Financial Analysis puzzles, solved step by step

Puzzles: 100
Traced to a firm: 47
Topics: 13
Hard: 30

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025A supermarket has annual cost of goods sold of Rs 3,650 crore. It pays suppliers in 45 days, holds 20 days of stock, and is paid in cash at the till. If its sales fall 10%, how much cash leaves the business through working capital?Working capital and cash riddlesCoreCorporate FP&ATreasury
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Sales fall 10% with payment and stock days unchanged. What happens to cash from working capital?
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About Rs 25 crore of cash leaves. Cost of goods sold is Rs 10 crore a day, so payables are 45 days, Rs 450 crore, and stock is 20 days, Rs 200 crore. With no receivables, net working capital is minus Rs 250 crore: suppliers fund the business. A 10% fall cuts daily cost to Rs 9 crore, payables to Rs 405 crore and stock to Rs 180 crore, so net working capital rises to minus Rs 225 crore. That Rs 25 crore is cash consumed.
How can a business be funded by its suppliers?
Think of a school canteen where parents pay for the term in advance and the canteen pays its vegetable seller at the end of each month. The canteen holds other people's money for weeks. A supermarket sells for cash at the till, keeps stock for 20 days and pays suppliers after 45, so it collects from customers about 25 days before it pays for the goods. Its net working capital is negative: suppliers are lending it money, free of interest, all year.
The relationship
$\text{NWC} = \underbrace{10 \times 20}_{\text{stock}} - \underbrace{10 \times 45}_{\text{payables}} = 200 - 450 = -250$
10 cost of goods sold per day, Rs 3,650 crore over 365
20 days of stock held
45 days taken to pay suppliers
What it says in wordsNet working capital is stock less payables when customers pay at the till; here suppliers fund Rs 250 crore.
Before the fall, payables of Rs 450 crore fund stock of Rs 200 crore, leaving net working capital of minus Rs 250 crore. After a 10% fall, payables of Rs 405 crore and stock of Rs 180 crore leave minus Rs 225 crore, so Rs 25 crore of cash has left the business.
Why does shrinking cost this business cash?
Run it as two movements. Stock falls by Rs 20 crore, which frees cash, but supplier credit falls by Rs 45 crore, which the supermarket has to pay out, so the net is Rs 25 crore out. Each day of lower sales means paying suppliers for last month's larger purchases while this month's till receipts are smaller. The mirror image is why such businesses love growth: a 10% rise in sales would release about Rs 25 crore.
What makes the real number worse?
The answer assumes the days stay fixed, and in a downturn they often do not. Suppliers who see sales fall may shorten credit; if payable days drop from 45 to 40, payables fall to Rs 360 crore and the cash outflow grows to about Rs 70 crore. On top of the working capital effect, lower sales also cut profit. Say both, then name the lesson a lender draws: a business funded by its suppliers can look cash-rich while it grows and turn cash-hungry quickly when it shrinks.
Where candidates lose it
The common loss is saying cash comes in, because less stock is needed. That counts only the asset side and forgets that supplier credit shrinks faster, since payables are more than twice the size of stock.
The second loss is saying nothing changes because the days are unchanged. Days are ratios; the rupee balances scale with sales, and the cash moves with the rupees.
What the interviewer asks next
If sales grew 10% instead, how much cash would working capital release?
How would the answer change if 20% of sales were on credit with 30-day terms?
Why might a supermarket's suppliers accept 45-day terms?
059A start-up has Rs 120 crore of cash and burns Rs 8 crore this month. From next month the burn falls by Rs 0.5 crore every month. Does the cash run out, and if not, what is the lowest balance it reaches?Working capital and cash riddlesCoreCorporate FP&ATreasury
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Does the cash run out?
