Equity Research puzzles, solved step by step

Puzzles: 100
Traced to a firm: 19
Topics: 11
Hard: 30

Topic

All topics Probability and brainteasers12 Expected value and decisions8 Market sizing and estimation12 Returns and compounding9 Valuation riddles12 Three statement riddles10 EPS and share count9 Cost of capital and rates8 Growth, mix and unit economics8 Mental maths6 Data and reasoning traps6

Level

Any Warm up Core Hard

Source

Any Reported at a firm Standard

Showing 61–70 of 100

061A company grew EPS 40% last year while its sector grew 10%. Assume that 30% of any company's growth above the sector average persists into the following year, a persistence coefficient of 0.3. What EPS growth should you forecast for next year?Data and reasoning trapsHardSell-side equity researchBuy-side equity research
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What growth do you forecast for next year?
Show the worked solution
About 19%. Start from the sector's 10%, the base rate, and keep only the part of the outperformance that tends to persist. The excess was 40% - 10% = 30 points, and a coefficient of 0.3 keeps 9 of them, so the forecast is 10% + 0.3 x 30 = 19%. Extreme results are partly luck, and luck does not repeat, so the forecast sits much nearer the average than last year's number.
Why not forecast 40% again?
A student who scores 95 in one mock exam, when the class averages 60, is probably both able and lucky that day. On the next mock she is likely to beat the class again, but by less, because the luck part does not come back. An extreme result is part skill and part luck, and only the skill carries forward, so the best forecast pulls the result back towards the average. The persistence coefficient says how much pulling to do: 0.3 means 30% of the gap survives and 70% fades.
At 40% growth last year, extrapolating gives 40% and assuming nothing persists gives the sector's 10%, while keeping 30% of the 30 point excess gives a forecast of 19%, much nearer the average than the outlier.
The relationship
$\hat g = \bar g + \beta\,(g - \bar g) = 10\% + 0.3 \times (40\% - 10\%) = 19\%$
\hat g next year's forecast growth
\bar g the sector average, the base rate
g the company's growth last year
\beta the persistence coefficient, the share of the excess that carries over
What it says in wordsThe forecast is the average plus the share of last year's excess that tends to persist.
Where does the 0.3 come from, and what if you are not given it?
It is an empirical fact about a set of companies, not a law. You would estimate it by comparing one year's growth with the next across many companies in your universe over several years. Without data, the question to ask is how much of last year's jump came from something that recurs, such as a new plant or share won from rivals, and how much from something that does not, such as a one-off order, a weak base year or a tax credit. A jump built on recurring drivers deserves a higher coefficient.
How does this show up on a research desk?
Forecasts for last year's winners are often extrapolations with a haircut too small. A stock priced as if 40% growth continues is exposed when growth drifts back towards the sector, even if the company stays better than average. Say that link after the number: it shows you understand why the interviewer framed the question around a forecast rather than a fact.
Where candidates lose it
Candidates either extrapolate 40% or, overcorrecting, snap all the way back to the sector's 10%. Both ignore the coefficient they were handed, which is the entire point of the question.
The quieter slip is multiplying the whole 40% by 0.3 and saying 12%. The shrinkage applies to the excess over the average, not to growth itself. Anchor on 10%, then add back 30% of the 30 point gap.
What the interviewer asks next
What would a coefficient of 1, or of 0, say about the business?
Why might growth that came from winning market share persist more than growth from a one-off order?
How would you estimate the coefficient from ten years of data?
062Russian roulette: a six-chamber revolver holds two bullets in adjacent chambers. The cylinder is spun, the trigger is pulled once and it clicks on an empty chamber. The trigger will be pulled once more. Should that second pull come straight away, or after the cylinder is spun again?Probability and brainteasersCoreSchonfeldCentral · 2022
Try it first
Straight away, or spin again?
Show the worked solution
