Mutual Fund Mastery puzzles, solved step by step

Puzzles: 100
Traced to a firm: 29
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Hard: 30

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006A broad equity index trades at 22 times earnings, an earnings yield of about 4.5%, while the 10-year government bond yields 7%. How much earnings growth does equity need just to match the bond, and which of the two is cheaper?Valuation riddlesCorePIMCOSan Diego · 2026
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Roughly what yearly earnings growth makes the index match the bond, before any extra reward for risk?
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About 2.5% a year of earnings growth just to tie, and about 5.5% if you demand an assumed 3 point premium for equity risk. Equity's expected return is roughly its earnings yield plus growth. At 22 times earnings the yield is 4.5%, 2.5 points below the bond. On starting yield the bond is cheaper; equity is cheaper only if you expect earnings growth comfortably above 5.5% a year.
How do you put a stock index and a bond on the same scale?
Think of two shops for sale. One pays its owner a fixed Rs 7 for every Rs 100 of price, forever. The other pays Rs 4.5 today, but its takings rise every year. Turn the P/E upside down to get an earnings yield, then add the growth the earnings will carry, and you have a number you can hold against the bond's yield. One over 22 is 4.55%, so the index starts 2.5 points behind the bond.
At 22 times earnings the index yields 4.5%, so it needs about 2.5% yearly earnings growth to match a 7% bond and about 5.5% once an assumed 3 point equity risk premium is added.
The relationship
$E[r_{eq}] \approx \frac{E}{P} + g \;\Rightarrow\; g = 7.0\% - 4.5\% = 2.5\%$
E/P the earnings yield, one over the P/E of 22
g the long-run growth rate of earnings
7.0% the government bond yield
What it says in wordsEquity's rough expected return is what the earnings pay now plus how fast they grow, so the growth needed is the bond yield minus the earnings yield.
So which is cheaper?
Answer with a condition, not a verdict. On starting yield the bond is cheaper, and equity is cheaper only if earnings can grow faster than about 5.5% a year for a long time. The 3 point premium is an assumption for this arithmetic; you should say you would set it from your own view of equity risk. Then compare the required growth with a sensible estimate of nominal earnings growth in that economy, and state which side of the line you think it falls.
Name the limitation that marks you out. The bond yield is nominal, while earnings rise with inflation, so comparing 4.5% directly with 7% mixes a real yield with a nominal one. This comparison, often called the Fed model, is a quick screen, not a valuation. It also ignores that some earnings are reinvested, and the payout and the return on that reinvestment both shape the growth you can expect.
Where candidates lose it
The common slip is comparing 4.5% with 7% and declaring bonds cheaper, full stop. That treats equity like a bond with a fixed coupon and throws away the growth that is the whole reason to own it.
The opposite slip is saying equity is cheaper because it grows, without putting a number on how much growth is already needed. The interviewer wants the 2.5% said out loud, the premium on top, and a view on whether that growth is achievable.
What the interviewer asks next
If the bond yield falls to 6%, what P/E gives the same required growth?
How would you adjust the comparison for inflation?
Why might an index with a lower earnings yield still be priced fairly?
Asked at PIMCO, Debt Capital Markets, San Diego, 2026 (Wall Street Oasis): Which is cheaper us bonds or us equities
016A value stock has a 5% dividend yield and 5% growth; a growth stock has a 1% yield and 9% growth. Both are priced at a 10% required return. If the required return rises to 10.5%, which price falls more, by how much, and what does that say about each stock's duration?Valuation riddlesHardBlackRockNew York · 2026
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Required return goes from 10% to 10.5%. How far does the growth stock fall?
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The growth stock falls about 33% and the value stock about 9%. With a constant-growth model, price is dividend over required return minus growth. The value stock goes from 5 over 0.05, 100, to 5 over 0.055, 90.9. The growth stock goes from 1 over 0.01, 100, to 1 over 0.015, 66.7. Their implied durations are 20 and 100 years.
Why can a stock have a duration at all?
Think of two people selling their future income for cash today. One will earn a steady amount starting now; the other will earn little for years and a lot later. If the lender's interest rate rises, the second one's offer falls much more, because every rupee of it has to be discounted over a longer wait. A stock is a stream of future cash, and the further out the cash sits, the more its price moves when the discount rate moves: that sensitivity is its duration. In the constant-growth modela valuation that prices a share as the dividend expected next year divided by the required return minus a steady growth rate, price is D over (r minus g), and duration works out to 1 over (r minus g).
