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  1. 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

    Try it first

    Required return goes from 10% to 10.5%. How far does the growth stock fall?

    Show the worked solution

    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).

    Same price, same required return, very different sensitivityPrice, before and after r rises to 10.5%10090.9-9.1%Value stockyield 5%, growth 5%10066.7-33.3%Growth stockyield 1%, growth 9%Implied duration, years: 1 / (r - g)20Value stock: 1 / 0.05100Growth stock: 1 / 0.01Growth stock: cash arrives far out,like a long bond
    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=Dr−g,−1PdPdr=1r−g:10.05=20,10.01=100P = \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
    Dnext year's dividend per 100 of price: 5 for value, 1 for growth
    rthe required return, 10% rising to 10.5%
    gthe 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

  2. 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?

    Show the worked solution

    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.

    Take both the value and the earnings down to shareholdersValue, Rs crore2,000EV-500Net debt1,500EquityEarnings, Rs crore200EBITDA-40D&A-50Interest110Pre-tax-27.5Tax 25%82.5Net profit1,500 / 82.5P/E = 18.2x
    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
    P/E=10×200−500(200−40−50)(1−0.25)=1,50082.5≈18.2\text{P/E} = \frac{10 \times 200 - 500}{(200 - 40 - 50)(1 - 0.25)} = \frac{1{,}500}{82.5} \approx 18.2
    10 x 200enterprise value, EV/EBITDA times EBITDA
    500net debt, the lenders' claim
    200 - 40 - 50profit before tax after depreciation and interest
    1 - 0.25the 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

  3. 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

    Try it first

    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.

    One price, two earnings figures, two very different multiplesEBITDA, Rs crore a yearCurrent EBITDAa strong year for margins1,500x 6.0 = Rs 9,000 croreMid-cycle EBITDAyour normal-margin view1,050Rs 9,000 / 1,050 = 8.6xWhat the price says if 6x is a fair multiple of normal earningsStreet enterprise valueRs 9,0006x mid-cycle EBITDARs 6,300-30%With Rs 3,000 crore of net debt, equity goes from Rs 6,000 to Rs 3,300 crore: -45%
    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
    EVEBITDAmid=6×1,5001,050=9,0001,050=8.6x\frac{EV}{EBITDA_{mid}} = \frac{6 \times 1{,}500}{1{,}050} = \frac{9{,}000}{1{,}050} = 8.6\text{x}
    EVenterprise value the street's price implies, Rs crore
    1,500current 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.