Pull again straight away: you survive with probability 3/4, against 2/3 after a fresh spin. The four empty chambers sit together in a row and the cylinder advances one chamber per pull. The click you heard came from one of those four, each equally likely. Only one of them, the last empty chamber before the bullets, is followed by a bullet, so the chance of dying without a spin is 1/4. A fresh spin puts you back at two bullets in six.
Why does the first click carry information?
Picture a street with four dark houses in a row, then two lit ones, laid out in a circle. You are told you are standing at a dark house and that you will walk to the next door. Three of the four dark houses have another dark house next door. The click tells you that you are somewhere in the run of four empty chambers, and because the bullets sit together, most of that run is followed by another empty chamber. A fresh spin throws that information away.
With the two bullets in chambers 1 and 2, a click means the cylinder was at chamber 3, 4, 5 or 6; chambers 3, 4 and 5 are followed by an empty chamber and only 6 by a bullet, so pulling again survives 75% of the time against 66.7% after a spin.
The relationship
$P(\text{survive} \mid \text{no spin}) = \frac{3}{4} \qquad P(\text{survive} \mid \text{spin}) = \frac{4}{6} = \frac{2}{3}$
3/4 three of the four empty chambers are followed by another empty chamber
4/6 four empty chambers out of six after a fresh spin
What it says in wordsWithout a spin you condition on being in the run of empty chambers; with a spin you start again from scratch.
Would the answer change if the bullets were not next to each other?
Yes, and saying so shows you understand the mechanism rather than the trick. Put the bullets in chambers 1 and 4. The empty chambers are 2, 3, 5 and 6, and two of them, 3 and 6, sit in front of a bullet. With the bullets apart, pulling straight away survives only 50% of the time, so a fresh spin at 66.7% becomes the better choice. The adjacency is what makes the empty chambers cluster, and the clustering is what makes the click informative in your favour.
Why would an investing firm ask this?
Because it is a small version of the question every analyst faces after new information: does what just happened change the odds of what comes next? An outcome you have already seen is data about the state of the world, and ignoring it in favour of the unconditional average is a common and costly habit. Say that link in one line after the numbers.
Where candidates lose it
Candidates say it makes no difference, or say spin because it resets the odds, treating the first click as if it told them nothing. The whole question turns on the click being information about where the cylinder sits.
The second slip is dividing two bullets by the five chambers that remain and getting 3/5. The cylinder does not pick a random remaining chamber; it advances to the next one. Say that out loud and the 3/4 follows.
What the interviewer asks next
What if the bullets were in chambers 1 and 4 instead?
Three bullets in adjacent chambers, a click, then another pull. Spin or not?
How is this like updating a forecast after a quarterly result?
Asked at Schonfeld, Quantitative Research, Central, 2022 (Wall Street Oasis): Coding, requires to know DP and divde and conquer., Russian Roulette
063A company is waiting for a regulator's decision on its main drug. The stock trades at Rs 190. You estimate it is worth Rs 320 if the drug is approved and Rs 150 if it is rejected. What probability of approval is the market pricing, and what is the stock worth to someone who puts the chance of approval at 30%?Expected value and decisionsCoreHedge fund long/shortBuy-side equity research
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What approval probability is the Rs 190 price implying?
Show the worked solution
The market is pricing about a 23.5% chance of approval; at 30% the stock is worth about Rs 201. Set the price equal to the probability-weighted outcomes: 190 = p x 320 + (1 - p) x 150, so p = 40/170 = 23.5%. At 30%, the value is 150 + 0.3 x 170 = Rs 201, about 5.8% above the price, ignoring the time value of money and any premium for bearing a binary risk.
How does a price turn into a probability?
Think of a ticket that pays Rs 320 if it rains tomorrow and Rs 150 if it does not. Nobody would sell it below Rs 150 or buy it above Rs 320, and where it trades in between tells you how likely the crowd thinks rain is. Where the price sits between the two outcomes is the market's probability: Rs 190 is 40 of the 170 rupees from the downside to the upside, 23.5% of the way.
The relationship