When the required return rises from 10% to 10.5%, the value stock falls from 100 to 90.9 while the growth stock falls from 100 to 66.7, because their implied durations are 20 and 100 years.
How do you work the two falls quickly?
Watch the gap, r minus g, not r. For the value stock the gap goes from 5 points to 5.5 points, ten per cent wider, so the price falls by 1 minus 5 over 5.5, which is 9.1%. For the growth stock the gap goes from 1 point to 1.5 points, fifty per cent wider, so the price falls by a third, 33.3%. The same half-point move is a small change to a wide gap and a large change to a narrow one.
The relationship
$P = \frac{D}{r-g},\qquad -\frac{1}{P}\frac{dP}{dr} = \frac{1}{r-g}: \quad \frac{1}{0.05} = 20, \quad \frac{1}{0.01} = 100$
D next year's dividend per 100 of price: 5 for value, 1 for growth
r the required return, 10% rising to 10.5%
g the steady growth rate: 5% for value, 9% for growth
What it says in wordsPrice is the dividend over the gap between required return and growth, and the narrower the gap, the more a change in the required return moves the price.
The duration numbers also show their own limit. Twenty years times half a point predicts a 10% fall, close to the true 9.1%. A hundred years times half a point predicts 50%, well off the true 33.3%, because a straight-line estimate fails when the move is large next to the gap. And the model assumes growth runs forever at 9% against a 10% required return, which is fragile; real growth stocks are valued with a high-growth phase that fades, but the direction of the answer holds.
Where candidates lose it
The common slip is answering that both fall about the same because both are priced at 100 at the same required return. Equal prices hide very different timing of the cash, and timing is what rate sensitivity measures.
The second slip is applying duration in a straight line and saying the growth stock falls 50%. Mention duration, then show the exact repricing: when r minus g is only 1 point, the curve matters as much as the slope.
What the interviewer asks next
Why did long-duration growth stocks fall hardest when interest rates rose sharply?
What happens to the growth stock's price if expected growth falls from 9% to 8.5% at a 10% required return?
How would you estimate the duration of an index rather than one stock?
Asked at BlackRock, Restructuring, New York, 2026 (Wall Street Oasis): Which equities have duration ? multiple stocks vs value stocks MSE Forecasting equation
025Without writing an equation: a company has an enterprise value of Rs 1,000 crore, debt of Rs 300 crore and cash of Rs 80 crore, with 20 crore shares. What is each share worth? Explain it using a house and its mortgage.Valuation riddlesWarm upPIMCONew York · 2023
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What is each share worth?
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Rs 39 a share. Enterprise value is the house: Rs 1,000 crore for the business itself. The debt is the mortgage, Rs 300 crore owed to the bank, which leaves the owner Rs 700 crore of the house. The cash is money in the drawer that the owner keeps on top, Rs 80 crore. Together that is Rs 780 crore for the shareholders, which over 20 crore shares is Rs 39 each.
What does the house stand for, and what does the mortgage stand for?
A family owns a house worth Rs 1 crore with a Rs 30 lakh home loan, and keeps Rs 8 lakh in a drawer. If they sold everything and settled up, they would walk away with the house's value, less the loan, plus the drawer: Rs 78 lakh. Enterprise value is the value of the operating business, the house; lenders are paid first out of it, and whatever cash the company already holds belongs to the shareholders on top. Scale the same family up a thousand times and you have this company.
The business is worth Rs 1,000 crore, lenders hold Rs 300 crore of it, and the shareholders own the remaining Rs 700 crore plus Rs 80 crore of cash, Rs 780 crore in all or Rs 39 a share.
Why is cash added back rather than subtracted?
Because enterprise value was built to leave it out. A buyer of the whole company would pay for the business and inherit the cash, so the price of the business alone nets the cash away. Going from enterprise value back to equity, you reverse that step: take off what the lenders are owed and add back the cash the shareholders already own. Subtracting cash as well, the common slip, gives 1,000 minus 300 minus 80, Rs 620 crore, or Rs 31 a share, which hands the drawer to the bank.