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The cash never runs out. Burn reaches zero in month 17, by which point Rs 68 crore has gone, so the balance bottoms at Rs 52 crore. The burns are 8, 7.5, 7 and so on down to 0.5 in month 16: sixteen payments averaging (8 + 0.5) / 2 = Rs 4.25 crore, Rs 68 crore in all. Quoting a 15-month runway from 120 / 8 ignores the improvement.
Why is 120 / 8 the wrong runway?
A student who spends Rs 8,000 this month and cuts back by Rs 500 every month does not run through savings at Rs 8,000 a month; each month costs less than the last. A runway is cash divided by burn only when the burn is constant; when the burn changes by a fixed amount each month, the total spent is an arithmetic series, and you sum it. Here the burn falls to zero after sixteen steps, so the question is whether the sum of those sixteen burns is more or less than Rs 120 crore.
The naive line runs out at month 15, but with burn falling Rs 0.5 crore a month the balance curves down and flattens at Rs 52 crore from month 16; if the burn fell only half as fast, the cash would run out in month 23.
How do you sum the burn quickly?
Pair the first and last months, as the schoolboy Gauss did: 8 + 0.5 = 8.5, 7.5 + 1 = 8.5, and so on. There are sixteen burns, so eight pairs of 8.5, which is Rs 68 crore. Equivalently, sixteen months at the average burn of 4.25. Month 17's burn is zero, so nothing more is spent. Rs 120 crore less Rs 68 crore leaves Rs 52 crore at the lowest point, reached at the end of month 16.
The relationship
$S = \frac{n\,(a_1 + a_n)}{2} = \frac{16 \times (8 + 0.5)}{2} = 68 \qquad 120 - 68 = 52$
n the number of months with a positive burn, 16
a_1 the first month's burn, Rs 8 crore
a_n the last positive burn, Rs 0.5 crore in month 16
What it says in wordsThe total burned is the number of months times the average of the first and last burn, and the floor is the starting cash less that total.
What would you warn the founder about?
The answer rests entirely on the slope of the improvement. If the burn fell by Rs 0.25 crore a month instead of 0.5, the burn would reach zero only in month 33, and the cumulative burn would pass Rs 120 crore in month 23: the company runs out of money. Halving the pace of improvement turns a comfortable floor into a cash-out, so test the slope before trusting the floor. The second warning is that Rs 52 crore is a forecast floor, not a cushion: a lender or a board would want headroom above it for a bad quarter.
Where candidates lose it
The usual loss is quoting 15 months from 120 / 8, which ignores the falling burn the interviewer spelled out. It sounds decisive and is wrong in direction: the company does not run out at all.
The quieter slip is counting seventeen burns instead of sixteen, or stopping the series at the wrong month. Write the first and last positive burn, count the terms, then average. A total of Rs 68 crore is easy to check: eight pairs of 8.5.
What the interviewer asks next
The burn falls by Rs 0.25 crore a month instead. When does the cash run out?
The company must keep Rs 60 crore as a minimum balance under a loan covenant. Does it breach?
How fast must the burn fall each month for the cash to bottom exactly at zero?
074A company says its cash rose Rs 50 crore thanks to better collections. Its days sales outstanding stayed at 73 days, and revenue fell from Rs 1,000 crore to Rs 750 crore. Where did the cash actually come from?Working capital and cash riddlesCoreCorporate FP&AEquity research
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Where did the Rs 50 crore come from?
Show the worked solution
From shrinking sales, not better collecting. With days sales outstanding fixed at 73, receivables are a fifth of revenue, so they fell from Rs 200 crore to Rs 150 crore as revenue fell Rs 250 crore, releasing Rs 50 crore. Unchanged days means customers paid no faster. The release is a one-off that reverses when sales recover, and it was bought with a quarter of the revenue.
Why does falling revenue release cash?
A tailor who gives customers two months to pay always has about two months of sales outstanding. If orders halve, the amount owed to him halves too, and for a while he collects old bills faster than he issues new ones: cash arrives. Receivables are revenue times the collection period, so when the period is fixed, receivables move with revenue, and a fall in sales releases cash once, mechanically. Here 73 days is 73 / 365, one fifth of a year, so receivables are a fifth of revenue: 200 on 1,000, 150 on 750. The Rs 50 crore is a fifth of the Rs 250 crore of sales that disappeared.