$p = \frac{P - V_{down}}{V_{up} - V_{down}} = \frac{190 - 150}{320 - 150} = 23.5\%$
P today's share price, Rs 190
V_up the value if the drug is approved, Rs 320
V_down the value if it is rejected, Rs 150
p the probability of approval the price implies
What it says in wordsThe implied probability is how far the price has climbed from the bad outcome, as a share of the gap between the outcomes.
The Rs 190 price sits 23.5% of the way from the Rs 150 rejection value to the Rs 320 approval value, which is the market's implied probability, while a 30% view places the value at Rs 201.
What does the gap between 23.5% and 30% actually buy you?
The expected edge is the difference in probability times the spread: 6.5 points x Rs 170, about Rs 11 a share, or 5.8% of the price. But the outcome is binary: the stock either falls 21% to Rs 150 or rises 68% to Rs 320, and on a 30% view it falls seven times in ten. That is why desks size binary positions small and spend their effort asking how confident the 30% itself is, not just whether it beats 23.5%.
What does the simple formula leave out?
Three things worth naming. The decision may be months away, so the outcomes should be discounted. Investors want paying for binary risk, so part of the gap between your view and the price is a premium, not a mistake. And the implied probability is only as good as the two end values: if the rejection value is Rs 160 instead of Rs 150, the implied probability drops from 23.5% to 18.8%. Most of the real work is in the end values, not the division.
Where candidates lose it
The common slip is dividing the price by the upside, 190 over 320, and saying 59%. That treats the stock as worthless if the drug fails, when it keeps Rs 150 of value. Probability is measured along the distance between the outcomes, not from zero.
The second loss is reading Rs 201 against Rs 190 as a clear opportunity. Say that the edge is small against a 21% downside that happens seven times in ten on your own numbers, and you sound like someone who has sized a position.
What the interviewer asks next
If the decision is a year away and your discount rate is 12%, how does the implied probability change?
The stock jumps to Rs 230 with no news. What probability is the market now pricing?
How would you size a position when your edge is 6.5 points of probability?
064Why should I buy your college, and how much would you sell it for? Put a price on a college with 5,000 students paying fees of Rs 3 lakh a year, running at a 25% EBITDA margin, if similar businesses change hands at 12 times EBITDA.Market sizing and estimationCoreWellington ManagementBoston · 2024
Try it first
What is the college worth at 12 times EBITDA?
Show the worked solution
About Rs 450 crore. Revenue is 5,000 students x Rs 3 lakh, Rs 150 crore a year. A 25% EBITDA margin gives Rs 37.5 crore, and at 12 times that is an enterprise value of Rs 450 crore, before subtracting any debt. The case for buying is fees paid in advance, a campus and approvals that are slow to copy, and demand that renews with a new batch every year.
How do you structure an open question like this?
The question has two halves and the interviewer wants both. It is like selling a flat: first you say what makes it worth having, the light, the location, the building, and then you give a price per square foot times the area. Give the reasons to own it in three short points, then build the price as revenue times margin times multiple, naming every input so the interviewer can push on any one of them. Leading with the structure also buys you time to do the arithmetic.
Five thousand students at Rs 3 lakh give Rs 150 crore of revenue, a 25% margin leaves Rs 37.5 crore of EBITDA, and twelve times that is a value of Rs 450 crore, three times one year's fees.
What makes the case for buying convincing?
Pick the features an investor would pay for. The strongest is that customers pay a term or a year in advance and come back every year, so the business funds its own working capital and its revenue is visible well before the year starts. Add that a campus, a faculty and regulatory approvals take years to replicate, which protects the fee level, and that demand refreshes with every new batch. Then name the risk that decides the price: how full the seats are. One caution belongs here too: in many countries, including India, degree-granting colleges are commonly run through not-for-profit trusts or societies, so confirm the legal structure first, because it decides whether an investor can own the profit at all.
Which number would you defend hardest?
