Financial Analysis puzzles, solved step by step

Puzzles
100
Traced to a firm
47
Topics
13
Hard
30
Topic
All topicsAccounting flow riddles10Valuation and multiples riddles10Ratio and margin riddles8Cost of capital, leverage and rates8Compounding and time value8Mental maths8Probability and expected value9Working capital and cash riddles6Percentages and averages7Estimation and market sizing7Logic and counting brainteasers7Pricing, costing and unit economics6Data and statistics intuition6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–1 of 1 · filtered from 100Clear filters
  1. 041A distributor prices at cost plus 25%. A competitor says it earns a 25% gross margin. Who keeps more on every Rs 100 of sales, and what markup would give the distributor a 25% margin?Ratio and margin riddlesWarm upCorporate FP&ACost accounting

    Try it first

    What markup on cost delivers a 25% gross margin?

    Show the worked solution

    The competitor keeps more: Rs 25 against Rs 20 on every Rs 100 of sales. Cost plus 25% means a price of 1.25 times cost, so on Rs 100 of sales cost is Rs 80 and the margin is 20%. A 25% gross margin needs cost of Rs 75 on a price of Rs 100, which is a markup of 25 over 75, or 33.3%.

    Why does the same 25% mean different money?

    Think of a vegetable seller who buys tomatoes for Rs 80 a kilo and adds Rs 20. To him, that is 25% on what he paid. To his customer, Rs 20 out of the Rs 100 she paid is 20%. Same Rs 20, two percentages. Markup divides profit by cost; margin divides it by price, and price is always the bigger number, so a margin is always smaller than the markup that produced it. The distributor's 25% markup is a 20% margin; the competitor's 25% margin is a 33.3% markup.

    On Rs 100 of sales, a 25% markup keeps Rs 20; a 25% margin keeps Rs 25Cost 80Margin 20Cost plus 25%25% of 80 = 20Cost 75Margin 2525% gross margin25 / 75 = 33.3%Price 100Price 100Markup is on costMargin is on pricemargin = k / (1 + k)markup = m / (1 - m)k = markup, m = marginGap in rupees on Rs 10025 - 20 = Rs 5
    On Rs 100 of sales, pricing at cost plus 25% means cost of Rs 80 and Rs 20 kept, while a 25% gross margin means cost of Rs 75 and Rs 25 kept, a markup of 33.3% on cost.
    Markup on costMargin on priceKept per Rs 100 of sales
    10%9.1%Rs 9.1
    20%16.7%Rs 16.7
    25%20.0%Rs 20.0
    50%33.3%Rs 33.3
    100%50.0%Rs 50.0
    Margin equals markup divided by one plus markup, so the gap widens as the markup grows: a 100% markup is only a 50% margin.

    Where does this mix-up cost real money?

    In pricing conversations, sales teams often quote markups because the numbers sound larger, while finance teams report margins. If a target says 25% margin and the price list is built at cost plus 25%, every sale falls 5 rupees short per Rs 100, a fifth of the profit the plan assumed. Discounts make it worse: a 10% discount off a cost-plus-25% price leaves a price of Rs 90 on cost of Rs 80, an 11.1% margin, so half the profit per unit is gone. Say the conversion formula out loud whenever someone gives you a percentage of profit, and ask which base it is on.

    Where candidates lose it

    The trap is answering that both keep the same, because both say 25%. The question is built to see whether you ask: 25% of what?

    The second loss is getting the conversion backwards and saying a 25% margin needs a 20% markup. Check with Rs 100 of price: cost Rs 75, profit Rs 25, and 25 over 75 is a third.

    What the interviewer asks next

    • What margin does a 40% markup give?
    • A retailer offers 20% off a product priced at cost plus 50%. What margin is left?
    • Why do sales teams often prefer to talk in markups?