Receivables fell from Rs 200 crore to Rs 150 crore while days sales outstanding stayed at 73, so the Rs 50 crore came from Rs 250 crore of lost sales, whereas real improvement to 60 days would have taken receivables to Rs 123 crore.
The relationship
$\text{Receivables} = \text{Revenue} \times \frac{\text{DSO}}{365} = 1{,}000 \times \tfrac{73}{365} = 200 \;\to\; 750 \times \tfrac{73}{365} = 150$
DSO days sales outstanding, the average number of days a sale waits to be collected
73 / 365 one fifth of a year, so receivables are a fifth of annual revenue
What it says in wordsReceivables equal revenue times the share of the year that sales wait to be collected, so with the share fixed, a quarter less revenue means a quarter less receivables.
How do you separate the volume effect from the collections effect?
Split the change in receivables into two pieces. The volume effect is the change in revenue times the old days: (750 - 1,000) x 73 / 365 = -50. The collections effect is the new revenue times the change in days: 750 x (73 - 73) / 365 = 0. Every rupee of the release is volume; the collections effect is exactly zero, and that is the number management's claim rests on. Had days improved to 60, receivables would be Rs 123 crore, a release of 76.7: 50 of volume and 26.7 of genuine improvement, and only that 26.7 would deserve the word collections.
What does the analyst say about the quality of the Rs 50 crore?
Three things. It is one-off: receivables cannot keep falling unless sales keep falling. It reverses: if revenue climbs back to Rs 1,000 crore at 73 days, receivables return to 200 and the Rs 50 crore is reabsorbed. And it was expensive: at a 30% contribution margin, Rs 250 crore of lost revenue costs about Rs 75 crore of contribution every year, more than the cash released once. The limit: this uses year-end revenue and year-end receivables, and a company whose sales fell late in the year can show a days figure that flatters or punishes it; check the quarterly pattern before concluding.
Where candidates lose it
The common loss is accepting the narrative because cash did rise. A cash increase is a fact; its cause is a claim, and the days sales outstanding figure is the test of the claim. Unchanged days means no change in collecting.
The second loss is treating the release as repeatable or as evidence of a stronger business. It came from losing a quarter of sales, which costs far more in contribution than the working capital it freed, and it comes back the moment sales do.
What the interviewer asks next
Revenue recovers to Rs 1,000 crore next year at 73 days. What happens to cash from working capital?
Days sales outstanding falls to 60 on the Rs 750 crore. How much of the release is now genuine, and how would you verify it?
Payables days rose from 40 to 70 in the same year. How would that change your reading of the cash improvement?
088A distributor's inventory rose 20% in rupees over the year, yet its inventory days fell from 60 to 50. What must have happened to cost of goods sold?Working capital and cash riddlesCoreCorporate FP&ACost accounting
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By how much must cost of goods sold have grown?
Show the worked solution
Cost of goods sold must have grown about 44%. Inventory days are inventory divided by daily cost of goods sold. For days to fall by a sixth while inventory rises a fifth, the denominator must grow by 1.2 x 60 / 50 = 1.44 times. So the larger stock is serving a much larger business, and is leaner relative to it. Had days stayed at 60, the distributor would be holding Rs 28.8 crore more stock in this example.
How can a bigger stock be leaner?
A kirana shop keeps Rs 60,000 of stock and sells Rs 1,000 a day at cost: two months of cover. A year later it keeps Rs 72,000 and sells Rs 1,440 a day: fifty days of cover. The shelf is fuller, yet each rupee of stock waits less time to be sold. Inventory days measure how long stock waits, not how much there is, so a larger rupee stock can still be leaner if what it serves grew faster.
