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Investment Banking puzzles, solved step by step

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  1. 060A share trades at Rs 50 and there are 100 crore basic shares. Three option tranches are outstanding: 10 crore at a strike of Rs 20, 5 crore at Rs 40 and 8 crore at Rs 60. What is the diluted share count under the treasury stock method?Enterprise value and dilutionHardJefferiesSan Francisco · 2026

    Try it first

    Before you work it: what is the diluted share count?

    Show the worked solution

    107 crore diluted shares. Only options with a strike below the Rs 50 share price are exercised. The Rs 20 tranche brings in Rs 200 crore, which buys back 4 crore shares, so it adds 6 crore net. The Rs 40 tranche also brings in Rs 200 crore, buying back 4 crore, so it adds 1 crore net. The Rs 60 tranche is out of the money and adds nothing.

    Why do only some options count?

    An option to buy a share at Rs 60 when it trades at Rs 50 is like a voucher to buy a shirt for more than its shelf price: nobody uses it. Only in-the-money options, those with a strike below the current share price, would be exercised, so only they add shares. Here the Rs 20 and Rs 40 tranches are in the money and the Rs 60 tranche is not. The 8 crore Rs 60 options are ignored today, but they come back into play if the price rises past Rs 60 or a bidder offers more than that.

    Each tranche: options in, shares bought back with the cash, the rest is dilutionTrancheExercise cashBought back at Rs 50Net new shares10 crore at Rs 20in the money10 x Rs 20 = Rs 200 cr200 / 50 = 4 crore+6 crore5 crore at Rs 40in the money5 x Rs 40 = Rs 200 cr200 / 50 = 4 crore+1 crore8 crore at Rs 60out of the money: ignoredstrike above the Rs 50 price: nobody exercises0Share count, crore100 basic= 107 crore dilutedlime: +6 and +1 net from the options
    At a Rs 50 share price the Rs 20 tranche adds 6 crore shares net and the Rs 40 tranche adds 1 crore, after the exercise cash buys back 4 crore shares each, while the Rs 60 tranche adds nothing, so 100 crore basic shares become 107 crore diluted.

    Why does each tranche add fewer shares than its option count?

    When holders exercise, they pay the strike price to the company. The treasury stock methodA way to count dilution that assumes the company uses the cash from option exercises to buy back its own shares at the current price. assumes the company uses that cash to buy back shares at today's price. Each in-the-money tranche adds its option count minus the shares its exercise cash can buy back. The Rs 20 tranche pays 10 crore x Rs 20 = Rs 200 crore, which buys 4 crore shares at Rs 50, so 6 crore net. The Rs 40 tranche pays 5 crore x Rs 40 = Rs 200 crore, again 4 crore bought back, so 1 crore net.

    TrancheIn the money?Exercise cash, Rs croreBought back, croreNet new shares, crore
    10 crore at Rs 20Yes20046
    5 crore at Rs 40Yes20041
    8 crore at Rs 60No0
    Diluted count, with 100 basic107
    Two in-the-money tranches add 7 crore shares net after buybacks, taking the basic 100 crore to 107 crore; the out-of-the-money Rs 60 tranche adds nothing at a Rs 50 share price.
    The relationship
    Net new shares=n(1−KP)10(1−2050)+5(1−4050)=6+1=7\text{Net new shares} = n\left(1 - \frac{K}{P}\right) \qquad 10\left(1 - \tfrac{20}{50}\right) + 5\left(1 - \tfrac{40}{50}\right) = 6 + 1 = 7
    noptions in the tranche, crore
    Kthe strike price of the tranche
    Pthe current share price, Rs 50
    What it says in wordsEach in-the-money tranche adds its option count times the part of the price the strike does not cover.

    Notice what the formula says. The deeper in the money an option is, the closer it comes to a full new share: the Rs 20 tranche dilutes at 60% of its count, the Rs 40 tranche at only 20%. Diluted equity value at Rs 50 is 107 crore x Rs 50 = Rs 5,350 crore, Rs 350 crore above the basic Rs 5,000 crore, and that diluted figure is the one that goes into an enterprise value bridge.

    Where candidates lose it

    The common miss is adding all 23 crore options, or both in-the-money tranches in full, to get 123 or 115 crore. Both ignore that exercise brings cash in, and that the method assumes the cash buys shares back.

    The other miss is forgetting to re-test the Rs 60 tranche in a takeover. At an offer price above Rs 60 it moves into the money, so the share count depends on the price you are testing.

    What the interviewer asks next

    • A bidder offers Rs 70 a share. What is the diluted share count now?
    • How would you treat a convertible bond in the same count?
    • The share count depends on the price, and the price depends on the share count. How do bankers handle that loop in a model?

    Asked at Jefferies, Technology, Media and Telecom (TMT), San Francisco, 2026 (Wall Street Oasis): It was a lot of stock option and technology specific questions.

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