The margin and the multiple, because each moves the answer one for one. At a 20% margin the value falls to Rs 360 crore, and at 10 times EBITDA it falls to Rs 375 crore; every input in the chain carries equal weight. Justify 12 times with the visibility of fee income and 25% with a campus that is nearly full. If asked for a range rather than a point, Rs 360 to 450 crore on those two sensitivities is honest.
Where candidates lose it
Candidates answer only one half: a warm speech about the campus with no number, or a number with no reason to buy. The question is built to see whether you can pitch and value in the same breath.
The arithmetic slip is applying the multiple to revenue and saying Rs 1,800 crore. EBITDA multiples go on EBITDA; say the margin step out loud and the error cannot happen.
What the interviewer asks next
Occupancy falls from 100% to 80% with fixed costs unchanged. What happens to EBITDA and the price?
What would you pay for a college that is only half built?
Why might a buyer pay more than 12 times for this college than for a coaching chain?
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?
065Money grows at 12% a year, compounded. Roughly how long does it take to double, and how long to grow eightfold?Returns and compoundingWarm upLong-only asset managementBuy-side equity research
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Answer inside ten seconds.
Show the worked solution
About 6 years to double and about 18 years to grow eightfold. The rule of 72 says the doubling time is roughly 72 divided by the percentage rate, so 72 / 12 = 6 years; the exact figure is 6.1 years. Eightfold is three doublings, 2 x 2 x 2, so it takes three doubling times, about 18 years, and exactly 18.3. It is not eight times six.
Why does 72 divided by the rate work?
Think of a savings pot that earns 12% a year and never has anything taken out. Each year's interest earns interest the next year, so the pot grows faster in rupees every year while growing at the same percentage. The time to double depends only on the rate, and for everyday rates it is close to 72 divided by the rate in percent. The exact answer is the log of 2 over the log of 1.12, 6.12 years. The number 72 is used because it sits near the exact constant and divides neatly by 2, 3, 4, 6, 8, 9 and 12.
One rupee at 12% is worth 1.97 after 6 years, 3.90 after 12 and 7.69 after 18, so each six-year stretch roughly doubles the pot and eightfold takes about 18 years.
Why is eightfold 18 years and not 48?
Because growth multiplies. Eight is 2 x 2 x 2, so eightfold is three doublings, and each doubling takes the same six years whatever the size of the pot. The same counting gives the other useful anchors: fourfold is two doublings, 12 years; a thousandfold is about ten doublings, since 2 to the power 10 is 1,024, so about 60 years. Tenfold is a bit more than three doublings, exactly 20.3 years.
The relationship
$t_{2\times} \approx \frac{72}{12} = 6 \qquad t_{8\times} = 3 \times t_{2\times} \approx 18$
t_2x years to double
t_8x years to grow eightfold
72 the rule of 72 constant
12 the growth rate in percent
What it says in wordsDivide 72 by the rate for one doubling, then count how many doublings the target needs.
Rate Rule of 72 Exact doubling time
4% 18.0 years 17.67 years
8% 9.0 years 9.01 years
12% 6.0 years 6.12 years
18% 4.0 years 4.19 years
24% 3.0 years 3.22 years
The rule of 72 is almost exact near 8%, a little generous below it and increasingly short of the true doubling time as rates climb above 15%.
Where does an analyst use this?
Anywhere a growth rate needs to be turned into a sense of scale, fast. A company promising 24% growth is promising to double every three years; a fund charging 2% a year in fees gives up about a third of the pot over twenty years; inflation at 6% halves the value of money in about 12 years. Turning rates into doubling times is the quickest way to check whether a claim is plausible before any spreadsheet is opened.
Where candidates lose it
Eight times six, 48 years, is the whole trap. It treats compounding growth as if it added the same amount each year, which is exactly the straight-line instinct the question is designed to catch.
The quieter slip is presenting the rule as exact. Say about 6, a touch over 6 exactly, and you have shown you know the rule is an approximation that works best near 8%.
What the interviewer asks next
How long does it take to grow tenfold at 12%? (about 20 years)
At what rate does money double in five years?
Prices rise 6% a year. How long until the same basket costs twice as much?

