Portfolio Management puzzles, solved step by step

Puzzles: 100
Traced to a firm: 31
Topics: 13
Hard: 30

Showing 51–60 of 100

051A two-year bond pays an 8% annual coupon and repays 100 at maturity. Market yields for this bond are 7%. What is its price, and why is it above par?Bond mathsWarm upJ.P. Morgancloumbus · 2026
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Before you discount anything: where does the price land?
Show the worked solution
About 101.81. Discount each cash flow at 7%: the year 1 coupon of 8 is worth 7.48 today and the year 2 payment of 108 is worth 94.33, which add to 101.81. The bond sits above par because it pays 8 when the market only asks for 7, and a buyer pays up for that extra coupon until the return on the price paid falls back to 7%.
What does pricing a bond actually mean?
Think of a friend who promises you Rs 8 next year and Rs 108 the year after. What would you hand over today? If you can earn 7% elsewhere, each promised rupee is worth less the further away it sits. A bond's price is every promised cash flow divided by one plus the yield, once for each year you wait, and then added up. Here that is 8 divided by 1.07, which is 7.48, plus 108 divided by 1.07 twice, which is 94.33. The total is 101.81.
The relationship
$P = \frac{8}{1.07} + \frac{108}{1.07^2} = 7.48 + 94.33 = 101.81$
8 the annual coupon on 100 of face value
108 the final coupon plus the principal
1.07 one plus the market yield
What it says in wordsDiscount each payment by the yield for as many years as you wait, then add.
Discounted at 7%, the year 1 coupon is worth 7.48 and the year 2 payment of 108 is worth 94.33, stacking to 101.81; the 1.81 above par is exactly the extra 1 a year of coupon over a 7% bond, valued today.
Why must a bond with a high coupon trade above par?
Suppose it traded at 100. A buyer would earn 8% on a bond when the market pays 7% for the same risk, so everyone would want it and the price would rise. The price climbs until the return on the price paid equals the market yield, and that happens at a premium over par. The premium is easy to see directly: compared with a 7% bond at 100, this one pays an extra rupee each year for two years, worth 0.93 plus 0.87, which is 1.81. That is a check on the long method, and it is quicker to say in the room.
The same logic runs the other way. A coupon below the market yield means a discount to par, and a coupon equal to the yield means exactly 100. If you are asked how you would price a bond in today's market, say that the yield comes from comparable bonds of the same credit and maturity; the arithmetic above is the easy part. A premium bondA bond whose price is above its face value, because its coupon is higher than the yield the market currently demands. also pulls back towards 100 as it nears maturity, so a buyer at 101.81 loses the premium slowly while collecting the fat coupon.
Where candidates lose it
The common slip is adding the extra coupons without discounting them and answering 102. The extra rupee in year 2 is worth only 0.87 today, and saying 102 tells the interviewer you know the direction but not the method.
The second loss is getting 101.81 without saying why it must be above 100. Give the one-line reason: the coupon beats the market yield, so buyers bid the price up until the return on the price paid is 7%.
What the interviewer asks next
What would the price be if yields were 9% instead?
Why does the premium on this bond shrink as it approaches maturity?
Where would you find the right yield to price a bond like this in practice?
Asked at J.P. Morgan, Generalist, cloumbus, 2026 (Wall Street Oasis): How would you price a bond in today's market
052A fund's NAV at six successive year-ends is 100, 130, 91, 120, 84 and 140. What is its maximum drawdown?Performance measurementWarm upPerformance analysisRisk management
Try it first
Pick the maximum drawdown before you work it.
Show the worked solution
Minus 35.4%, from the peak of 130 to the trough of 84. Track the running peak: 100, then 130, which holds until 140 in the final year. The deepest fall below that peak is 84, and 84 over 130 minus 1 is -35.4%. The earlier dip to 91 was only minus 30%, and the fall from the starting 100 looks like just 16%.
Measured from where?
Picture a climber on a ridge. How far she has fallen is measured from the highest point she reached, not from the car park and not from the step she took a moment ago. A drawdown is the fall from the running peak, the highest NAV seen so far, and the peak only resets when the NAV climbs above it. Here the peak jumps to 130 in year 1 and then sits there through the dip to 91, the recovery to 120 and the slide to 84. Every one of those years is inside the same drawdown.
The running peak holds at 130 from year 1 until the NAV reaches 140 in year 5, and the deepest point under that peak is 84 in year 4, so the maximum drawdown is -35.4%, much deeper than the 16% fall the start value suggests.
