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. 012A supplier lists a part at Rs 100. It offers two schemes: 5% off every unit if you buy 1,000 or more, or 10% off only the units above 1,000. At what volume do the two schemes cost the same? And why might a buyer who needs 990 units order 1,000?Pricing, costing and unit economicsHardCorporate FP&ACost accounting

    Try it first

    At what order size do the two schemes cost exactly the same?

    Show the worked solution

    The schemes cost the same at 2,000 units, Rs 1,90,000 each. The all-units deal costs 95 times the quantity; the incremental deal costs Rs 1,00,000 for the first 1,000 and Rs 90 after that, which equals 95Q only at 2,000. Below that, all-units is cheaper. It also creates a cliff: 990 units cost Rs 99,000 but 1,000 cost Rs 95,000, so anyone ordering more than 950 should round up to 1,000.

    How do you set the two schemes side by side?

    Think of two mobile data plans, one with a flat lower price on everything once you cross a usage level and one that only discounts the extra data. They feel similar, but they reward different amounts of use. Write each scheme as total cost against quantity, then find where the two formulas are equal. All-units: 95Q once Q reaches 1,000. Incremental: 1,00,000 for the first 1,000 units, plus 90 for each unit beyond.

    The relationship
    95Q=100,000+90(Q−1,000)  ⇒  5Q=10,000  ⇒  Q=2,00095Q = 100{,}000 + 90(Q - 1{,}000) \;\Rightarrow\; 5Q = 10{,}000 \;\Rightarrow\; Q = 2{,}000
    Qunits ordered, at least 1,000
    95all-units price after 5% off
    90incremental price on units above 1,000
    What it says in wordsThe incremental deal saves Rs 5 a unit more on every unit above 1,000, and needs 2,000 units in total to make up the Rs 5,000 head start the all-units deal gives at 1,000.

    A quicker way to see it: at 1,000 units the all-units scheme is Rs 5,000 cheaper. Each extra unit costs Rs 95 under all-units and Rs 90 under incremental, so the incremental deal claws back Rs 5 a unit. It needs another 1,000 units to recover Rs 5,000, so the schemes meet at 2,000. Above that the incremental scheme wins: at 3,000 units it costs Rs 2,80,000 against Rs 2,85,000.

    Average price per unit: a cliff against a slopeRs 90Rs 95Rs 10001,0002,0003,000Units orderedAverage price paid per unitEqual at 2,000 unitscliff: 5% off every unitAll units, 5% offIncremental, 10% above 1,000: Rs 93.3 at 3,000Both: Rs 100 a unit below 1,000
    The all-units scheme drops the average price from Rs 100 to Rs 95 the moment an order reaches 1,000 units, while the incremental scheme lowers it gradually. The incremental average only reaches Rs 95 at 2,000 units, which is where the two schemes cost the same.

    Why would anyone order more than they need?

    Because the all-units scheme makes buying more cost less. 990 units at Rs 100 cost Rs 99,000, while 1,000 units at Rs 95 cost Rs 95,000, so ten extra parts arrive with Rs 4,000 back in your pocket. The same logic holds for any order above 950 units, because 1,000 units cost Rs 95,000 and anything from 951 to 999 costs more. A buyer with somewhere to store the spares should always round up.

    Near the threshold, ordering more costs less90,00095,0001,00,0001,05,0009009501,0001,0501,100Units ordered (all-units scheme)Total cost, Rs990 units: Rs 99,0001,000 units: Rs 95,00010 more units, Rs 4,000 lessShaded: 951 to 999units cost more than1,000 would
    Under the all-units scheme, 990 units cost Rs 99,000 but 1,000 units cost only Rs 95,000. Any order between 951 and 999 units costs more than rounding up to 1,000, which is the cliff an all-units discount creates.

    Say the limit from both sides of the deal. Extra units carry storage, handling and the risk they are never used, so the saving is only real if the spares have a use. For the supplier, the cliff means giving away Rs 4,000 on a sale that would have happened anyway, which is why incremental schemes are common where buyers order close to a threshold.

    Where candidates lose it

    The common loss is answering 1,000, the point where the discounts start, instead of finding where the costs meet. Writing both costs as formulas takes ten seconds and makes 2,000 obvious.

    The second loss is missing the cliff. Interviewers add the 990 question to see whether you notice that an all-units discount makes total cost fall as quantity rises, which is the opposite of what a cost curve normally does.

    What the interviewer asks next

    • What is the smallest order at which rounding up to 1,000 saves money?
    • If storing each spare part costs Rs 3 a year, does the 990 buyer still round up?
    • Which scheme would you offer as the supplier, and why?