Rate	Rule of 72	Exact doubling time
4%	18.0 years	17.67 years
8%	9.0 years	9.01 years
12%	6.0 years	6.12 years
18%	4.0 years	4.19 years
24%	3.0 years	3.22 years

066A company trades at 10 times EBITDA of 100. Depreciation and amortisation is 20, interest expense is 10, the tax rate is 25% and net debt is 200. What is its P/E?Valuation riddlesCoreSell-side equity researchIndian brokerage research

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What is the P/E?

Show the worked solution

About 15.2x. Convert the numerator and the denominator separately. Enterprise value is 10 x 100 = 1,000; take off net debt of 200 and equity value is 800. EBITDA of 100 less D&A of 20 and interest of 10 is pre-tax profit of 70; after 25% tax, net income is 52.5. The P/E is 800 / 52.5 = 15.2x.

Why can't you read the P/E straight off the EV multiple?

A flat worth Rs 1 crore with a Rs 20 lakh loan on it is worth Rs 80 lakh to its owner, and the rent the owner keeps is what is left after the loan interest and the tax. The flat's value and the owner's stake are different numbers, and so are the rent and the owner's income. EV and EBITDA belong to lenders and shareholders together; equity value and net income belong to shareholders alone, so a multiple must pair one with the other of the same kind.

Enterprise value of 1,000 becomes equity value of 800 after net debt, and EBITDA of 100 becomes net income of 52.5 after D&A, interest and tax, so the P/E is 15.2x, well above the 10x EV multiple.

The relationship

\frac{P}{E} = \frac{10 \times 100 - 200}{(100 - 20 - 10)(1 - 0.25)} = \frac{800}{52.5} = 15.2\times

10 x 100	enterprise value, the EV multiple times EBITDA
200	net debt, taken off to reach equity value
100 - 20 - 10	pre-tax profit, EBITDA less D&A and interest
1 - 0.25	the share of pre-tax profit left after tax

What it says in wordsThe P/E is equity value over net income, and each comes from converting its EV-side counterpart.

Why is the P/E higher than the EV multiple here?

Because the two sides shrink by different amounts. The price side loses 20% on the way from EV to equity, but the earnings side loses nearly half on the way from EBITDA to net income, so the P/E ends above the EV multiple. Leverage changes the balance: with net debt of 400 and interest of 20, equity value is 600, net income is 45 and the P/E is 13.3x. Heavy D&A or a high tax rate pushes the P/E up; debt that costs less than the earnings yield pulls it down.

When would an analyst do this conversion for real?

Whenever two sources quote different multiples for the same company, or when a sector trades on EV/EBITDA but a client thinks in P/E. Saying out loud which claims each number belongs to, all funders or shareholders only, is the habit that stops the conversion going wrong. Assume here that D&A is tax deductible in full and that the company has no minority interests or associates, and say so.

Where candidates lose it

The two fast errors each convert one side only. Dividing enterprise value by net income, 1,000 over 52.5, gives 19.0x; dividing equity value by EBITDA gives 8x. Both mix a number that belongs to all funders with one that belongs to shareholders.

The other slip is forgetting that interest sits between EBITDA and net income. It is the lenders' share of the profit, which is exactly why net debt comes off the price side too.

What the interviewer asks next

Net debt rises to 400 and interest to 20. What is the P/E now? (13.3x)
The company holds 200 of net cash instead of net debt, earning 5%. What is the P/E?
Why do analysts prefer EV/EBITDA when comparing companies with very different debt levels?

