Equity Research puzzles, solved step by step
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021Convert USD 2.4 billion into rupees at Rs 83 to the dollar and express the answer in crore. Then say how many crore make one billion rupees.Indian brokerage researchResearch KPO and GCC
Try it first
How many crore make one billion?
Show the worked solution
Rs 19,920 crore, and 100 crore make a billion. USD 2.4 billion at Rs 83 is Rs 199.2 billion. A crore is ten million, 10 to the 7, and a billion is 10 to the 9, so a billion rupees is 100 crore. Rs 199.2 billion times 100 is Rs 19,920 crore, just under a fifth of a lakh crore.
Why do people get the crore conversion wrong?
Think of two rulers marked in different units, one in inches and one in centimetres. Reading a length off one and writing it in the other is easy once you line them up, and error-prone if you do it from memory. Indian and Western number names are two rulers on the same powers of ten. The Indian system groups by lakh and crore, 10 to the 5 and 10 to the 7, while the Western system groups by thousands, so the two only line up at a thousand and at a billion, which equals 100 crore.
On one ruler of powers of ten, a lakh is 10 to the 5, a crore is 10 to the 7 and a billion is 10 to the 9, so a billion is 100 crore and Rs 199.2 billion is Rs 19,920 crore. What is the fastest safe route in the room?
Do the currency first, then the units. 2.4 x 83 is 199.2, so Rs 199.2 billion. Multiply billions by 100 to get crore, and divide crore by 1,00,000 to get lakh crore; never convert through million unless you have to. That gives Rs 19,920 crore, or about 0.2 lakh crore. If you prefer the Western route: Rs 199,200 million divided by 10 million per crore gives the same 19,920.
Indian Power of ten Western 1 lakh 10^5 100 thousand 10 lakh 10^6 1 million 1 crore 10^7 10 million 100 crore 10^9 1 billion 1 lakh crore 10^12 1 trillion The two naming systems on the same powers of ten; the rows to remember are a crore as ten million and a billion as 100 crore. In an Indian research role this comes up every day, because company filings report in crore or lakh while global peers and many investors think in millions and billions. The exchange rate here is the one given in the question; for real work, use the rate on the date of the numbers you are converting and state it.
Where candidates lose it
The common loss is dropping or adding a zero: answering Rs 1,992 crore or Rs 1,99,200 crore. It happens when the conversion is done through million in the head. Line up billion with 100 crore and the error disappears.
The second is mixing digit groupings when writing the number, for example writing 19,920 crore with Western commas in one place and Indian commas in another. Pick one system per number and say which.
What the interviewer asks next
- Express Rs 3.5 lakh crore in US dollars at Rs 83.
- A company reports revenue of Rs 8,450 crore. What is that in million rupees?
- How would you present a peer table that mixes Indian and US companies?
046A company's EBITDA margin moves from 12% to 15%. Is that a 3% improvement or a 25% improvement?Sell-side equity researchIndian brokerage research
Try it first
Which sentence would you write in a results note?
Show the worked solution
Both, if you say it properly: the margin rose 3 percentage points, which is a 25% relative rise. The difference between two percentages is measured in percentage points, here 15 minus 12, or 300 basis points. The relative change is 3 divided by 12, which is 25%. On flat sales of Rs 1,000 crore, that is EBITDA rising from Rs 120 crore to Rs 150 crore, 25% more.
Why are both numbers right and one of them misleading?
If a bank's loan rate moves from 8% to 9%, nobody says the rate rose 1%; they say it rose one percentage point, even though the interest bill rose 12.5%. A percentage point is the difference between two percentages; a per cent change is that difference measured against the starting value. Saying margin improved 3% leaves the reader guessing whether the margin went to 15% or to 12.36%, which is 3% more than 12%.
The margin gap from 12% to 15% is 3 percentage points, or 300 basis points, and the same move is a 25% rise measured against the old 12%, which on flat sales of Rs 1,000 crore takes EBITDA from Rs 120 crore to Rs 150 crore. When does the 25% matter more than the 3 points?
When you are forecasting profit. At flat sales, a margin that rises by a quarter of itself lifts EBITDA by a quarter, so the 25% is what flows into earnings and valuation. On Rs 1,000 crore of sales, EBITDA moves from Rs 120 crore to Rs 150 crore. The same 3 points on a 30% margin would be only a 10% rise in EBITDA, which is why the same points of margin matter much more for a thin-margin business.
Starting margin Up 3 points to Relative rise 6% 9% 50% 12% 15% 25% 20% 23% 15% 30% 33% 10% The same 3 points is a 50% rise on a 6% margin and a 10% rise on a 30% margin. In the room, give the answer in one line: 3 percentage points, 300 basis points, a 25% relative improvement. Then add the one caution that shows judgement: check whether sales were flat, because a margin can rise while EBITDA falls if revenue shrinks.
Where candidates lose it
Candidates pick one number and defend it, which misses the point of the question. The interviewer wants to hear the vocabulary: percentage points or basis points for the difference, per cent for the relative change.
The second loss is saying 3% in a note. It reads as a 3% relative change, and a portfolio manager who takes it that way will model the wrong EBITDA.
What the interviewer asks next
- A bank's net interest margin moves from 3.2% to 3.5%. Say the change two ways.
- Margin rises from 12% to 15% while revenue falls 20%. What happens to EBITDA?
- Why do rates desks talk in basis points rather than per cent?