Investment Banking puzzles, solved step by step

About Rs 450 crore. At full run-rate the synergies add Rs 75 crore of after-tax earnings, which the market capitalises at 8x: Rs 600 crore. Two things the headline ignores come off. Year 1 delivers only half, a shortfall of Rs 37.5 crore after tax, and the one-off cost of Rs 150 crore is Rs 112.5 crore after its tax saving.

Why can you not just multiply Rs 100 crore by 8?

A shop owner expects a new supplier to cut her costs by Rs 1 lakh a year. Before celebrating, she has to pay tax on the extra profit, wait for the new contract to start, and pay the one-off cost of switching. A synergy is worth the after-tax earnings it adds, capitalised, less everything it costs to achieve and every rupee that arrives late. The 8x multiple applies to after-tax earnings, so the pre-tax Rs 100 crore first becomes Rs 75 crore at 25% tax, and 75 x 8 is Rs 600 crore.

What comes off the Rs 600 crore?

Two things. Phasing: the market value assumes the full run-rate, but year 1 delivers only half, so Rs 50 crore of pre-tax savings, Rs 37.5 crore after tax, never arrive. Cost to achieve: Rs 150 crore of severance, systems work and site closures, assumed tax deductible, so it costs Rs 112.5 crore after tax. Net of phasing and the cost to achieve, the synergies are worth about Rs 450 crore, a quarter less than the after-tax figure and 44% less than the pre-tax headline.

What does this rough answer leave out?

Three refinements, each worth naming. The year-1 items fall a year from now, so discounting them would trim the deductions slightly. The 8x assumes the market gives synergies the same multiple as the core earnings, while in practice cost synergiesSavings from combining two businesses, such as closing duplicate offices or merging purchasing. earn more credit than revenue synergies and both are discounted for execution risk. The deductibility of integration costs is an assumption to confirm for the jurisdiction. The answer to give is the method and Rs 450 crore, then one line on which assumption you would test first.

The number matters because it caps what a buyer can sensibly pay away. A premium above roughly Rs 450 crore hands the target's shareholders more than the whole value the deal creates, before any risk that the savings slip.

Dilutive, by about 5.3%. At Rs 45 a share, Rs 1,200 crore needs 26.7 crore new shares, taking the count to 126.7 crore. Earnings rise to Rs 360 crore, so EPS falls from Rs 3.00 to about Rs 2.84. The shortcut: in an all stock deal, buying at a higher P/E than your own always dilutes, because each rupee of earnings bought costs more than each rupee handed over. It takes Rs 20 crore of after-tax synergies to break even.

What is the shortcut that answers it in ten seconds?

Picture swapping a shop for a share in a friend's shop. If your shop is priced at 15 times its yearly profit and your friend's at 20 times, every rupee of your profit you hand over buys only three quarters of a rupee of theirs. In an all stock deal the acquirer gives up its own earnings yield and receives the target's, so a target on a higher P/E means dilution. Here the acquirer's earnings yieldEarnings divided by price, the inverse of the P/E. A P/E of 15 is an earnings yield of 6.7%. is 1 over 15, 6.7%, and the target's is 1 over 20, 5.0%.

How do the full numbers work?

New shares: Rs 1,200 crore divided by Rs 45 is 26.7 crore, so the count rises from 100 to 126.7 crore. Earnings rise from Rs 300 crore to Rs 360 crore. When the share count grows faster than earnings, EPS falls: Rs 360 crore over 126.7 crore shares is Rs 2.84, down 5.3% from Rs 3.00.

What would make the deal break even?

Turn it round. The enlarged share count needs Rs 3.00 of earnings per share, so Rs 3.00 times 126.7 crore, which is Rs 380 crore. The deal needs Rs 20 crore a year of after-tax synergies, a third of the target's own earnings, before EPS is back where it started. Saying that number tells the interviewer how big the problem is, which matters more than the sign. Close with the limit: one year of EPS is not value, and a dilutive deal can still be worth doing if the target grows much faster than the acquirer.

Under the fixed ratio, target holders receive Rs 90 of value per share instead of Rs 100. They still get 0.5 acquirer shares, but each is now worth Rs 180. Under a fixed price they would still receive Rs 100, and the acquirer would issue 100 over 180, about 0.556 shares per target share, 11.1% more than planned. A fixed ratio shares the price risk with the target; a fixed price keeps it with the acquirer and its shareholders.

What does each structure actually fix?

Think of agreeing to swap your car for 50 grams of gold, rather than for Rs 5 lakh paid in gold. If the gold price falls before the swap, the first deal still hands you 50 grams, now worth less; the second hands you more grams so that you still get Rs 5 lakh. A fixed exchange ratioThe number of acquirer shares paid for each target share in a stock deal. fixes the number of shares the target receives; a fixed price fixes their rupee value, and the share count moves instead. Whichever number floats carries the risk of the acquirer's share price between signing and closing.

How do the two structures play out across the whole deal?

Assume the target has 10 crore shares and the acquirer 50 crore. Fixed ratio: target holders receive Rs 900 crore of value instead of Rs 1,000 crore, and own 5 crore of 55 crore shares, 9.1% of the combined company. Fixed price: they still receive Rs 1,000 crore, so the acquirer issues 5.56 crore shares, 11.1% more than planned, and the target's holders own 10.0%. The acquirer's existing shareholders give up more of the company to pay the same rupees.