The relationship
$\text{MDD} = \min_t \left(\frac{V_t}{\max_{s\le t} V_s} - 1\right) = \frac{84}{130} - 1 = -35.4\%$
V_t the NAV at year-end t
max over s up to t the running peak, the highest NAV seen so far
What it says in wordsAt each date, compare the NAV with the best level reached so far; the worst of those comparisons is the maximum drawdown.
Why does the recovery to 120 not end the drawdown?
Because 120 is still below 130. Anyone who invested at the peak was still under water at 120, and the slide to 84 took them further down. A partial recovery does not reset the peak, so two separate-looking dips can be one long drawdown. Treating 120 as a new start gives a fall of 30% to 84, which is wrong on the question asked, though it is a correct answer to how bad the single year was.
Say what the number misses as well. Maximum drawdown is one path and one worst point, so it tells you nothing about how long the fund stayed under water, here four years from year 1 to year 5, and a longer history almost always shows a deeper one. Allocators read it next to the recovery time for that reason.
Where candidates lose it
The fast answer is 16%, the fall from the starting 100 to 84. It measures the investor who bought at launch, not the worst experience, and interviewers ask this with the path deliberately chosen so the start value misleads.
The second trap is resetting the peak at 120 and answering 30%. Say the rule out loud before you calculate: the peak only moves when the NAV beats it.
What the interviewer asks next
How long was the fund under water, and why do allocators care about that as much as the depth?
What gain was needed from 84 to recover the 130 peak?
Why does a longer track record almost always show a deeper maximum drawdown?
053You have nine bags of coins that look identical. Eight weigh the same and one is lighter. Using a balance scale with no weights, what is the fewest number of weighings that always finds the light bag?Logic brainteasersWarm upAsset management
Try it first
What is the fewest weighings that is guaranteed to work?
Show the worked solution
Two weighings. Put three bags on each side and leave three aside. Whichever side rises holds the light bag; if the pans balance, it is among the three on the table. Take that group of three and weigh one bag against another: the one that rises is light, and if they balance, it is the third. A balance gives three outcomes per weighing, and three times three covers nine bags.
Why is halving the pile the wrong instinct?
Halving is what you would do with a question that answers yes or no, like guessing a number between 1 and 100. A balance tells you more than that. A balance scale has three outcomes, left pan rises, right pan rises, or level, so each weighing should split the suspects into three equal groups, not two. The group left on the table is not wasted: a level balance is information too. With four and four plus one aside you would learn little from a level result except that the odd bag is the spare one, and an unlucky run needs three weighings.
Weighing three bags against three splits nine suspects into three groups of three, whichever way the pans move, and weighing one bag against one then names the light bag, so two weighings give nine end points, one for each bag.
How do you prove two is the minimum?
Count outcomes. One weighing produces at most three different results, and three results cannot point to nine different bags. With k weighings you can separate at most 3 to the power k bags, so nine bags need at least two weighings, and the method above shows two is enough. The same count answers the natural follow-up: three weighings handle up to 27 bags, four handle 81.
The relationship
$3^k \ge n \quad\Rightarrow\quad 3^2 = 9 \ge 9$
k the number of weighings
n the number of bags, one of which is light
3 outcomes of one weighing: left light, right light, balanced
What it says in wordsEach weighing multiplies the number of distinguishable outcomes by three, so you need enough weighings for the outcomes to cover every bag.
Why would an asset manager ask this? It is a test of whether you use all the information a measurement gives you. A risk report, a performance attribution or a data screen can be read in more ways than pass and fail, and the candidate who spots the third outcome here is the one who reads the level result as a finding.
Where candidates lose it
The trap is answering three or four because you split into halves. It is the natural instinct, and the interviewer is watching whether you notice that a balance can come out level, which is a result in its own right.
The second loss is giving two without the counting proof. Say the 3 to the power k rule in one sentence: it shows you know the answer is a minimum, not just a method that happened to work.
What the interviewer asks next
How many weighings do you need for 27 bags? For 100?
Now you do not know whether the odd bag is heavier or lighter, and there are twelve. How many weighings?
You may take any number of coins from each bag and weigh once on a scale that shows grams. How do you find the light bag?
054Without a calculator: what IRR turns money into 2.5 times in four years, and what IRR turns it into 3 times in five years?Private and real asset mathsWarm upNeuberger BermanLondon · 2026
Try it first
Which pair is closest?
