Investment Banking puzzles, solved step by step

Net income falls Rs 60, cash falls Rs 10, debt rises Rs 50 and retained earnings fall Rs 60. The full Rs 100 is expensed, so pre-tax income drops 100 and, after 40% tax, net income drops 60. The cash flow statement adds back the Rs 50 of PIK as a non-cash expense. On the balance sheet the PIK accrues to the debt, and assets of minus 10 equal liabilities and equity of plus 50 minus 60.

What does paid in kind mean in plain terms?

Suppose you owe a friend Rs 100 of interest, pay Rs 50 in cash and write an IOU for the other Rs 50. Your wallet is Rs 50 lighter, and you now owe Rs 50 more than before. Paid in kindInterest settled by adding it to the loan principal instead of paying cash. Often shortened to PIK. interest works exactly like that IOU. PIK interest is a real expense paid with more debt instead of cash, so it reduces profit while adding to the loan. That one sentence tells you where every number in the walk will land.

Why does cash fall by only Rs 10?

Because tax is worked out on the whole expense, not just the cash part. Assume both halves of the interest are tax deductible, which is the usual set-up for this question; real deductibility rules vary by country and are often capped, so say the assumption. The Rs 100 expense saves Rs 40 of tax, and the only cash going out is the Rs 50 of cash interest, so cash falls Rs 50 minus Rs 40, which is Rs 10. On the cash flow statement the same Rs 10 appears as net income of minus 60 plus the Rs 50 PIK add-back.

How do you prove the balance sheet balances?

Say it in one breath. Assets fall 10 through cash. Liabilities rise 50 because the PIK interest is added to the principal of the debt. Equity falls 60 through retained earnings. Minus 10 on the asset side equals plus 50 minus 60 on the other side, so the balance sheet balances. Saying the check out loud is what turns a recited answer into a reasoned one, and it catches the slip of forgetting where the PIK went.

Net income falls Rs 7.5, cash rises Rs 2.5, inventory falls Rs 10 and retained earnings fall Rs 7.5. The write-down is an expense, so pre-tax income falls 10 and, after the Rs 2.5 tax saving, net income falls 7.5. No cash left the business, so the cash flow statement adds the 10 back and cash ends Rs 2.5 higher. Assets fall 7.5 and equity falls 7.5, so it balances.

Why does a loss leave the company with more cash?

A shopkeeper finds a carton of biscuits past their date. They cost Rs 10 and are now worth nothing. No money changes hands today; the cash went out when the biscuits were bought. What changes is that the loss lowers this year's taxable profit. A write-down is a non-cash loss, so its only cash effect is the tax it saves, and cash rises by 25% of Rs 10. Inventory is carried at the lower of cost and net realisable valueWhat the stock can be sold for, less the costs of selling it., which is why the carrying amount is cut when goods lose value.

How does each statement move?

Income statement: the write-down usually sits inside cost of goods sold, so pre-tax income falls 10, tax falls 2.5 at 25%, and net income falls 7.5. Cash flow statement: start from net income of minus 7.5, add back the 10 because no cash left, and operating cash flow is plus 2.5. Balance sheet: inventory is down 10 and cash is up 2.5, so total assets are down 7.5, and retained earnings are down 7.5. The check is minus 10 plus 2.5 on the asset side equalling minus 7.5 in equity.

What assumption should you say out loud?

That the write-down is deductible for tax now, as the question states. Whether a tax system allows the deduction when the stock is written down or only when it is sold depends on its rules, which you would confirm. If the deduction comes later, cash does not move this year and the company records a deferred tax asset of Rs 2.5 instead, with the balance sheet still balancing. Offering that variant in one sentence shows you understand why the cash moved in the first place.

EBITDA rises to Rs 120 crore, enterprise value to Rs 950 crore, and EV/EBITDA eases from 8.0x to about 7.9x. Rent leaves operating costs and comes back as depreciation and interest, which sit below EBITDA, so EBITDA gains the full Rs 20 crore. The lease liability is debt-like, so it joins EV. The multiple barely moves because both sides change together, and it slips only because the lease enters at 7.5x.