The relationship
$\text{Days} = \frac{\text{Inventory}}{\text{COGS}} \times 365 \;\Rightarrow\; \frac{\text{COGS}_1}{\text{COGS}_0} = \frac{\text{Inv}_1}{\text{Inv}_0} \times \frac{\text{Days}_0}{\text{Days}_1} = 1.2 \times \frac{60}{50} = 1.44$
Inventory the stock held at the balance sheet date
COGS cost of goods sold over the year
Days inventory days, how long the stock would last at the current rate of sale
What it says in wordsThe growth in cost of goods sold equals the growth in inventory times the ratio of old days to new days.
Put rupees on it. Last year: COGS of Rs 730 crore is Rs 2.0 crore a day, and Rs 120 crore of stock is 60 days of it. This year inventory is Rs 144 crore. For that to be 50 days, daily COGS must be Rs 2.88 crore, an annual Rs 1,051.2 crore, up 44%.
Inventory grew 20% while cost of goods sold grew 44%, so stock fell from 60 to 50 days of cover, and at the old 60 days the distributor would hold Rs 28.8 crore more inventory.
What is the cash meaning of the change?
Compare the stock with what it would have been at the old turn. At 60 days, this year's cost of goods sold would need Rs 172.8 crore of inventory. The distributor holds Rs 144 crore. The faster turn means Rs 28.8 crore less cash tied up in stock than the business would otherwise need, even though the balance sheet shows inventory up Rs 24 crore. An analyst who reads only the rupee change calls this a working capital problem; the ratio says it is a working capital improvement.
What would make you distrust the 50 days?
Three checks. Year-end timing: inventory is a snapshot, and a stock-light last week of March can flatter the ratio; average inventory over the year is a better numerator. The denominator: some analysts compute days on revenue, not COGS, and mixing the two across years breaks the comparison. And mix: if the growth came from a fast-moving new product line, the old lines may be turning as slowly as ever. The ratio summarises; it does not explain.
Where candidates lose it
The common slip is adding instead of multiplying: inventory up 20%, days down about 17%, so COGS up about 37%. Ratios combine through their growth factors, 1.2 times 1.2, which gives 44%. The additive shortcut drifts further the bigger the moves.
The second loss is reading the rupee rise in inventory as bad news. The question is built to see whether you look past the level to the rate: more stock, held for less time, against much higher sales. Say what cash the faster turn saved.
What the interviewer asks next
Inventory fell 10% while days rose from 45 to 60. What happened to cost of goods sold?
Why might average inventory give a different answer from closing inventory here?
How would you split the change in inventory into a part from growth and a part from efficiency?

10	cost of goods sold per day, Rs 3,650 crore over 365
20	days of stock held
45	days taken to pay suppliers

n	the number of months with a positive burn, 16
a_1	the first month's burn, Rs 8 crore
a_n	the last positive burn, Rs 0.5 crore in month 16

DSO	days sales outstanding, the average number of days a sale waits to be collected
73 / 365	one fifth of a year, so receivables are a fifth of annual revenue

Inventory	the stock held at the balance sheet date
COGS	cost of goods sold over the year
Days	inventory days, how long the stock would last at the current rate of sale

Try it first

How can a business be funded by its suppliers?

Why does shrinking cost this business cash?

What makes the real number worse?

Where candidates lose it

What the interviewer asks next

Try it first

Why is 120 / 8 the wrong runway?

How do you sum the burn quickly?

What would you warn the founder about?

Where candidates lose it

What the interviewer asks next

Try it first

Why does falling revenue release cash?

How do you separate the volume effect from the collections effect?

What does the analyst say about the quality of the Rs 50 crore?

Where candidates lose it

What the interviewer asks next

Try it first

How can a bigger stock be leaner?

What is the cash meaning of the change?

What would make you distrust the 50 days?

Where candidates lose it

What the interviewer asks next