The relationship
$\text{Equity} = EV - \text{Debt} + \text{Cash} = 1{,}000 - 300 + 80 = 780, \qquad \frac{780}{20} = \text{Rs } 39$
EV enterprise value, the operating business, Rs 1,000 crore
Debt what is owed to lenders, Rs 300 crore
Cash cash the company holds, Rs 80 crore
What it says in wordsShareholders own the business less what lenders are owed, plus the cash in hand, shared across the shares.
Add the refinements an interviewer will probe. Anything else with a claim ahead of the ordinary shareholders comes off too, such as preference shares or a minority partner's share of a subsidiary, the way a second loan on the house would. And the share count should include options and convertibles that are likely to become shares. The limitation of the analogy is that a house is easy to price on its own; a business's enterprise value is itself an estimate, and every rupee of error in it lands on the equity.
Where candidates lose it
The common slip is subtracting cash along with debt because both sound like balance sheet adjustments, giving Rs 31. It treats the company's own cash as if it belonged to someone else.
The other slip is dividing enterprise value by the shares and answering Rs 50, forgetting that lenders are paid before shareholders. The house picture prevents both: the mortgage comes off, the drawer stays.
What the interviewer asks next
How would Rs 50 crore of preference shares change the answer?
If the company uses Rs 80 crore of cash to repay debt, what happens to enterprise value and to the share price?
Why do analysts value a bank on equity rather than enterprise value?
Asked at PIMCO, Financial Institutions Group (FIG), New York, 2023 (Wall Street Oasis): How do you get from enterprise value to equity value without an equation
033A lender's shares trade at 3 times book value and it earns a 15% return on equity. What P/E is that? If its ROE falls to 12% and the price-to-book stays at 3 times, what happens to the P/E?Valuation riddlesCoreEquity research at AMCsGlobal asset managers
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Before you work it: what P/E does 3 times book and a 15% ROE imply?
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A P/E of 20x, rising to 25x if ROE falls to 12% while the P/B stays at 3. Earnings are ROE times book value, so P/E equals P/B divided by ROE: 3 over 0.15 is 20. At 12% ROE the same P/B gives 3 over 0.12, or 25. The shares look no dearer on book, but each rupee of earnings now costs 25% more.
How do P/B and ROE give you the P/E?
Suppose a shop is sold for three times the money the owner has put into it, and the shop earns 15% a year on that money. A buyer paying 300 for every 100 put in gets 15 of profit a year for her 300, which is 20 years of profit. ROE is the bridge between book value and earnings, so P/E is simply P/B divided by ROE. Price sits on top of both ratios, and it cancels.
The relationship
$\frac{P}{E} = \frac{P/B}{E/B} = \frac{P/B}{ROE} = \frac{3.0}{0.15} = 20\times \qquad \frac{3.0}{0.12} = 25\times$
P/B price to book value per share, 3.0
ROE earnings divided by book value, 15% then 12%
P/E price to earnings per share
What it says in wordsDivide price-to-book by the return on equity and you have price-to-earnings.
With book value of Rs 100 a share and a price of Rs 300, a 15% ROE gives earnings of Rs 15 and a P/E of 20x. If ROE falls to 12% and the P/B stays at 3, earnings drop to Rs 12 and the same price becomes a P/E of 25x.
What does an unchanged P/B after a fall in ROE tell you?
If returns fall and the price-to-book does not, the shares have become more expensive per rupee of profit, even though nothing on the book-value screen moved. For a lender, book value is the natural anchor, and many investors screen on P/B alone. This is the case where that screen misleads: the same 3.0x now buys 12% returns instead of 15%. To hold a 20x P/E at 12% ROE, the P/B would have to fall to 2.4x.
There are fair reasons the market might hold the P/B: it may expect ROE to recover, or the fall may be a one-off provision. Say that, then say the test: if ROE stays at 12%, a P/B of 3.0 is paying for returns that are no longer there. The ratios here are illustrations; the relationship holds for any company whose book value is meaningful.
Where candidates lose it
The common slip is multiplying instead of dividing: 3 times 0.15 gives 0.45, which some candidates then misread as 4.5x. Earnings are smaller than book here, so the P/E has to be larger than the P/B, not smaller. A quick sense check catches it.
The second trap is saying the P/E falls when ROE falls, because lower returns sound cheaper. With the price and book unchanged, lower earnings mean a higher P/E.
What the interviewer asks next
What P/B would keep the P/E at 20x if ROE is 12%?
If the cost of equity is 12%, what does a 12% ROE suggest about a fair P/B for a lender that does not grow?
