Financial Analysis puzzles, solved step by step

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  1. 016A one-page summary shows revenue Rs 500 crore, cost of goods sold Rs 300 crore, gross profit Rs 200 crore, operating expenses Rs 120 crore, EBITDA Rs 90 crore, D&A Rs 20 crore and EBIT Rs 60 crore. Exactly one number is wrong. Which is it, and how do you prove it?Ratio and margin riddlesCoreJefferiesNew York · 2025

    Try it first

    Which line is wrong?

    Show the worked solution

    EBITDA is wrong: it should be Rs 80 crore, not Rs 90 crore. Check every subtotal. Revenue less cost of goods sold is 200, so gross profit is right. Gross profit less opex is 80, not 90. EBITDA less D&A is 70, not the 60 shown. EBITDA is the only number in both failed checks, and setting it to 80 makes every line reconcile, including EBIT at 60.

    Where do you start when one number in a page is wrong?

    Think of a shop's daily cash sheet where the till, the card machine and the total do not agree. You do not stare at the biggest number; you re-add each subtotal and see which ones break. A P&L is a chain of subtractions, so every subtotal can be tested against the lines above it and the lines below it. Write the three identities out loud: gross profit is revenue less cost of goods sold; EBITDA is gross profit less operating expenses; EBIT is EBITDA less D&A.

    Test every subtotal both ways; the wrong line fails twiceSummary P&L, Rs croreRevenue500Cost of goods sold(300)Gross profit2001Operating expenses(120)EBITDA9023D&A(20)EBIT6031Revenue less COGS: 500 - 300 = 200Gross profit passes2Gross profit less opex: 200 - 120 = 80EBITDA says 90: fails3EBITDA less D&A: 90 - 20 = 70EBIT says 60: fails4Try EBITDA = 80: 80 - 20 = 60Everything reconcilesEBITDA sits in both failed checks.Correct it to 80 and one change fixes both.
    Gross profit passes its check, but EBITDA fails twice: 200 less 120 is 80, not 90, and 90 less 20 is 70, not 60. Changing EBITDA to 80 makes both checks pass, so it is the one wrong number on the page.

    Why is EBITDA the culprit and not opex or EBIT?

    Two checks fail, and they share exactly one line. The wrong number is the one whose single correction fixes every failed check at once. Suppose opex were wrong instead: setting it to 110 makes EBITDA of 90 look right, but 90 less 20 still is not 60, so a second error would be needed. Suppose EBIT were wrong: 70 would fix the bottom check but leave 200 less 120 against 90. Only EBITDA at 80 repairs both. The puzzle says exactly one number is wrong, so that settles it.

    If this line were the errorIt would need to beDoes everything then reconcile?
    Operating expenses110No: 90 less 20 is still 70, not 60
    EBITDA80Yes: 200 - 120 = 80 and 80 - 20 = 60
    D&A30No: 200 - 120 is still 80, not 90
    EBIT70No: 200 - 120 is still 80, not 90
    Testing each suspect line in turn. Only EBITDA has a single corrected value that makes every subtotal hold.

    What should you say beyond the answer?

    State the assumption that made the puzzle solvable: operating expenses here exclude D&A, so EBITDA is gross profit less opex. If opex included depreciation, the chain would read differently. On the job, this test is the first thing a reviewer runs on any summary table, because subtotal errors usually come from a hard-coded number that did not update when the line above changed. Say where you would look next: the cell that feeds EBITDA, and whether margins quoted elsewhere in the pack used the wrong 90. At 90, the EBITDA margin reads 18% instead of 16%.

    Where candidates lose it

    The common loss is checking top-down, finding that 200 less 120 is 80, and declaring opex or EBITDA wrong without deciding which. Either could explain the first failure; only the second check separates them.

    The other loss is silent work. Say each identity as you test it, so the interviewer hears a method rather than a guess, and finish with the corrected figure, Rs 80 crore.

    What the interviewer asks next

    • If two numbers could be wrong, could you still identify them from this page alone?
    • What is the EBITDA margin before and after the correction?
    • How would you build a check into a model so a broken subtotal shows up automatically?

    Asked at Jefferies, Investment Banking, New York, 2025 (Wall Street Oasis): one question they laid out a set a financials where one number was wrong and asked me to find the error

  2. 055A company has revenue of Rs 100 crore, cost of goods sold of Rs 60 crore and other costs of Rs 25 crore, so EBITDA is Rs 15 crore. Which adds the most EBITDA: revenue up 10% with COGS moving in line, COGS down 5%, or EBITDA up 5%? At what gross margin does the answer flip?Ratio and margin riddlesCoreNomuraSan Francisco · 2026

    Try it first

    Which lever adds the most EBITDA for this company?