Show the worked solution
About 26% and about 25%. For 2.5 times in four years, take the square root of 2.5 twice: 1.58 and then 1.257, so 25.7% a year. For 3 times in five years, anchor on the fact that 2 times in three years is 26%; 3 times in five sits just below it at 24.6%. The bigger multiple over the longer hold is actually the lower annual return.
Why is the simple average so far off?
A savings account that pays 26% a year does not add 26 rupees every year to your 100. It adds 26 in year one, then 26% of 126 in year two, and so on, so by year four you have about 250. The IRR is the steady annual rate that compounds to the multiple, so it is always well below the total gain divided by the years. The simple average for 2.5 times in four years would be 150% over 4, or 37.5%, which overstates the true 25.7% by more than ten points.
The relationship
$\text{IRR} = M^{1/n} - 1 \qquad 2.5^{1/4} - 1 = 25.7\% \qquad 3^{1/5} - 1 = 24.6\%$
M the money multiple, cash back over cash in
n the years held, with one cash flow in and one out
What it says in wordsThe IRR is the nth root of the multiple, less one.
How do you get there in your head?
Use one of two tricks. For four years, take the square root twice: the square root of 2.5 is about 1.58, and the square root of 1.58 is about 1.257. For odd holding periods, use logs: the natural log of 3 is about 1.10, divided by five is 0.22, and adding a little for compounding turns 22% into about 24.6%. Faster still is a small grid of anchors you know by heart, because interviewers ask the same handful of multiples and periods.
A grid of IRRs by multiple and holding period shows 2.5 times in four years at 25.7% and 3 times in five years at 24.6%, and a band of 2 times in three, 2.5 times in four and 3 times in five years all near 25%.
Notice the diagonal band. Two times in three years, two and a half in four and three in five all land within a point of 25%. That one pattern lets you place almost any private equity outcome in a second. Say the limitation too: this shortcut assumes a single cash flow in and a single cash flow out. Real funds call and return money in stages, and the IRR then depends on the timing, not just the multiple.
Where candidates lose it
The trap is dividing the gain by the years, 150% over four and 200% over five, and answering 37.5% and 40%. It sounds confident and is wrong by more than ten points, and a private markets interviewer hears it as not understanding compounding.
The quieter miss is thinking 3 times must be the better deal because the multiple is bigger. The extra year costs more than the extra half turn of money earns.
What the interviewer asks next
What multiple does a 20% IRR give over five years?
A fund returns 2 times in three years and another 2.5 times in six. Which would you rather have, and what else would you ask?
Why can two deals with the same multiple and the same holding period show different IRRs?
Asked at Neuberger Berman, Generalist, London, 2026 (Wall Street Oasis): The associate interview was quite technical, covered 5-7 questions on valuation and understanding of returns in private equity
055An open-ended fund holds Rs 500 crore of assets across 20 crore units, a NAV of Rs 25. Investors redeem Rs 50 crore. What happens to the NAV and to the number of units?Funds, ETFs and implementationWarm upMorningstarMumbai · 2025
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Straight after the redemption, what is the NAV?
Show the worked solution
The NAV stays at Rs 25; the units fall from 20 crore to 18 crore. Redemptions are paid at NAV, so Rs 50 crore buys back 2 crore units at Rs 25 each and those units are cancelled. The fund is left with Rs 450 crore of assets across 18 crore units, which is still Rs 25 a unit. A redemption shrinks the fund, not the value of each unit.
Why does money leaving not lower the NAV?
Think of a pizza cut into 20 equal slices. If two friends leave and take their slices with them, 18 slices remain, and each one is exactly as big as before. An open-ended fund cancels the units that are redeemed and pays out exactly what they were worth, so assets and units fall in the same proportion and the NAV per unit does not move. Rs 50 crore at Rs 25 a unit is 2 crore units cancelled, leaving Rs 450 crore across 18 crore units.
Rs 50 crore of redemptions cancels 2 of the fund's 20 crore units at Rs 25 each, so assets fall to Rs 450 crore and units to 18 crore, and the NAV is still Rs 25 a unit.
The relationship
$\text{NAV} = \frac{\text{assets} - \text{liabilities}}{\text{units}} = \frac{500 - 50}{20 - 2} = 25$
assets the market value of everything the fund holds, Rs crore
units units outstanding, crore
2 units cancelled, 50 divided by the NAV of 25
What it says in wordsTake the same amount off the top and the bottom in the same proportion, and the ratio does not change.