067On the last day of its financial year, a company borrows Rs 100 crore at 9% and uses it to buy equipment. Walk through the three statements on that day, and again at the end of the following year, with the equipment depreciated straight line over 10 years and a 25% tax rate.Three statement riddlesCoreSell-side equity researchBuy-side equity research
Try it first
On the day of the purchase, what happens to net income?
Show the worked solution
On day one nothing touches the income statement: equipment and debt each rise by Rs 100 crore, and cash flow shows minus 100 in investing and plus 100 in financing. A year later, depreciation of Rs 10 crore and interest of Rs 9 crore cut pre-tax profit by Rs 19 crore and net income by Rs 14.25 crore. Cash falls Rs 4.25 crore, equipment is Rs 90 crore, debt is still Rs 100 crore and equity is down Rs 14.25 crore.
Why does nothing hit profit on the day of purchase?
Buy a delivery van on the last evening of March with a bank loan and you are no poorer that night: you swapped borrowed money for a van. The costs come later, as the van wears out and as the loan collects interest. Buying an asset with borrowed money swaps one balance sheet item for another; costs reach the income statement only as the asset is used up and as time passes on the loan. So on day one the only movements are equipment up 100, debt up 100, and the cash flow statement showing the money coming in through financing and going out through investing.
On the purchase day equipment and debt rise by Rs 100 crore with no effect on profit, while a year later depreciation of Rs 10 crore and interest of Rs 9 crore cut net income by Rs 14.25 crore and cash by Rs 4.25 crore.
How do the numbers flow through at the end of year one?
Start on the income statement. Depreciation is 100 / 10 = Rs 10 crore and interest is 9% of 100 = Rs 9 crore, so pre-tax profit falls Rs 19 crore. Tax falls by 25% of that, Rs 4.75 crore, so net income falls Rs 14.25 crore. On the cash flow statement, add back the Rs 10 crore of depreciation, which never left the bank: cash falls Rs 4.25 crore. The cash cost of the year is the interest less the tax it saves, 9 - 2.25 = 4.25; depreciation costs profit but not cash.
Rs crore Day one End of year one
Net income 0 -14.25
Operating cash flow 0 -4.25
Investing cash flow -100 0
Financing cash flow +100 0
Cash 0 -4.25
Equipment +100 +90
Debt +100 +100
Equity 0 -14.25
Every line is a change against the balance sheet before the deal; at the end of year one assets are up 85.75 and debt plus equity is up 85.75, so it balances.
What assumptions should you say out loud?
Four of them. Interest is paid in cash at the end of the year. The tax saving is real because the company has other profits to set it against. Tax depreciation matches book depreciation. No principal is repaid in year one. Stating the assumptions turns a walkthrough into an argument the interviewer can follow, and each one is a lever for the next question. Change the second, and a loss-making company saves no tax this year, so net income falls the full Rs 19 crore.
Where candidates lose it
The common slip is putting the Rs 100 crore through the income statement on day one, as if buying equipment were an expense. It is an investment: the cost reaches profit only through depreciation, over ten years.
The second slip is forgetting to add depreciation back on the cash flow statement, which makes cash fall Rs 14.25 crore instead of Rs 4.25 crore. Check it by asking what actually left the bank: the interest, less the tax it saved.
What the interviewer asks next
The company repays Rs 10 crore of the loan at the end of year one. What changes?
How would the statements differ if the equipment were leased instead of bought?
What do the three statements show at the end of year two?
068A company's net income grows 8% a year, and every year it buys back 3% of its shares. How fast does its EPS grow, and how much higher is EPS after five years?EPS and share countCoreLong-only asset managementBuy-side equity research
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What is EPS growth per year?
Show the worked solution
About 11.3% a year, and about 1.71 times after five years. EPS is net income over shares. Net income is multiplied by 1.08 each year and the share count by 0.97, so EPS is multiplied by 1.08 / 0.97 = 1.113. Over five years that compounds to about 1.71x, against 1.47x for net income alone. Adding 8% and 3% to get 11% is close, but slightly understates it.
Why divide by 0.97 rather than add 3%?
Picture a pot of profit shared among a group of friends. If the pot grows 8% and one friend in every 33 leaves each year, each remaining friend's share grows by more than 8%, and a little more than 3% on top. EPS growth is (1 + net income growth) divided by (1 - buyback rate), minus one, because the share count sits in the denominator. Dividing by 0.97 is multiplying by 1.0309, a 3.09% boost, and that compounds with the 8%: 1.08 x 1.0309 = 1.1134.
