference in structure shows up as a difference in weighted average life, and that number drives pricing, investor appetite and how long the credit risk lasts.
Term loan A returns 200 of principal every year and has a weighted average life of 3.0 years, while term loan B returns only 10 a year before a 940 bullet in year 7, giving a weighted average life of 6.79 years.
How is weighted average life calculated?
Think of lending a friend Rs 1,000 who repays Rs 200 a year: on average your money is out about three years, even though the last rupee comes back in year five. Weighted average life weights each repayment date by the share of principal repaid on it, and ignores interest. For term loan B: six payments of 10 contribute 10 x (1 + 2 + 3 + 4 + 5 + 6) = 210 year-rupees, and the bullet contributes 940 x 7 = 6,580. Total 6,790 over 1,000 is 6.79 years.
The relationship
$WAL = \frac{\sum_t t \cdot P_t}{\sum_t P_t}: \quad A = \frac{200(1+2+3+4+5)}{1{,}000} = 3.0 \qquad B = \frac{10(1+\dots+6) + 940 \times 7}{1{,}000} = 6.79$
P_t principal repaid in year t
t the year of repayment
What it says in wordsWeighted average life is the average repayment date, weighted by how much principal comes back on each date.
Why does the desk care?
A loan's pricing is spread over its weighted average life, not its stated maturity, so an upfront fee or discount is spread over 3 years on term loan A and nearly 7 on term loan B. In practice term loans B are often repaid early from refinancings or cash sweeps: if this one were refinanced in full at year 4, its weighted average life would fall to 3.94 years. Weighted average life is also not duration; it ignores interest and discounting, so it always sits above the loan's duration.
Where candidates lose it
The common error is quoting maturity: 5 years and 7 years. The question is about how long the money is out on average, and the answer for term loan A is two years shorter than its maturity.
The second is guessing term loan B's life at half its term because it amortises. It amortises so little that the bullet dominates. Say the 94% bullet share first and the answer follows.
What the interviewer asks next
If term loan A amortised 5%, 10%, 15%, 20% and 50% over the five years, what is its weighted average life?
Why do institutional loan investors prefer the term loan B structure?
A 2 point upfront fee is spread over the weighted average life. What does it add to the yield on each loan?
Asked at Scotiabank, Debt Capital Markets, New York, 2026 (Wall Street Oasis): Tell me about the two different types of loans in the broadly syndicated loan market.

D_p	portfolio modified duration, the value-weighted average
\Delta y	the parallel rise in yields, 0.25%
V	portfolio value, Rs 500 crore

P_-	price after yields fall 50 basis points, 102.40
P_+	price after yields rise 50 basis points, 99.10
P_0	today's price, 101.20
\Delta y	the yield shock as a decimal, 0.005

n	orders per investor list, 1,000
K	number of investor lists, 64
\log_2 K	height of the heap, 6 for 64 lists

n	number of seats and passengers, 100
k	the passenger's boarding position, from 2 to n

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What does modified duration convert?

How do you combine two blocks of bonds?

What would make the true loss differ from Rs 7.5 crore?

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Why do you shock the yield both ways instead of using a formula?

What does the lopsided move say about convexity?

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What is the naive way, and where does it waste effort?

Why does a heap fix it?

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Which seats actually matter to the last passenger?

How do you get the answer for any passenger?

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How is value shared out when it falls short of the debt?

Why does the fulcrum matter to a credit investor?

At what value does the equity come back to life?

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What order do you walk the lines in?

Why tax EBIT rather than profit after interest?

Where does the cash go between EBITDA and free cash flow?

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What the interviewer asks next

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Why does the discount come off before the debt?

Why does a 15% discount cost the shareholders more than 15%?

What should you say about where the discount is applied?

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Why does a bowl with one ball count as much as a bowl with 99?

How do you show that nothing beats it?

Where candidates lose it

What the interviewer asks next

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Why does the performance fee base change?

Is the manager really indifferent?

Where candidates lose it

What the interviewer asks next

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What are the two loans, and why do they amortise so differently?

How is weighted average life calculated?

Why does the desk care?

Where candidates lose it

What the interviewer asks next