Why does EBITDA rise when nothing about the business changed?

Think of a family that rents its flat. If you decide to treat the flat as bought with a loan, the monthly rent disappears from the household budget and reappears as loan interest plus wear and tear on the flat. The family pays the same cash; only the labels moved. Under the new standard, rent leaves operating costs and returns as depreciation and interest, both below EBITDA, so EBITDA rises by the whole Rs 20 crore.

Why must enterprise value move too?

Enterprise value has to match the earnings line it is divided into. Once EBITDA no longer bears the rent, the claim that rent used to pay for, the lease liabilityThe present value of the rent a company has committed to pay over the lease term, carried on the balance sheet like a loan., must be counted like debt and added to EV, taking it from Rs 800 crore to Rs 950 crore. Move one side without the other and the multiple jumps to 9.5x or collapses to 6.7x, though the business is exactly the same. Those two numbers are what candidates produce when they mix bases.

What does this mean for a comps table?

Some peers report under standards that capitalise leases and some under rules that leave rent in operating costs. A comps table means something only if every company sits on the same basis, either all before lease capitalisation or all after. For a retailer or an airline with large leases the gap is far bigger than here, so the adjustment can move the valuation more than any view on growth. Indian companies report under an equivalent standard; confirm which rule each peer follows before you build the table.

About Rs 54 crore. Receivables today are Rs 730 crore times 45 over 365, which is Rs 90 crore. Next year revenue is Rs 876 crore and collection takes 60 days, so receivables are Rs 144 crore. The increase of Rs 54 crore is cash the business has earned but not collected. Rs 18 crore of it comes from growth and Rs 36 crore from slower collection, twice as much.

Why does growth eat cash at all?

Think of a tailor who lets regular customers pay a month and a half after collecting their clothes. If the business grows, more money is out with customers at any moment, even though nobody is paying late. Receivables are revenue earned but not yet collected, so when revenue grows at the same collection period the balance grows with it, and the increase is cash the business has to fund. Here 20% more revenue at 45 days lifts receivables from Rs 90 crore to Rs 108 crore.

How do you split the Rs 54 crore?

Take the two changes one at a time. Growth first: Rs 876 crore at the old 45 days is Rs 108 crore, so growth absorbs Rs 18 crore. Then slower collection: going from 45 to 60 days on Rs 876 crore adds 15 days of sales, Rs 36 crore. Fifteen extra days of collection on the larger business costs twice as much cash as 20% growth. The line to watch is days sales outstandingReceivables divided by revenue, times 365: the average number of days customers take to pay..

Does the order of the split matter?

A little. Slower collection first, on today's revenue, costs Rs 30 crore, and growth then adds Rs 24 crore; the Rs 6 crore difference is growth and slower collection compounding each other. The total is Rs 54 crore whichever way you split it, and slower collection is the bigger cause either way. Say which order you used. Then say what it means: a business growing fast while collecting slowly can report rising profit and falling cash at the same time, which is the pattern a lender looks for first.

Only the balance sheet changes. Property, plant and equipment rises by Rs 100 crore and accounts payable rises by Rs 100 crore, so both sides grow by the same amount. No cash has moved, so the cash flow statement is untouched, and no time has passed for depreciation, so the income statement is untouched too. Cash and capex appear in 60 days, when the supplier is paid.

Why does a purchase on credit touch neither cash nor profit?

Think of buying a refrigerator on a shop's 60-day credit. The fridge is in your kitchen today and you owe the shop, but your bank balance has not moved and nothing has come out of this month's budget. A credit purchase adds an asset and a debt of the same size, so the balance sheet grows on both sides and nothing else moves. The machine will be used for years, so its cost is not an expense on the day it arrives. It reaches the income statement slowly, through depreciation, over the years it is used.

What happens over the next 60 days and beyond?