The relationship
$g_{EPS} = \frac{1.08}{0.97} - 1 = 11.3\% \qquad \left(\frac{1.08}{0.97}\right)^{5} = 1.71$
1.08 net income growth factor per year
0.97 share count factor per year after a 3% buyback
g_EPS EPS growth per year
What it says in wordsEPS grows by the net income growth factor divided by the share count factor, compounded each year.
Net income rises from 100 to 146.9 over five years while the share count falls to 85.9, so EPS rises to 171.1 and the gap between the two lines widens every year.
Is buyback-driven EPS growth as good as profit growth?
Not automatically. EPS growth from a shrinking share count is paid for with cash that could have been reinvested or paid out, and it adds value for the remaining holders only when the shares are bought below what they are worth. A company buying back stock at a high multiple can show fast EPS growth while transferring value to the shareholders who sell. The question to ask is what the cash would have earned elsewhere.
What would an analyst check before trusting the 11.3%?
Two things. First, whether the 8% net income growth already carries the cost of funding the buyback: interest lost on cash, or interest paid on new debt. Second, whether staff share awards are quietly adding shares back. What matters is the net fall in the share count: if awards add 2% a year, EPS growth drops to about 9.2%. The share count line in the notes to the accounts settles both.
Where candidates lose it
Most candidates say 11% by adding the two rates, which is close enough to pass but misses the point the interviewer is testing: growth rates in a ratio combine by multiplying and dividing, not by adding.
The costlier slip is saying 5% by subtracting, on the instinct that buying shares uses money. The buyback reduces the denominator, so it adds to EPS growth; whatever it costs in lost interest is already inside the net income figure given.
What the interviewer asks next
Staff share awards add 2% to the share count each year. What is EPS growth now? (about 9.2%)
Net income is flat and the company buys back 5% a year. What is EPS growth? (about 5.26%)
Why might the P/E fall even while buybacks lift EPS growth?
069Your nominal cost of capital is 11% and expected inflation is 5%. What is the real discount rate, and what goes wrong if you discount a forecast built in today's prices at the nominal 11%?Cost of capital and ratesCoreSell-side equity researchResearch KPO and GCC
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Discounting a forecast in today's prices at the nominal 11% makes the value...
Show the worked solution
The real rate is about 5.7%, and discounting real cash flows at the nominal rate understates value. Real and nominal rates are linked by multiplying: 1.11 / 1.05 = 1.0571, so the real rate is 5.71%, a little below the 6% you get by subtracting. A forecast in today's prices has no inflation in it, so an 11% rate removes inflation twice. Rs 100 in year 10 is worth Rs 57.4 at the matched rate but Rs 35.2 at the mismatched one.
How are real and nominal rates linked?
Your salary rises 11% in a year when prices rise 5%. You can buy more, but not 6% more: you have 1.11 rupees for every 1.05 rupees of goods you used to buy, which is 5.71% more stuff. A real rate is the nominal rate with inflation divided out, not subtracted, so 1 plus the real rate equals 1.11 over 1.05. At low rates the two methods differ by a fraction of a point; at high inflation the gap matters.
The relationship
$1 + r_{real} = \frac{1 + r_{nom}}{1 + \pi} = \frac{1.11}{1.05} = 1.0571$
r_nom the nominal cost of capital, 11%
\pi expected inflation, 5%
r_real the real discount rate, the growth in buying power demanded
What it says in wordsOne plus the real rate is one plus the nominal rate divided by one plus inflation.
Rs 100 of year-10 cash in today's prices is worth Rs 57.4 whether you pair real cash with the real rate or nominal cash with the nominal rate, but mixing them gives Rs 35.2 or Rs 93.4, wrong in both directions.
Why does the mismatch understate value?
A nominal discount rate assumes the cash flows it meets include inflation, and discounting removes it. If the forecast was built in today's prices, the inflation was never added, so the nominal rate removes it anyway and the value falls by about 39% on a year-10 cash flow. The reverse mistake, inflated cash flows at a real rate, overstates value by just as much in the other direction. Both errors grow with the length of the forecast, which is why they hurt long-lived assets most.
Which approach does an analyst use?
Either, as long as it is consistent. Most equity models are nominal, because reported accounts, debt costs and tax are all in current rupees. Real models are common for long-lived assets such as infrastructure, where prices are linked to inflation. One trap sits inside real models: tax depreciation is fixed in rupees at the purchase price, so in a real model its value must be deflated or it is overstated. Check the terminal growth rate too: a 6% nominal growth rate is only about 1% in real terms at 5% inflation.