Which side wants which, and how do bankers split the difference?

A target worried that the acquirer's shares will fall wants a fixed price; an acquirer worried about issuing too many shares wants a fixed ratio. A collar is the usual compromise: in one common form the ratio is fixed while the acquirer's price stays inside a band and the value is fixed outside it, so each side carries the risk only up to a point. Interviewers ask this to see whether you think about who carries risk between signing and closing, not just the headline value.

A 25% premium. Each target share is exchanged for 0.5 acquirer shares worth Rs 200 each, so the offer is worth Rs 100 a share. The target trades at Rs 80 undisturbed, so holders get Rs 20 more, and 20 over 80 is 25%. The exchange ratio is not itself the premium: a straight swap at market prices would be 80 over 200, or 0.4.

How do you turn an exchange ratio into rupees?

Picture a swap where someone offers you half a gold coin for your silver one. To judge the offer you price both coins first. Multiply the exchange ratio by the acquirer's share price to get what each target share is being offered: 0.5 x Rs 200 = Rs 100. Then compare that with the undisturbed priceThe target share price before news or rumours of the deal moved it., Rs 80. The premium is the gap over the undisturbed price, Rs 20 on Rs 80, which is 25%.

How do you check it a second way?

Work out the ratio that would be a straight swap at today's prices: Rs 80 over Rs 200, or 0.4 acquirer shares per target share. An offer of 0.5 is 25% more shares than 0.4, the same premium seen through share counts instead of rupees. Two routes agreeing is what an interviewer wants to hear before you commit to a number.

What can happen to the premium before the deal closes?

In a fixed exchange ratio deal, the target holders' payout moves with the acquirer's share price. If the acquirer falls 10% to Rs 180, the offer is worth Rs 90 and the premium shrinks to 12.5%; if the acquirer rises, the premium grows. That is why target boards push for collars or cash, and why the premium quoted on announcement day is only a snapshot.

Rs 400 crore, and the coverage test binds. Leverage of 5.0x allows Rs 500 crore. Coverage of 2.5x caps interest at 100 divided by 2.5, which is Rs 40 crore, and at 10% that interest supports Rs 400 crore of debt. The borrower must pass both tests, so the lower number is the ceiling. Below an 8% rate, leverage would bind instead.

Why are there two answers, and why take the smaller?

A bank deciding your home loan asks two things: is the loan too large against your salary, and can you afford the monthly payment? You can pass one and fail the other. Lenders to a company ask the same pair. Leverage limits the size of the debt; coverage limits the cost of carrying it, and the borrower must clear both, so the binding test is whichever gives less. Compute both every time, then name the one that bites.

Leverage is one step: 5.0 times EBITDA of 100 is Rs 500 crore. Coverage works backwards from the payment. Interest coverEBITDA divided by interest expense: how many times over the operating profit pays the interest bill. of at least 2.5 means interest can be at most 100 divided by 2.5, which is Rs 40 crore. At a 10% rate, Rs 40 crore of interest corresponds to Rs 400 crore of debt.

When would the answer flip to the leverage test?

The coverage ceiling moves with the rate; the leverage ceiling does not. Set the two equal: interest of 40 on 500 of debt is an 8% rate. Below 8%, leverage binds; above it, coverage binds, which is why debt capacity shrinks when rates rise even if earnings do not move. At 7%, coverage would allow about Rs 571 crore, so the 500 leverage cap becomes the limit.

Say the limitation too. Real covenants often test cover on EBITDA less capex, or on a fixed charge basis that includes leases, and lenders size a deal with headroom below both ceilings rather than at them. The two-test logic stays the same.

MOIC is 2.72x: equity grows from Rs 320 crore to Rs 870 crore. Of the Rs 550 crore gain, EBITDA growth contributes 240 (30 x 8x), multiple expansion 130 (one turn on 130), and debt paydown 180 (480 - 300). The three add exactly to 550. Over five years that would be an IRR of about 22%, though the question gives no holding period.

How do you get entry and exit equity quickly?

Equity is what is left of the business's value after the debt. Entry: 8 x 100 is an enterprise value of 800, less 480 of debt, so the sponsor put in 320. Exit: 9 x 130 is 1,170, less 300 of debt, leaving 870. MOIC is exit equity over entry equity, 870 / 320 = 2.72x. Say both enterprise values out loud before subtracting debt, so the interviewer can follow each step.

Why split the gain into three sources?

Think of a house you bought, renovated and sold. Your profit came partly from adding a room, partly from the neighbourhood getting more popular, and partly from paying down the mortgage. Only the first is a skill you can repeat on the next house. Attribution shows which part of the return came from the sponsor's own work and which came from the market, which is what investors in the fund want to know. EBITDA growth and debt paydown come from running the business; multiple expansion mostly comes from market conditions at exit.

Say the convention. The growth and multiple pieces share a cross term: 30 of extra EBITDA times one extra turn, which is 30. Here it sits inside multiple expansion. Value growth at the exit multiple instead and growth becomes 270 while multiple expansion falls to 100. The total does not change, but the story does, so state which order you used.