So what does a redemption change?
Two things, both real. First, the manager must raise the Rs 50 crore, usually by selling holdings, and the transaction costsBrokerage, taxes and the price impact of selling, paid out of the fund when it trades. of those sales are paid by the whole fund, including the investors who stayed. Large redemptions dilute the remaining investors through trading costs, not through the NAV arithmetic. Exit loads, where a scheme charges them and credits them back to the scheme, go the other way and cushion those who stay. Second, a fund that has to sell in a hurry may sell what is easiest to sell, which leaves the remaining portfolio less liquid than before.
The day's NAV is the one used, struck after the market closes, which is why a redeeming investor cannot know the exact price when placing the request. The precise cut-off times and load rules are set by the regulator and the scheme documents, so confirm the current ones rather than quoting them from memory.
Where candidates lose it
The trap is answering Rs 22.50: dividing the smaller Rs 450 crore by the old 20 crore units. Candidates who think of NAV as a share price picture money leaving as bad news for the price. In a fund, the leavers take their units with them.
The opposite miss, Rs 27.78, divides the old assets by the new unit count. Say it as one sentence: units are cancelled at NAV, so both halves of the ratio fall together.
What the interviewer asks next
Who bears the cost when a large redemption forces the fund to sell illiquid holdings?
What happens to the NAV when new money comes in instead?
How does an ETF handle outflows differently from an open-ended fund?
Asked at Morningstar, Private Markets, Mumbai, 2025 (Wall Street Oasis): They asked questions such as: What are derivatives? Can you explain NAV? What are ETFs?
056You roll a fair die and are paid its face value in thousands of rupees. After seeing the first roll you may reroll once, but then you must take the second result. On which faces do you reroll, and what is the game worth?Probability and expected valueCoreQuantitative asset managementHedge funds
Try it first
What is the most you should pay to play?
Show the worked solution
Reroll on 1, 2 or 3; keep 4, 5 or 6. The game is worth Rs 4,250. A reroll is worth 3.5 on average, so you keep any face above 3.5 and swap any face below it. The kept faces contribute 4, 5 and 6 each with a one-in-six chance, 2.5 in all; the other half of the time you get 3.5. The total is 2.5 plus 1.75, which is 4.25 thousand.
How do you decide whether to reroll?
Think of a job offer in hand against the option to keep interviewing. You take the offer if it beats what you expect to get by walking away. The rule is to keep a result only when it is worth more than the option you give up, and here the option is a fresh roll worth 3.5. A 3 is below 3.5, so reroll it. A 4 is above, so keep it. Nothing about how you feel about a 4 enters into it; the comparison is one number against another.
Faces 4, 5 and 6 beat the 3.5 a fresh roll is worth and are kept, while 1, 2 and 3 are rerolled, which lifts the value of the game from 3.5 to 4.25 thousand rupees.
The relationship
$V = \frac{4+5+6}{6} + \frac{3}{6} \times 3.5 = 2.5 + 1.75 = 4.25$
V the value of the game, thousand rupees
(4+5+6)/6 the kept faces, each weighted by its one-in-six chance
3/6 x 3.5 half the time you reroll and get a fresh roll's average
What it says in wordsAdd the value of each face you keep, weighted by its chance, to the chance of rerolling times what a reroll is worth.
Why is this called working backwards?
Because you value the last decision first. The second roll has no choice left in it, so it is worth 3.5. Only once you know that can you decide the first roll. Every multi-stage game is solved from the final stage back to the first, because each decision depends on what the later stages are worth. Allow two rerolls and the same logic stacks: the last reroll is worth 3.5, the middle stage is worth 4.25, so on the first roll you keep only a 5 or 6, and the game is worth 4.67.
Rerolling only on 1 and 2, a common cautious answer, gives 4.17: you keep the 3 when a reroll would have averaged half a point more. The portfolio version is the same idea. A position is kept only while its expected return beats what the capital would earn redeployed, which is an opportunity cost, not a sunk cost.
Where candidates lose it
The trap is anchoring on the average face and saying the game is worth 3.5, as if the reroll were decoration. The option to reroll is worth three quarters of a thousand rupees, and missing it is missing the point of the question.
The second loss is the wrong threshold. Candidates reroll only a 1, or reroll up to 4, because they compare the face with the middle of the die rather than with the value of the alternative. Say the rule first, then the faces.