Why do analysts value lenders on P/B more often than on P/E?
043A project costs Rs 100 crore today and pays Rs 30 crore a year at the end of each of the next five years. What is its NPV at a 12% discount rate, and at what discount rate does the NPV fall to zero?Valuation riddlesCoreVanguardMalvern · 2024
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Before you work it: roughly what is the NPV at 12%?
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An NPV of about Rs 8.1 crore at 12%, and the NPV reaches zero at about 15.2%, the IRR. Five payments of Rs 30 crore discounted at 12% are worth 30 times 3.605, about Rs 108.1 crore, against a cost of Rs 100 crore. Raising the rate shrinks the payments' present value, and at 15.2% they are worth exactly Rs 100 crore.
How do you value the five payments quickly?
A rupee promised next year is worth less than a rupee in your hand, the same way a friend's promise to repay in five years is worth less than cash today. Discount each payment back to today, and because the payments are equal you can use one annuity factor instead of five divisions. At 12% the five-year annuity factor is 3.605, so Rs 30 crore a year is worth about Rs 108.1 crore today. Subtract the Rs 100 crore cost: the NPV is about Rs 8.1 crore. Positive NPV means the project earns more than 12%.
The relationship
$NPV = -100 + \sum_{t=1}^{5} \frac{30}{(1.12)^t} = -100 + 30 \times 3.605 = 8.14$
30 the yearly payment, Rs crore
1.12 one plus the 12% discount rate
3.605 the five-year annuity factor at 12%
What it says in wordsNPV is the present value of the payments less what you pay today.
The project's NPV is Rs 50 crore with no discounting, about Rs 8.1 crore at 12%, and falls to zero at 15.2%, the IRR; any discount rate above that makes the project destroy value.
How do you find the rate where NPV is zero without a calculator?
Bracket it. You need an annuity factor of 100 over 30, about 3.333. At 12% the factor is 3.605, too high, so the rate is above 12%. At 15% the factor is about 3.352, still a touch above 3.333; at 16% it is about 3.274, below. The IRRInternal rate of return: the discount rate at which the present value of a project inflows equals its cost, so the NPV is zero. is simply the discount rate at which the NPV curve crosses zero, here about 15.2%. In an interview, saying between 15% and 16%, closer to 15%, and showing the bracket, is a full answer.
State the limits of IRR alongside it. It assumes the payments can be reinvested at the IRR itself, it can mislead when comparing projects of very different size, and a project with cash flows that change sign more than once can have more than one IRR. NPV at the right cost of capital is the cleaner decision rule; IRR is the useful headline.
Where candidates lose it
The fast wrong answer is Rs 50 crore, five times 30 less 100, which ignores discounting entirely. Say the annuity factor out loud and the slip cannot happen.
The second loss is the IRR direction. Candidates who see a positive NPV at 12% sometimes guess the IRR is below 12%. A positive NPV at a rate means the project earns more than that rate, so the IRR is above it.
What the interviewer asks next
The payments grow 5% a year instead of staying flat. Is the NPV higher or lower, and roughly by how much?
A second project costs Rs 10 crore and has an IRR of 30%. Which would you take if you could take only one?
Why does a higher discount rate hurt long-dated projects more than short-dated ones?
Asked at Vanguard, Mutual Funds, Malvern, 2024 (Wall Street Oasis): A DCF walkthrough was asked for along with NPV with a whole question on CPV
052A company trades at 10 times EBITDA of Rs 200 crore. It has net debt of Rs 500 crore, depreciation of Rs 40 crore, interest of Rs 50 crore and a 25% tax rate. What P/E is the market paying?Valuation riddlesHardHoulihan LokeyChicago · 2026
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Before you work it: which is closest to the P/E?
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About 18.2x. Enterprise value is 10 x 200, Rs 2,000 crore. Take off Rs 500 crore of net debt and shareholders own Rs 1,500 crore. Earnings for shareholders are EBITDA of 200 less depreciation of 40 and interest of 50, which is 110 before tax and 82.5 after 25% tax. Rs 1,500 crore over Rs 82.5 crore is 18.2x.
Why can you not read the P/E straight off the EV multiple?