Day 60 is when the cash flow statement wakes up. The company pays the supplier: cash falls by 100 and payables fall by 100. The Rs 100 crore appears as capital expenditure in investing cash flow in the year it is paid, not the year the machine arrived. The notes to the accounts usually flag the year-end purchase as a non-cash investing item, so a reader is not surprised. From the following year, depreciation starts: on a 10-year straight line, Rs 10 crore a year comes off pre-tax profit, is added back in operating cash flow, and lowers the machine's book value.

Close by saying the balance check out loud. Assets up 100, liabilities up 100: the sheet balances, and that one sentence tells the interviewer you walk the statements in a fixed order rather than guessing. Interviewers use small timing questions like this one to see whether you separate when something is owned, when it is paid for and when it is expensed.

Take the 10% revenue rise: it adds Rs 0.4 crore of EBITDA. Revenue rises by Rs 1 crore, and with variable COGS at 60%, Rs 0.4 crore of it reaches EBITDA, a 20% jump. A 5% cut in COGS saves 5% of Rs 6 crore, Rs 0.3 crore. A 5% rise in EBITDA is 5% of the smallest number, Rs 0.1 crore. Translate every option into rupees of EBITDA before choosing.

Why can't you compare the three percentages directly?

Ten per cent off a car and ten per cent off a cup of coffee are not the same saving. Each percentage is taken on a different base, so convert all three into one unit, rupees of EBITDA, before you choose. Revenue is the biggest base at Rs 10 crore, COGS is Rs 6 crore and EBITDA is the smallest at Rs 2 crore. A small percentage of a big number can beat a big percentage of a small one, and here it does.

What should you ask before you answer?

Two readings change the numbers, and asking about them is part of the answer. First, is the revenue rise from volume or from price? Selling 10% more units drags 60% of the new revenue away as COGS, but a 10% price rise costs nothing extra, so all Rs 1 crore reaches EBITDA. Second, does a 5% fall in COGS mean 5% of COGS, or COGS falling from 60% to 55% of revenue? The first saves Rs 0.3 crore; the second saves Rs 0.5 crore and would beat a volume-led revenue rise.

Close with what a banker adds beyond the arithmetic. Operating leverageHow much profit swings for a given change in sales, because fixed costs do not move with volume. is why the revenue rise is so strong: with Rs 2 crore of fixed costs, a 10% rise in sales lifts EBITDA by 20%. The same leverage works in reverse, so a 10% fall in volume would cut EBITDA by 20% as well.

A deferred tax liability of Rs 2.5 crore at year 1, Rs 12.5 crore at year 5, and it unwinds to zero by year 10. Book depreciation is Rs 10 crore a year; tax depreciation is Rs 20 crore for five years then nothing. In years 1 to 5 taxable profit is Rs 10 crore below book profit, so the company pays Rs 2.5 crore less tax than it charges, and the difference accrues as a liability. From year 6 the position reverses and the liability drains at Rs 2.5 crore a year.

Why is there a liability when the company has paid less tax?

Think of a shopkeeper allowed to pay this year's electricity bill next year. Cash looks better today, but the bill has not vanished; it sits as something owed. Faster tax depreciation lets the company deduct the asset's cost sooner, so it pays less tax now and more later, and the accounts record the later tax as a liability the moment the saving is taken. The income statement charges tax on book profit, Rs 2.5 crore a year more than the cash actually paid in years 1 to 5, and that extra charge is what builds the balance.

How do you get the balance without a schedule?

Compare the two values of the asset. The deferred tax liability is the tax rate times the gap between the asset's book value and its tax value, because that gap is profit the tax authority has not yet taxed. At year 1 the book value is Rs 90 crore and the tax value Rs 80 crore, a gap of 10, and 25% of 10 is Rs 2.5 crore. At year 5 the book value is Rs 50 crore and the tax value is zero, a gap of 50, so the liability is Rs 12.5 crore. At year 10 both are zero and so is the liability.

Why does a banker care about a timing difference?

Because it is cash. In years 1 to 5 the company keeps Rs 2.5 crore a year more cash than its income statement suggests, which shows up as an increase in deferred tax liabilities in operating cash flow, and in years 6 to 10 the same amount drains out. A model that uses book tax on EBIT misses both legs, and a buyer of a company with a large and growing deferred tax liability should ask whether it is still growing because the company keeps buying assets, or about to reverse. Say the limitation: the balance reverses only if the company stops adding new assets, and tax rules on depreciation differ by country and change, so confirm the current rates before building this into a model.