What the interviewer asks next
What is the game worth with two rerolls, and on which faces do you stop?
What if you must pay Rs 500 for each reroll?
Now you may keep the higher of your two rolls. What is that worth?
057Fund A has an average annual return of 9% with 10% volatility. Fund B averages 11% with 30% volatility. Over the long run, which one compounds faster, and by roughly how much?Compounding and fee dragCoreMulti-assetWealth management
Try it first
Which fund grows a rupee more over twenty years?
Show the worked solution
Fund A, by about two points a year: roughly 8.5% against 6.5%. Long-run compound growth is approximately the average return less half the variance. For A that is 9% less half of 0.10 squared, 0.5 points. For B it is 11% less half of 0.30 squared, 4.5 points. Over twenty years a rupee in A grows to about Rs 5.11 and in B to about Rs 3.52.
Why is the average return not what you earn?
A shop that marks a price up 30% and then down 30% does not end where it started. Rs 100 becomes Rs 130 and then Rs 91, although the average move is zero. Returns compound by multiplying, so a swing up and an equal swing down always leave you behind, and the loss grows with the size of the swing. For moderate returns the loss is close to half the variance, half of volatility squared. That is why a fund's compound annual growth sits below its average annual return, and the gap widens sharply as volatility rises.
The relationship
$g \approx \mu - \tfrac{1}{2}\sigma^2 \qquad A: 9 - 0.5 = 8.5\% \qquad B: 11 - 4.5 = 6.5\%$
g long-run compound growth rate a year
mu the average annual return
sigma annual volatility, as a decimal
What it says in wordsCompound growth is roughly the average return less half the square of volatility.
Fund B has the higher average return but loses 4.5 points a year to volatility against half a point for fund A, so A compounds at about 8.5% and B at about 6.5%, and a rupee grows to Rs 5.11 in A against Rs 3.52 in B over twenty years.
How precise is the half-variance rule?
It is an approximation, good when returns and volatility are modest, and it overstates the drag when volatility is large. A more careful calculation that treats returns as lognormal puts A at 8.5% and B at 7.2%. The size of B's handicap moves with the method, but the ranking does not: the higher-volatility fund compounds more slowly. Say that in the room. The rule is a tool for spotting the direction and rough size, not a precise forecast.
The portfolio consequence is the reason the question exists. Two funds with the same average return are not equal if one is far more volatile, and a client who holds a single volatile fund lives with the compound number, not the average in the brochure. Combining volatile assets that do not move together lowers portfolio variance, which is one of the few ways to raise compound growth without raising the average return.
Where candidates lose it
The trap is picking B because 11% beats 9%. Candidates read the average return as the growth rate and treat volatility as a separate risk topic, when here it is a direct cost to the return itself.
The second loss is subtracting the volatility rather than half its square, which gives nonsense for B. Write the rule down, square first, halve second, and give both numbers.
What the interviewer asks next
At what volatility would fund B's compound growth fall to match fund A's?
Why do fund fact sheets that show the average annual return flatter volatile funds?
How does rebalancing between two volatile assets relate to this drag?
058Every stock in a market has 35% volatility and every pair of stocks has a correlation of 0.25. What is the volatility of an equally weighted portfolio of 1 stock, of 10 stocks, and of infinitely many?Portfolio risk mathsCoreNorthern TrustChicago · 2025Northern TrustChicago · 2025
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With infinitely many stocks, where does portfolio volatility settle?
Show the worked solution
35% for one stock, about 20% for ten, and a floor of 17.5% for infinitely many. Portfolio variance is the stock variance times one over n, plus the correlation times what is left. With ten stocks that is 0.1225 times 0.325, a volatility of 20.0%. As n grows the one-over-n part vanishes and only the correlation term remains: 35% times the square root of 0.25, or 17.5%.
Why does adding stocks lower risk at all?
Ten shops in ten different towns do not all have a bad week at once; ten shops in one mall often do. Some of what moves a stock is its own news and some is the market everyone shares. Stock-specific shocks cancel out as you add names, because one company's bad quarter is offset by another's good one, but the shared market shock hits every name together and does not cancel. Correlation measures how much of each stock's movement is shared.