Think of a house worth Rs 1 crore with a Rs 40 lakh home loan. The owner's stake is Rs 60 lakh, and the rent left for the owner is the rent after the loan interest is paid. An EV multiple compares the whole business with profit before lenders and the tax office are paid; a P/E compares the shareholders' slice with the profit left for them. So you must take both the value and the earnings down to the shareholder line before you divide. Converting one side and not the other is the usual slip.
Enterprise value of Rs 2,000 crore less Rs 500 crore of net debt leaves Rs 1,500 crore of equity, and EBITDA of Rs 200 crore less depreciation, interest and tax leaves Rs 82.5 crore of net profit, so the P/E is 18.2x.
Why does the P/E come out higher than the EV multiple here?
Both sides shrink on the way down, but not by the same share. Value falls from 2,000 to 1,500, a quarter lost to lenders. Earnings fall from 200 to 82.5, well over half lost to depreciation, interest and tax, so the denominator shrinks faster and the multiple rises. Heavy depreciation, heavy interest or a high tax rate all push the P/E above the EV/EBITDA; a debt-free, low capex business has the two much closer together.
The relationship
$\text{P/E} = \frac{10 \times 200 - 500}{(200 - 40 - 50)(1 - 0.25)} = \frac{1{,}500}{82.5} \approx 18.2$
10 x 200 enterprise value, EV/EBITDA times EBITDA
500 net debt, the lenders' claim
200 - 40 - 50 profit before tax after depreciation and interest
1 - 0.25 the share of pre-tax profit kept after 25% tax
What it says in wordsTake the lenders out of the value and the lenders, the asset wear and the tax out of the earnings, then divide.
A quick check catches the common half-conversion. If you remember the tax but forget the interest, earnings are 160 x 0.75, which is 120; divide the full EV of 2,000 by that and you get 16.7x, a number that mixes the whole business with a shareholders' profit line. State the assumption that net debt is the only claim between EV and equity: minorities or preference capital would sit there too.
Where candidates lose it
The fast wrong answer is 10x, treating the two multiples as the same thing with a different name. The second wrong answer converts only one side: equity value over EBITDA, or EV over net profit, each of which pairs a value with an earnings line that belongs to someone else.
Say the matching rule before you calculate: enterprise value goes with profit before interest, equity value goes with profit after interest and tax. Then the arithmetic takes thirty seconds.
What the interviewer asks next
The company repays Rs 200 crore of debt from cash. What happens to the P/E if the EV multiple stays at 10x?
Which is the better multiple for comparing two companies with very different debt levels, and why?
Interest falls to zero and the tax rate rises to 30%. What is the P/E now?
Asked at Houlihan Lokey, Private Funds Advisory, Chicago, 2026 (Wall Street Oasis): Valuation ratio questions like if EV/EBITDA is 10x, what is
061Three unnamed companies. A has a gross margin of 22% and 45 inventory days. B has a gross margin of 78% and no inventory. C has a gross margin of 35% and capital employed of three times sales. One is a grocery retailer, one a software firm and one a cement maker. Which is which?Valuation riddlesCoreT. Rowe PriceBaltimore · 2022
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Which company is the cement maker?
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A is the grocery retailer, B is the software firm and C is the cement maker. A thin 22% gross margin with stock turning every 45 days is a reseller living on volume. A 78% gross margin with no inventory is a product that costs almost nothing to copy. Capital employed of three times sales means huge fixed plant, which among these three only cement needs.
What does each number tell you about how the business makes money?
Picture three shops on one street. The kirana store buys packets for Rs 78 and sells them for Rs 100 within weeks. The tutor sells the same recorded lesson a thousand times. The brick kiln on the edge of town cannot sell a single brick until it has built a furnace. Gross margin tells you how much of each sale the company keeps after paying for what it sells; inventory and capital tell you what it must hold to make that sale. Company A keeps 22 paise of each rupee and holds 45 days of stock, which is about 9.6% of a year's sales sitting on shelves: a reseller. Company B keeps 78 paise and holds no stock, so its costs sit below gross profit, in salaries: software.
Company A's 22% gross margin and 45 inventory days mark a grocery retailer, Company B's 78% gross margin with no stock marks a software firm, and Company C's capital employed of three times sales marks the cement maker.
Why is the cement maker C and not A?