EBITDA is unchanged, net income falls by 50, cash is unchanged, and goodwill and equity both fall by 50. The impairment sits below EBITDA, so operating profit and pre-tax profit drop 50. Because it is not deductible, tax does not change and net income falls the full 50. The cash flow statement adds the non-cash charge back. On the balance sheet goodwill drops 50 and retained earnings drop 50.

What is an impairment actually admitting?

Suppose you paid Rs 10 lakh for a used car three years ago and a dealer now offers 6 lakh. Writing the car down in your notebook does not take money out of your wallet; the money left when you bought it. A goodwill impairment admits that an acquisition was overpaid for in the past; it does not spend any new cash. GoodwillThe part of an acquisition price above the fair value of the identifiable net assets bought, carried as an asset on the buyer balance sheet. is the premium paid above the target's net assets, and the write-down says part of that premium is no longer supported by the business's expected cash flows.

Why does net income fall the full 50 rather than 37.5?

Tax is what makes most non-cash charges reach cash. Depreciation, for example, usually cuts the tax bill, so a 50 charge at 25% lowers tax by 12.5. Goodwill impairment is generally not deductible, so the tax line does not move and the whole 50 hits net income. Confirm the rule in the relevant tax regime before relying on it. If the charge were deductible at 25%, net income would fall 37.5, cash would rise 12.5 from the lower tax bill, and the balance sheet would show cash up 12.5, goodwill down 50 and equity down 37.5.

Why does an analyst care if nothing happened to cash?

Because it tells you something about management's past decisions and future cash flows. An impairment says an acquisition is earning less than was paid for it, which usually reflects weaker expected cash flows. It also lowers book equity, which can push up leverage ratios measured on book values and occasionally trip a covenant. Most analysts strip it out of adjusted earnings as a one-off, but a string of them is a pattern worth asking about.

Capitalising makes EBITDA 50 higher and net income 30 higher, but free cash flow is identical. Expensed, the 50 hits EBITDA and net income falls 37.5 after tax. Capitalised, only 10 of amortisation hits profit, so net income falls 7.5, and the 50 moves into investing cash flow as capex. Operating cash flow is 50 higher, capex 50 higher, and free cash flow is minus 37.5 under both.

If the same cash goes out, what actually changes?

Buying a laptop for work: you can think of it as this month's expense, or as a tool that lasts five years and costs a fifth each year. Your bank balance falls by the full price either way. Capitalising versus expensing changes which profit lines carry the cost and which cash flow section shows the outflow; it does not change the cash that left. That is why analysts compare companies on free cash flow when accounting choices differ.

Expensed: EBITDA falls 50, tax falls 12.5, net income falls 37.5. Capitalised: EBITDA is untouched, the year's amortisation is 50 over 5, which is 10, and net income falls 7.5. So capitalising shows EBITDA 50 higher and net income 30 higher in year one. In operating cash flow the capitalised company shows +12.5 against -37.5, a 50 swing, but it also shows 50 of capex in investing.

What assumption is doing the work on tax?

The question says the spend is deductible in year one either way, so the cash tax saving is 12.5 under both. In the capitalised books, tax expense follows the smaller 10 charge, and the 10.0 difference becomes a deferred tax liabilityTax that the accounts recognise as owed later because taxable profit was lower than book profit this year. that is added back in operating cash flow. If the tax authority instead required capitalisation too, the cash tax saving would fall to 2.5 and free cash flow under capitalisation would be -47.5, 10 lower: tax timing is the only route by which the choice reaches cash. State which rule you are assuming.

Why bankers care: two otherwise identical software companies, one capitalising development and one expensing it, will show different EBITDA margins. Valuing both on EV/EBITDA without adjusting flatters the one that capitalises. Look at capitalised development in the cash flow statement and either add it back to the expensing peer or deduct it from the capitalising one.