Investment Banking puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 36
- Topics
- 12
- Hard
- 29
009A company has Rs 100 of interest expense: Rs 50 paid in cash and Rs 50 paid in kind. The tax rate is 40%. Walk the effect through the three statements.MizuhoNew York · 2026
Try it first
What happens to the company's cash?
Show the worked solution
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.
Net income falls Rs 60 after the Rs 40 tax saving, the Rs 50 of PIK is added back so cash falls only Rs 10, and on the balance sheet debt rises Rs 50 while retained earnings fall Rs 60, which balances the Rs 10 drop in cash. 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.
The relationship-100 x (1 - 0.40) net income after the full expense and the 40% tax saving 50 the PIK interest, expensed but not paid in cash What it says in wordsCash moves by net income plus any expense that was not paid in cash, which here is the PIK half.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.
Where candidates lose it
The usual slip is to treat PIK as if it never touched the income statement, so net income falls only 30 and the balance sheet refuses to balance. PIK is a full expense; it simply is not paid in cash.
The second slip is losing the PIK after the add-back. It does not vanish: it accrues to the principal of the debt, and that Rs 50 increase is what makes the balance sheet tie.
What the interviewer asks next
- What changes if the PIK interest is not tax deductible?
- Next year interest is charged on the larger principal. What happens to the three statements?
- Why would a borrower accept a PIK note at a higher rate than cash-pay debt?
Asked at Mizuho, Generalist, New York, 2026 (Wall Street Oasis):
walk through 100 interest expense, 50 cash interest, 50 pik interest, 40 tax rate
033A company pays Rs 20 crore of rent a year. Moving to IFRS 16 puts a Rs 150 crore lease liability on its balance sheet. Before the change its EBITDA was Rs 100 crore and its enterprise value Rs 800 crore. What happens to EBITDA, enterprise value and EV/EBITDA?Credit SuisseSão Paulo · 2021
Try it first
After the change, where does EV/EBITDA land?
Show the worked solution
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.
Before the change EBITDA is Rs 100 crore and EV Rs 800 crore, 8.0x; after it EBITDA is Rs 120 crore and EV Rs 950 crore, 7.92x, while mixing the two bases gives a wrong 9.5x or 6.7x for the same business. 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.
The relationship150 the lease liability, added to enterprise value 20 the rent, added back to EBITDA 7.5x the multiple at which the lease itself enters What it says in wordsThe new multiple is a blend of the old 8.0x and the lease's own 7.5x, weighted by size, so it lands just below 8.0x.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.
Where candidates lose it
The losing move is adjusting one side. Candidates add the Rs 150 crore liability to EV and stop, report 9.5x, and conclude the company now looks expensive, when the business has not changed at all.
The second miss is insisting the multiple stays exactly at 8.0x. It moves slightly, and the reason, that the lease is priced at 7.5x, is what separates an answer from a guess.
What the interviewer asks next
- What happens to net income in the first year of the lease, and why?
- Which cash flow statement lines change, and does free cash flow change?
- A peer reports under rules that keep rent in operating costs. How do you put it on the same basis?
Asked at Credit Suisse, Investment Banking, São Paulo, 2021 (Wall Street Oasis):
can you explain how changes in accounting principles, such as the transition from GAAP to IFRS, might impact the DCF valuation process
063A company has Rs 10 crore of revenue, variable COGS of 60% of revenue and fixed operating costs of Rs 2 crore, so EBITDA is Rs 2 crore. Which would you rather have: a 10% rise in revenue, a 5% fall in COGS, or a 5% rise in EBITDA?NomuraSan Francisco · 2026
Try it first
Which option adds the most EBITDA?
Show the worked solution
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.
On Rs 10 crore of revenue with 60% variable COGS and Rs 2 crore of fixed costs, a 10% revenue rise adds Rs 0.4 crore of EBITDA, a 5% COGS cut adds Rs 0.3 crore and a 5% EBITDA rise adds only Rs 0.1 crore. 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.
Reading of the option EBITDA gain, Rs crore New EBITDA, Rs crore Revenue +10% from volume 0.4 2.4 Revenue +10% from price 1.0 3.0 COGS down 5% of itself 0.3 2.3 COGS down 5 points of revenue 0.5 2.5 EBITDA +5% 0.1 2.1 The EBITDA option comes last under every reading. The revenue rise wins unless the COGS cut means five points of revenue and the revenue rise comes from volume, in which case the cut adds Rs 0.5 crore against Rs 0.4 crore. 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.
Where candidates lose it
Candidates pick the 10% because it is the biggest number, or the EBITDA option because EBITDA is what gets valued, without converting anything. Both are guesses; the interviewer wants rupees on one line.
The other loss is answering without asking whether the revenue rise is volume or price and what the COGS cut means. Asking takes ten seconds and shows you know the answer can flip.
What the interviewer asks next
- At what variable COGS percentage would the 5% COGS cut and the 10% volume rise be worth the same?
- Which option would a buyer of the business value most, and why might it not be the biggest EBITDA gain?
- How does the answer change if fixed costs were Rs 3.5 crore instead of Rs 2 crore?
Asked at Nomura, Generalist, San Francisco, 2026 (Wall Street Oasis):
$10 million in revenue. Do u want a 10% increase in revenue, 5% decrease in COGS, or 5% increase in EBITDA