Cement is a commodity, so candidates often pin it to the lowest margin. But a cement maker does not resell anything; it turns limestone and fuel into a product, and its gross margin sits well above a pure reseller's. What gives it away is capital intensityHow much capital a business must tie up to produce a rupee of sales. Plant-heavy industries need several rupees; retailers and service firms need little.: capital employed of three times sales means Rs 300 of plant and working capital for every Rs 100 of sales. A grocer leases its stores and pays suppliers after it has sold the goods, so it might need only Rs 25 per Rs 100 of sales.
A: grocer B: software C: cement
Gross margin 22% 78% 35%
Sales / capital employed 4.0x 2.5x 0.33x
Illustrative EBIT margin 4% 25% 15%
Return on capital = margin x turnover 16% 62.5% 5%
Only C's turnover is given; the other turnovers and all three EBIT margins are illustrative, chosen to show how each model reaches its return on capital.
The table shows why the pattern matters to an analyst, not just to a quiz. The grocer earns a thin margin many times over; software earns a fat margin on little capital; the cement maker needs a fair margin just to cover the plant it had to build, which is why cement returns swing so hard with prices and plant utilisation. The limit: companies define gross margin differently. Some put power and freight inside cost of sales, some below it, so check the definition before reading a margin across two companies.
Where candidates lose it
The fast wrong move is to sort by margin alone: lowest margin is the commodity, so cement is A. That ignores that a reseller's gross margin is thin by nature, because it buys finished goods.
The second miss is not using the capital line at all. Interviewers give three clues because each one rules out a different pairing; say which clue decides each match and the answer becomes an argument, not a guess.
What the interviewer asks next
Add a fourth company: gross margin 60%, inventory days 200. What might it be?
Which of the three would you expect to have negative working capital, and why?
A cement maker's sales rise 10% with no new plant. What happens to its return on capital?
Asked at T. Rowe Price, Investments, Baltimore, 2022 (Wall Street Oasis): Guess what type of company it is based on a few lines of income statement
071A stock trades at 20 times earnings and pays out 40% of its profit as dividends. What is its dividend yield?Valuation riddlesWarm upHoulihan LokeyChicago · 2026
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What is the dividend yield?
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2%. Flip the P/E to get the earnings yield: a P/E of 20 means the company earns 1/20, or 5%, of its share price each year. It pays out 40% of those earnings, so the dividend is 40% of 5%, which is 2% of the price. A Rs 400 share earning Rs 20 pays Rs 8, and 8 / 400 is 2%.
How do you get from a P/E to a yield?
If a flat costs Rs 20 lakh and earns Rs 1 lakh a year in rent, it costs 20 years of rent, and the rent is 5% of the price. The same flip works for shares. A P/E of 20 means the share costs 20 years of earnings, so the earnings yieldEarnings per share divided by the share price: the P/E turned upside down. A P/E of 20 is an earnings yield of 5%. is 1/20 = 5%. Only part of those earnings reach the shareholder as cash. With a payout ratioThe share of profit a company pays out as dividends. The rest is retained and reinvested in the business. of 40%, the dividend is 0.4 x 5% = 2% of the price, and the other 3% stays in the company.
A P/E of 20 is an earnings yield of 5%, and paying out 40% of it gives a dividend yield of 2% with 3% retained, as a Rs 400 share earning Rs 20 and paying Rs 8 shows.
The relationship
$\frac{D}{P} = \frac{D}{E} \times \frac{E}{P} = 0.40 \times \frac{1}{20} = 2\%$
D / P dividend yield, dividend per share over price
D / E payout ratio, dividend per share over earnings per share
E / P earnings yield, the inverse of the P/E
What it says in wordsDividend yield is the payout ratio times the earnings yield, because the earnings cancel out.
What does the other 3% do, and where does this identity help?
The retained 3% is not lost; it is reinvested. If the company earns 15% on what it reinvests, keeping 60% of profit lets it grow earnings by about 0.6 x 15% = 9% a year, and the dividend yield plus that growth, 11%, is a rough estimate of the shareholder's long-run return. That is the logic of a dividend discount model in one line. The identity also works backwards in an interview: a stock yielding 2% with a 40% payout must be on a P/E of 20.
The limits: the P/E uses one year's earnings, which may be unusually high or low, and the payout ratio can change from year to year. Buybacks return cash too, so a company paying low dividends but buying back shares can return more than its dividend yield suggests. And the growth estimate assumes the company keeps earning 15% on new money, which gets harder as it grows.
Where candidates lose it
The trap is dividing the wrong things: 40% by 20 gives 2 by luck, but candidates who do it cannot explain why and fall over on the follow-up. Others turn 20 into 20% or forget to flip the P/E at all.