The relationship
$\sigma_p^2 = \sigma^2\left[\frac{1}{n} + \left(1-\frac{1}{n}\right)\rho\right] \;\to\; \sigma\sqrt{\rho} = 0.35 \times 0.5 = 17.5\%$
sigma each stock's volatility, 35%
rho the correlation between any two stocks, 0.25
n the number of stocks, equally weighted
What it says in wordsPortfolio variance is a shrinking stock-specific part plus a fixed shared part, and only the shared part survives as the portfolio grows.
Portfolio volatility falls from 35% with one stock to 20.0% with ten and then flattens towards a floor of 17.5%, because adding names removes stock-specific risk but cannot remove the risk all the stocks share.
How much of the benefit do the first ten stocks deliver?
Most of it. Going from one stock to ten cuts volatility from 35% to 20.0%, about 86% of the whole distance to the floor. Going from ten to thirty takes it only to 18.4%. Diversification pays off quickly and then almost stops, and the level where it stops is set by correlation, not by the number of holdings. That is why a manager worried about risk gains more from adding assets that are less correlated than from adding a fortieth stock of the same kind.
Say the limitation. Correlations are not fixed: in a sell-off they tend to rise together, which raises the floor exactly when diversification is needed. Real stocks also differ in volatility and correlation, so this uniform market is a teaching model; the shape of the curve survives, the exact numbers do not.
Where candidates lose it
The trap is saying diversification takes risk to zero, or reaching for the correlation without the square root and answering 8.75%. The floor is the square root of the shared variance, so it is volatility times the square root of the correlation.
The second miss is getting 20% for ten stocks by guesswork and being unable to show it. Write the variance formula first and plug in: 0.1225 times 0.1 plus 0.9 times 0.25.
What the interviewer asks next
What correlation would make a 10-stock portfolio half as risky as one stock?
Why do correlations tend to rise in a market sell-off, and what does that do to this floor?
How would you lower the floor itself rather than approach it?
Asked at Northern Trust, Asset Management, Chicago, 2025 (Wall Street Oasis): First one was more technical and asked about my understanding of AM, portfolio diversification and strategy
Asked at Northern Trust, Asset Management, Chicago, 2025 (Wall Street Oasis): Asked about my understanding of asset management, portfolio diversification and strategy
059Why should I buy your college, and how much would you sell it for? Suppose it earns an operating surplus of Rs 40 crore this year, the surplus grows 5% a year for the foreseeable future, and a buyer wants a 12% return.Valuation riddlesCoreWellington ManagementBoston · 2024
Try it first
What price does the growing surplus support, before land?
Show the worked solution
About Rs 600 crore for the operating business, before any value in the land. Next year's surplus is Rs 40 crore grown 5%, or Rs 42 crore. A surplus that grows forever at 5% and is valued at 12% is worth next year's amount divided by the 7-point gap: 42 over 0.07 is Rs 600 crore. The reason to buy is the durability of that surplus: steady demand for seats and fees that can rise with costs.
What is the question really asking?
It is a stock pitch in disguise. The interviewer wants two things in order: why this asset produces reliable cash, and what that cash is worth. Answer the why with the quality of the surplus, and the how much with a valuation you can do out loud. For a college the why is simple to say: students keep applying every year, fees are paid in advance, and a college with a good name can raise fees roughly in line with its costs. Those are the reasons the surplus can be treated as growing and durable.
Why divide by 12% less 5%?
Think of a rented flat whose rent rises every year. A buyer asking for a 12% return on a rent that grows 5% needs only 7% from the current rent; the other 5% arrives through growth. A cash flow growing at g forever, valued at a required return r, is worth next year's cash flow divided by r minus g. Here that is Rs 42 crore over 0.07, which is Rs 600 crore. Dividing this year's Rs 40 crore instead gives Rs 571 crore, a common small slip: the buyer receives next year's surplus, not this year's.
The relationship
$V = \frac{S_1}{r - g} = \frac{40 \times 1.05}{0.12 - 0.05} = \frac{42}{0.07} = 600$
S_1 next year's surplus, Rs crore
r the buyer's required return
g the permanent growth rate of the surplus
What it says in wordsA growing perpetuity is worth next year's payment divided by the gap between the required return and the growth rate.
With growth fixed at 5%, the college is worth Rs 600 crore at a 12% required return, but Rs 700 crore at 11% and Rs 525 crore at 13%, because value depends on the gap between return and growth and that gap is small.
