Sanjeevik Health runs a dual track: a cash sale now or an IPO in nine months. Value both for the fund's 18% stake, counting delay, the pulled case and a lock-up, and say which track the fund should push for.

Push for the sale: Rs 504 crore in cash today against about Rs 444.7 crore for the IPO track in today's money. The IPO's probability-weighted value for the stake is Rs 569.7 crore, but the lock-up costs Rs 38.3 crore and waiting nine to fifteen months at 20% costs another Rs 86.7 crore. The IPO wins only if the good case prices above about Rs 4,309 crore or the fund's discount rate is far lower.

Suppose someone offers to buy your car for Rs 5 lakh today, or a dealer says he can probably sell it for Rs 6 lakh in nine months, might get only Rs 4.5 lakh, and might fail and leave you to sell at Rs 4 lakh a year from now. You would weigh the outcomes and the wait before choosing. A dual track is the same choice: a certain price today against a set of possible prices later, each reached on a different date and some only partly in cash. For the fund, the sale is 18% of Rs 2,800 crore, Rs 504 crore, today. The IPO has three branches, and in the two that list, half the stake is stuck in a lock-upA period after a listing, often six months, during which existing shareholders agree not to sell their shares..

Take the good branch. The stake is 18% of Rs 3,600 crore, Rs 648 crore. Half, Rs 324 crore, is sold at listing in nine months. The other half is sold fifteen months out, after falling 15%, so it brings Rs 275.4 crore. Discount each piece to today at 20% a year: Rs 324 crore over 1.2 to the power 0.75, plus Rs 275.4 crore over 1.2 to the power 1.25, which is Rs 501.9 crore. The middle branch works the same way and gives Rs 376.4 crore. If the IPO is pulled, the buyer pays 18% of Rs 2,200 crore, Rs 396 crore, a year out: Rs 330.0 crore today.

Walk it down in steps, because the partner will ask which assumption does the damage. The Rs 648 crore headline falls to Rs 569.7 crore once the weaker and pulled outcomes are weighted in, to Rs 531.4 crore after the lock-up, and to Rs 444.7 crore after waiting. No single step kills the IPO; the three together turn a Rs 65.7 crore headline lead into a Rs 59.3 crore deficit. The delay is the largest piece, Rs 86.7 crore, because 20% a year is a high price for nine to fifteen months of waiting.

Three inputs, each worth stating as a number. The good case would have to price above about Rs 4,309 crore for the IPO to match the sale, about 20% above the bankers' Rs 3,600 crore. At a 10% discount rate the IPO track is worth Rs 484.1 crore, still short of the sale. With no lock-up fall it is worth Rs 475.2 crore. The fund is not the only voice, though: founders who want to stay independent may prefer the IPO, and a public listing can carry a later sale at a higher price. The honest recommendation to the board is that, for this fund, the cash offer is worth more, and the IPO is worth running only as a lever to get the buyer to raise its price. The limitation: bankers' probabilities are soft, and the 15% pull risk could be higher in a weak market.