Say the identity out loud before the number: dividend yield equals payout ratio times earnings yield. Then the arithmetic is one line and every variation of the question is the same line.
What the interviewer asks next
A stock yields 3% and pays out 60% of earnings. What is its P/E?
The company raises its payout to 80% with no change in price. What happens to the yield and to future growth?
Why might a fund manager prefer a 1% yielder that buys back shares to a 3% yielder that does not?
Asked at Houlihan Lokey, Private Funds Advisory, Chicago, 2026 (Wall Street Oasis): Mostly technical, with standard accounting and valuation ratio questions.
078A commercial building has gross potential rent of Rs 12 crore a year. Vacancy runs at 8%, and operating costs are 20% of the rent actually collected. Buyers of similar buildings pay a cap rate of 8%. What is the building worth?Valuation riddlesCoreInvescoNew York · 2025
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Which income figure do you divide by the cap rate?
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About Rs 110.4 crore. Start from Rs 12 crore of gross potential rent and take off 8% vacancy to reach Rs 11.04 crore collected. Take off operating costs of 20% of that, Rs 2.208 crore, to reach net operating income of Rs 8.832 crore. Divide by the 8% cap rate: Rs 8.832 crore over 0.08 is Rs 110.4 crore.
Why does a cap rate turn one year's income into a price?
Imagine a flat that brings you Rs 30,000 a month after society charges and the odd empty month, Rs 3.6 lakh a year. If similar flats sell for Rs 72 lakh, buyers are accepting a 5% yield, and you can price any flat on the street by dividing its net rent by 5%. A cap rate is that street yield for commercial property: value equals net operating income divided by the rate buyers accept. It works like a perpetuity with expected rent growth folded into the rate, which is why a lower cap rate means a higher price.
Rs 12 crore of rent on paper shrinks to Rs 11.04 crore collected after 8% vacancy and to Rs 8.832 crore of net operating income after running costs, which at an 8% cap rate is worth Rs 110.4 crore.
Why does every cost line move the value so much?
Because each rupee of net income is multiplied by one over the cap rate, 12.5 times at 8%. A cost saving of Rs 10 lakh a year adds Rs 1.25 crore of value, and a rise in vacancy from 8% to 12% cuts value by about Rs 4.8 crore. That is why a buyer picks apart the rent roll and the service charge budget before arguing about the cap rate at all. The cap rate moves value too: the same income is worth Rs 117.8 crore at 7.5% and Rs 103.9 crore at 8.5%.
The relationship
$V = \frac{GPR \times (1-v) \times (1-c)}{\text{cap}} = \frac{12 \times 0.92 \times 0.80}{0.08} = 110.4$
GPR gross potential rent, if every unit were let all year
v vacancy, 8%
c operating costs as a share of collected rent, 20%
cap the cap rate buyers accept, 8%
What it says in wordsValue is the rent that is actually collected, less what it costs to run the building, divided by the market's yield.
Say the limitation before the interviewer does. A single cap rate prices a stable, well-let building. A building with a large lease expiring next year, or one mid-refurbishment, needs its cash flows laid out year by year rather than one year's income capitalised. The cap rate method is a shortcut for the ordinary case, and the valuer's job is to spot when the case is not ordinary.
Where candidates lose it
The common slip is dividing gross potential rent by the cap rate and quoting Rs 150 crore. Gross potential rent is a ceiling that assumes every square foot is let and nothing costs anything to run; no market cap rate was ever quoted on it.
The second slip is taking the 20% cost ratio on gross rent instead of collected rent. That gives costs of Rs 2.4 crore and a value of Rs 108.0 crore. Read which base a percentage is quoted on before you multiply.
What the interviewer asks next
The buyer funds 60% of the price with debt at 9%. Does that change the value of the building?
What cap rate would make the building worth Rs 120 crore?
Why do cap rates tend to rise when interest rates rise?
Asked at Invesco, Real Estate, New York, 2025 (Wall Street Oasis): Walk me through how to get the exit value of a property from Gross Potential rent, using Cap rate.
087The street values a refining company at 6 times its current EBITDA of Rs 1,500 crore. You think mid-cycle EBITDA, at normal refining margins, is Rs 1,050 crore. What multiple of mid-cycle EBITDA is the street really paying, and what does that say about your variant view?Valuation riddlesHardFranklin TempletonSan Mateo · 2024
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What multiple of mid-cycle EBITDA does the street's price imply?
