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.

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.

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.

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.