Where candidates lose it
The question is not really about 5.7% against 6%. The trap is the pairing: candidates happily build a forecast in today's prices and then pick up the company's nominal cost of capital from a different sheet, which quietly takes a third or more off the value of distant cash flows.
The secondary slip is subtracting inflation. It is fine as a quick estimate at low rates; say that it is an approximation and give the exact figure.
What the interviewer asks next
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070An airline's load factor rises from 80% to 85% while its yield, the revenue it earns per passenger kilometre flown, falls 4%. What happens to its revenue per available seat kilometre, RASK?Growth, mix and unit economicsCoreSell-side equity researchIndian brokerage research
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What happens to RASK?
Show the worked solution
RASK rises about 2%. RASK is yield times load factor: revenue per passenger kilometre times the share of seat kilometres that carry a passenger. The load factor rises by 85/80 = 1.0625, a 6.25% gain, not 5%, and yield is multiplied by 0.96. Together 1.0625 x 0.96 = 1.02, so RASK is up 2.0%.
Why is RASK yield times load factor?
Think of a 50-seat bus. Revenue per seat on a trip is the fare each rider pays times the share of seats with a rider in them. Fill more seats at a lower fare and revenue per seat can go either way, depending on the sizes. Revenue per available seat kilometre splits exactly into what each flown passenger kilometre earns, the yield, and the share of available seat kilometres that are flown, the load factor, so percentage changes in the two multiply.
Drawn as an area, the higher load factor adds a green strip worth 6.25% and the lower yield removes a thin red strip worth 4%, so RASK rises from 80 to 81.6, a gain of 2.0%.
The relationship
$\text{RASK} = \text{yield} \times \text{LF} \qquad 0.96 \times \frac{85}{80} = 1.020$
RASK revenue per available seat kilometre
yield revenue per revenue passenger kilometre, the price actually earned
LF load factor, revenue passenger kilometres over available seat kilometres
What it says in wordsRevenue per seat offered is the price per seat sold times the share of seats sold.
Why is the load factor gain 6.25% and not 5%?
Because 5 is the change in percentage points, and the question needs the percentage change. A move from 80% to 85% is 5 points, but 5 on a base of 80 is a 6.25% increase in seats filled, and it is the percentage change that multiplies through to revenue. Get that wrong and you add +5 and -4 to say +1%, which halves the true answer. The break-even is useful too: with yield down 4%, RASK stays flat at a load factor of 83.3%.
What should an analyst ask next?
Whether the two changes are linked, and what happened to cost. Airlines often fill seats by cutting fares, so a higher load factor and a lower yield can be one decision, not two pieces of news. RASK only matters against CASK, the cost per available seat kilometre: a 2% gain in RASK is a margin gain only if cost per seat kilometre rose by less. A change in the average trip length also moves yield, since longer flights earn less per kilometre, so check the route mix before reading the fall in yield as weaker pricing.
Where candidates lose it
The fast wrong answer is plus 1%: five up, four down. It adds percentage points to percentages, and it adds changes that should be multiplied. Both slips point the same way, which is why the answer comes out at half the truth.
The second loss is stopping at revenue. Say that the number means little without cost per seat kilometre, and that a fuller plane at lower fares may be a pricing choice, and you sound like an airline analyst rather than a calculator.
What the interviewer asks next
With yield down 4%, what load factor keeps RASK flat? (83.3%)
Cost per seat kilometre is unchanged. What happens to the operating margin if it started at 8%?
Why might yield fall when the airline adds long-haul routes, even if fares are unchanged?

\hat g	next year's forecast growth
\bar g	the sector average, the base rate
g	the company's growth last year
\beta	the persistence coefficient, the share of the excess that carries over

3/4	three of the four empty chambers are followed by another empty chamber
4/6	four empty chambers out of six after a fresh spin

P	today's share price, Rs 190
V_up	the value if the drug is approved, Rs 320
V_down	the value if it is rejected, Rs 150
p	the probability of approval the price implies

t_2x	years to double
t_8x	years to grow eightfold
72	the rule of 72 constant
12	the growth rate in percent

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