Show the worked solution
About 8.6 times mid-cycle EBITDA, so the stock is cheap only if today's margins last. Six times Rs 1,500 crore is an enterprise value of Rs 9,000 crore. On your normal earnings of Rs 1,050 crore that is 8.6x. If 6x is a fair multiple of normal earnings, the business is worth about Rs 6,300 crore, 30% less. Your variant view is really a view on earnings, not on the multiple.
Why can a low multiple be expensive?
A cricketer who scores 600 runs in a dream season is not a 600-run player; his normal year is nearer 400. Pay for 600 every year and you have overpaid, however modest the fee looks against this season's scorecard. A multiple is a price divided by one year's earnings, so when that year is a cyclical peak, the multiple looks cheap precisely because the earnings are temporarily high. Refiners are a textbook case: their profit swings with the gap between crude oil costs and product prices, which moves in cycles.
The street's Rs 9,000 crore is 6.0 times peak EBITDA of Rs 1,500 crore but 8.6 times mid-cycle EBITDA of Rs 1,050 crore, and at 6 times normal earnings the business would be worth Rs 6,300 crore, 30% less.
How do you turn the gap into a variant view?
Hold the price still and change only the earnings. The street pays Rs 9,000 crore of enterprise value. Divided by your mid-cycle Rs 1,050 crore, that is 8.6 times normal earnings, a premium multiple hiding behind a discount one. Suppose refiners have usually traded near 6 times normal earnings. Then the price you can defend is 6 x 1,050, or Rs 6,300 crore, and the street is implicitly assuming that today's Rs 1,500 crore is the new normal. Your disagreement is a 30% lower view of sustainable EBITDA.
The relationship
$\frac{EV}{EBITDA_{mid}} = \frac{6 \times 1{,}500}{1{,}050} = \frac{9{,}000}{1{,}050} = 8.6\text{x}$
EV enterprise value the street's price implies, Rs crore
1,500 current EBITDA, Rs crore
EBITDA_{mid} your estimate of EBITDA at normal margins, Rs crore
What it says in wordsKeep the price the street pays, swap in normal earnings, and see what multiple you are really being asked to pay.
Why does the equity fall further than the enterprise value?
Because debt does not shrink when margins do. With an assumed Rs 3,000 crore of net debt, the street's equity value is Rs 6,000 crore; at Rs 6,300 crore of enterprise value it is Rs 3,300 crore. A 30% fall in the value of the business becomes a 45% fall for shareholders, because all of the loss lands on the equity slice. Say the weak point of your own view too: mid-cycle is an estimate of an average over a cycle whose length and depth nobody knows, and if capacity is genuinely scarce for years, today's margins may be closer to normal than you think. The defence is to show the history of margins and say what would make you wrong.
Where candidates lose it
Candidates argue about the multiple: refiners deserve 5x, or 7x, or the sector average. That misses the point of the question, which is that the street and you can agree on 6x and still disagree by Rs 2,700 crore, because you are applying it to different earnings.
The second loss is calling the stock cheap at 6x without asking which year's EBITDA sits underneath. For a cyclical business, always ask whether the denominator is a peak, a trough or a normal year before reading the multiple at all.
What the interviewer asks next
At the bottom of the cycle EBITDA is Rs 600 crore and the stock trades at 15x. Is it expensive?
How would you estimate mid-cycle EBITDA for a refiner, and what history would you need?
What would make you abandon the variant view?
Asked at Franklin Templeton, Oil & Gas, San Mateo, 2024 (Wall Street Oasis): Why did I have a variant view of the multiple I applied to a refiner company relative to street expectations.

E/P	the earnings yield, one over the P/E of 22
g	the long-run growth rate of earnings
7.0%	the government bond yield

D	next year's dividend per 100 of price: 5 for value, 1 for growth
r	the required return, 10% rising to 10.5%
g	the steady growth rate: 5% for value, 9% for growth

EV	enterprise value, the operating business, Rs 1,000 crore
Debt	what is owed to lenders, Rs 300 crore
Cash	cash the company holds, Rs 80 crore

P/B	price to book value per share, 3.0
ROE	earnings divided by book value, 15% then 12%
P/E	price to earnings per share

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