    Show the worked solution

    Revenue up 10% adds the most, Rs 4 crore, against Rs 3 crore for the COGS cut and Rs 0.75 crore for EBITDA up 5%. New revenue brings only its gross margin: 10% of Rs 40 crore of gross profit. The COGS cut saves 5% of Rs 60 crore. The two levers tie when 10% of gross profit equals 5% of COGS, at a gross margin of 33.3%; below that, cutting COGS wins.

    Why is a revenue increase worth less than it sounds?

    A tea stall that sells 10% more cups also buys 10% more milk and tea leaves. When costs move with sales, extra revenue adds only its gross margin to profit, not the whole rupee. Here each extra rupee of sales brings 40 paise of gross profit, so Rs 10 crore of new revenue adds Rs 4 crore. The Rs 25 crore of other costs is assumed fixed; if part of it rose with sales too, the revenue lever would shrink further.

    The COGS cut is simpler: 5% of Rs 60 crore is Rs 3 crore straight to EBITDA. EBITDA up 5% is the decoy: 5% of a Rs 15 crore base is only Rs 0.75 crore, because a percentage of a small number is a small number.

    Which lever wins depends on the gross marginEBITDA added, Rs crore, at a 40% gross marginRevenue up 10%4COGS down 5%3EBITDA up 5%0.75Revenue adds 10% of gross profit (40)COGS cut adds 5% of COGS (60)EBITDA up 5% adds 5% of only 1505100%50%100%Gross margin33.3%: tiethis company: 4 vs 3Revenue up 10%COGS down 5%
    At a 40% gross margin, revenue up 10% adds Rs 4 crore of EBITDA against Rs 3 crore for a 5% COGS cut and Rs 0.75 crore for EBITDA up 5%; the revenue and COGS levers tie at a gross margin of 33.3%, and the cost cut wins below it.

    At what gross margin does the answer flip?

    Write both gains per rupee of revenue. The revenue lever adds 10% times the gross margin; the COGS lever adds 5% times the cost ratio, which is one minus the gross margin. They tie when 0.10 x GM = 0.05 x (1 - GM), which gives a gross margin of one third. Above 33.3%, growing sales does more; below it, as in grocery or commodity processing, the cost cut does more. At the tie each lever adds Rs 3.33 crore on Rs 100 crore of revenue.

    The relationship
    0.10⋅GM=0.05⋅(1−GM)  ⇒  GM=13≈33.3%0.10 \cdot GM = 0.05 \cdot (1 - GM) \;\Rightarrow\; GM = \tfrac{1}{3} \approx 33.3\%
    GMgross margin, gross profit over revenue
    0.10 x GMEBITDA added by revenue up 10%, per rupee of revenue
    0.05 x (1 - GM)EBITDA added by COGS down 5%, per rupee of revenue
    What it says in wordsThe revenue lever beats the cost lever whenever the gross margin is above one third.

    What does the interviewer want to hear beyond the number?

    Ask for the margin structure before answering, because the right lever depends on it. Then add the practical view: a 5% cost cut is often more within management's control than 10% more sales, which may need price cuts or marketing spend that eat into the gain. Finally, EBITDA up 5% can never beat the revenue lever, since EBITDA can never exceed gross profit; it beats the COGS cut only when EBITDA is larger than COGS, as in some software businesses. If half the other costs were variable, the revenue lever would fall to Rs 2.75 crore and the COGS cut would win.

    Where candidates lose it

    Candidates hear 10% and assume revenue wins because it is the biggest percentage, or pick EBITDA up 5% because it sounds as if it lands straight on the bottom line. Both skip the question of what each percentage is a percentage of.

    The other miss is forgetting that COGS moves with revenue. Treating a 10% revenue rise as Rs 10 crore of extra EBITDA overstates the gain two and a half times.

    What the interviewer asks next

    • Half the other costs are variable. Does the ranking change?
    • Which lever would a grocery chain prefer, and why?
    • What kind of business would make EBITDA up 5% the best of the three?

    Asked at Nomura, Generalist, San Francisco, 2026 (Wall Street Oasis): $10 million in revenue. Do u want a 10% increase in revenue, 5% decrease in COGS, or 5% increase in EBITDA