Now say what the number is sensitive to. One point on the required return moves the value by Rs 100 crore up or Rs 75 crore down, because a 7-point gap becoming 6 or 8 is a large change in proportion. The land and buildings may be worth more than the operating surplus, so a seller would also ask what the campus fetches as property. And check the structure before promising anyone the surplus: many colleges, in India among other places, are run by trusts or societies, and whether an owner can take surplus out at all is a legal question to confirm.
Where candidates lose it
The trap is diving into a formula without answering why. The question starts with why should I buy, and a candidate who opens with a number has skipped the half the interviewer cares about most.
The arithmetic trap is dividing Rs 40 crore by 12%, which treats a growing surplus as flat and values it at Rs 333 crore. Name the growth, use next year's surplus, and divide by the gap.
What the interviewer asks next
What growth rate is the seller implicitly assuming if he asks Rs 800 crore?
How would you value the land separately, and when would it exceed the value of the operating business?
What would make you use a higher required return for this college than for a listed education company?
Asked at Wellington Management, Investment Research, Boston, 2024 (Wall Street Oasis): Why should I buy your College and how much would you sell it for?
060Estimate how many narrow-body passenger jets, the single-aisle planes used on most short and medium routes, are delivered to airlines worldwide in a year.Market sizing and estimationCoreRothschild & CoParis · 2026
Try it first
What drives yearly deliveries of a plane that flies for decades?
Show the worked solution
About 1,200 a year, within a range of roughly 1,000 to 1,500. Size the fleet first: about 100,000 flights a day, three quarters on narrow-bodies, at five flights per jet a day, needs about 15,000 jets. Yearly demand is replacement plus growth: 15,000 over a 25-year life is 600, and 4% growth adds 600. Every input is an assumption to state and then check against published fleet data.
Where do you start with a plane that lasts 25 years?
Think of refrigerators in a city. Almost every home has one, but the shops sell only the ones that break down plus the ones new homes need. For a long-lived asset, yearly sales are a small flow out of a large stock: the stock divided by its life, plus the stock times its growth rate. So the job splits into two parts. Size the fleet from how the planes are used, then turn the fleet into a yearly flow.
About 75,000 narrow-body flights a day at five flights per jet needs a fleet of about 15,000, and replacing a twenty-fifth of that each year plus 4% growth gives roughly 1,200 deliveries a year.
How do you size the fleet without knowing it?
From usage, which is easier to guess. Take about 100,000 commercial flights a day worldwide, a round number to state as an assumption. Most flights are short and medium routes, so put three quarters on narrow-bodies: 75,000. A narrow-body on short routes flies several sectors a day; call it five. That needs 15,000 jets. Each assumption is a round number said out loud, so the interviewer can challenge one without losing the structure.
The relationship
$D = \frac{F}{L} + gF = \frac{15,000}{25} + 0.04 \times 15,000 = 1,200$
D deliveries a year
F the narrow-body fleet
L service life in years
g the fleet's yearly growth rate
What it says in wordsYearly deliveries are the jets that retire plus the jets that growth adds.
Now sanity-check. 1,200 deliveries is about 8% of the fleet, which sounds right for an asset that lasts decades. If the question asks about one maker, split by an assumed market share; two main makers sharing the market would each deliver around 600. For an asset manager the useful point is the sensitivity: deliveries swing with the growth assumption far more than the fleet does, which is why aircraft makers' order books are so cyclical. Treat every number here as an assumption to check against published fleet and delivery data before using it.
Where candidates lose it
The trap is sizing the whole fleet and calling that the yearly number, or dividing all passengers by seats per plane. Both answer how many jets exist, not how many are delivered, and they are wrong by a factor of ten or more.
The second loss is presenting assumptions as facts. Say each input as a round assumption, then show the answer moves predictably when one changes.
What the interviewer asks next
If fleet growth drops to zero for two years, what happens to deliveries?
How would you estimate the value of those deliveries in dollars a year?
What would you check first to test the 25-year life assumption?
Asked at Rothschild & Co, Asset Management, Paris, 2026 (Wall Street Oasis): Can You estimate number of flights solds by airbus

V_t	the NAV at year-end t
max over s up to t	the running peak, the highest NAV seen so far

k	the number of weighings
n	the number of bags, one of which is light
3	outcomes of one weighing: left light, right light, balanced

M	the money multiple, cash back over cash in
n	the years held, with one cash flow in and one out

assets	the market value of everything the fund holds, Rs crore
units	units outstanding, crore
2	units cancelled, 50 divided by the NAV of 25

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