Case 043Fund economics and LP mathsHard

Kaalvik Growth Fund I is in year eleven with two assets left. The GP proposes a continuation vehicle at a 10% discount to NAV. What does a selling LP get, what must the assets reach for a rolling LP to do better, and where is the conflict?

The situation

Kaalvik Growth Fund I is past its ten-year life and holds two companies, carried at a NAVNet asset value: the current valuation the GP itself puts on what the fund holds, not a price anyone has paid. of Rs 400 crore and Rs 150 crore. Rather than sell them now, the GP proposes a continuation vehicleA new fund, run by the same GP, that buys the remaining assets from the old fund. Existing LPs can take cash or roll their stake into the new fund; a secondary buyer supplies the cash for those who sell.: a secondary buyer prices the pair at a 10% discount to NAV, Rs 495 crore. Every LP may sell its share for cash or roll it into the new vehicle on the same price. The sale crystallises Rs 60 crore of carry for the GP under the old fund's waterfall, which the GP rolls into the new vehicle rather than taking in cash.

You advise an LP that holds 10% of the fund. Its own alternative investments are expected to earn 20% a year, and the new vehicle is planned to run four years. Assume the new vehicle charges 20% carry on gains above its purchase price, and ignore its fees.

Your task

What does the LP receive if it sells, what must the assets be worth in four years for rolling to beat selling, and where exactly does the GP's conflict sit?

Quick check

If the LP sells, roughly what does it receive?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

A selling LP with 10% receives about Rs 43.5 crore; a rolling LP needs the two assets to reach about Rs 1,026 crore in four years, Rs 1,159 crore after the new vehicle's carry. That is 16.9% a year on today's NAV just to match selling, because the roll starts from a price 10% below NAV and must then beat 20% a year. The conflict: the GP negotiated the price, rolls its carry at that price, and earns new carry on the discount it granted.

Step 1What does selling actually put in the LP's hands?

Picture a family that owns a tenth of a building being sold by the manager, who also takes a cut of the sale. What the family gets is a tenth of the price after the manager's cut, not a tenth of the valuation in the brochure. The LP's cash is its share of the price, after the carry the sale triggers: Rs 495 crore less Rs 60 crore is Rs 435 crore to LPs, and 10% of that is Rs 43.5 crore. Compared with 10% of NAV, Rs 55 crore, the LP gives up Rs 5.5 crore to the discount and Rs 6 crore to carry. That is the price of liquidity now instead of a sale at some unknown date.

Sell at the price today, or roll and need the assets to earn that price back and moreTwo assets, NAV Rs 550 crPriced at 10% off: Rs 495 crLPs choose: sell or rollsellrollSell: a 10% LP gets Rs 43.5 crore nowRs 495 cr less Rs 60 cr of crystallised carry = Rs 435 cr to LPsCash, certain, and free to redeploy at the LP's own 20% a yearRoll: the pair must reachRs 1,026 crore by year 4= Rs 495 cr x 1.2 to the power 4; 16.9% a year on today's NAVWith 20% carry on the new vehicle: Rs 1,159 cr, 20.5% a yearA 10% LP's Rs 43.5 cr must become Rs 90.2 crThe GP is on both sidesSells as manager of the old fund,buys as manager of the new vehicle,rolls Rs 60 cr of carry at a priceit negotiated, and earns new carryon the Rs 55 cr discount:Rs 11 cr if the NAV is right.
Selling gives a 10% LP Rs 43.5 crore today; rolling means the pair must reach Rs 1,026 crore in four years, Rs 1,159 crore once the new vehicle's 20% carry is paid, and the GP sits on both sides of the Rs 495 crore price.
Step 2What must the assets reach for rolling to beat selling?

Rolling means the LP keeps its Rs 43.5 crore in the new vehicle instead of investing it elsewhere at 20% a year. To beat that, the rolled stake must be worth Rs 43.5 crore times 1.2 to the power four, Rs 90.2 crore, in four years. Scaled to the whole vehicle, the pair must grow from the Rs 495 crore price to Rs 1,026 crore, which is 16.9% a year on today's Rs 550 crore NAV. The first 10% of that is just recovering the discount. And if the new vehicle takes 20% of gains above its price, the LP keeps only 80% of the rise, so the gross target becomes Rs 1,159 crore, 20.5% a year.

The relationship
V4=495×1.204≈1,026g=(1,026550)1/4−1≈16.9%V4net=495+1,026−4950.8≈1,159V_4 = 495 \times 1.20^4 \approx 1{,}026 \qquad g = \left(\frac{1{,}026}{550}\right)^{1/4} - 1 \approx 16.9\% \qquad V_4^{\text{net}} = 495 + \frac{1{,}026 - 495}{0.8} \approx 1{,}159
495the continuation vehicle's purchase price, Rs crore, 10% below NAV
1.20one plus the LP's 20% a year alternative return
550today's NAV, the base the assets actually grow from
0.8the LP's share of gains after 20% carry in the new vehicle
What it says in wordsThe rolled stake must match what the sale proceeds would earn elsewhere; measured against today's NAV that needs about 17% a year, and more once the new vehicle's carry takes a fifth of the gain.
What the assets must earn for rolling to beat selling, Rs crore4006008001,0001,200TodayYear 1Year 2Year 3Year 4Needed by year 4: Rs 1,026 cr (Rs 495 cr growing 20% a year)8651,0261,14020% a year: rolling wins12% a year: selling was betterSale price Rs 495 crNAV Rs 550 cr
At 12% a year the two assets reach about Rs 865 crore in four years and the LP should have sold; at 16.9% they reach the Rs 1,026 crore break-even; only at 20% or more, about Rs 1,140 crore, does rolling clearly beat selling.
Growth of the pair, a yearValue in year 4, Rs cr10% LP's stake before new carry, Rs crAfter 20% new carry, Rs crAgainst Rs 90.2 cr from selling and reinvesting
12.0%86576.169.5selling wins
16.9%1,02690.280.9selling wins
20.0%1,140100.288.9selling wins
Rs crore. The LP's rolled stake is its share of the vehicle, so the numbers scale with the Rs 43.5 crore it rolled; at 12% growth it ends well below the Rs 90.2 crore selling would have produced, and even 20% growth only just beats selling once the new carry is paid.
Step 3Where exactly is the conflict?

In three places, and name each. First, price: the GP negotiates the Rs 495 crore as seller for the old fund and as buyer for the new one, and it keeps managing the assets either way, so a low price costs it little and gives its new vehicle a cheap start. Second, carry: Rs 60 crore crystallises on a sale the GP arranged, and the new vehicle will pay carry on gains above Rs 495 crore, so if the assets are really worth their Rs 550 crore NAV the GP earns Rs 11 crore of new carry merely for the discount it granted. Third, information: the GP knows the companies better than the secondary buyer or the LPs, and it chose the moment to propose this.

What you ask for before advising either way: an independent fairness opinion on the price, a competitive process with more than one secondary bidder, approval from the LP advisory committee, the GP rolling all of its crystallised carry rather than part, and the option to roll on the old fund's terms with no new carry on the rolled portion. The limitation of the maths is that it treats the four-year horizon and the 20% alternative return as certain; a secondary buyer paying 10% below NAV is itself a signal of what an arms-length price looks like. The judgement: sell unless the LP has an independent reason to believe the pair can compound at over 17% a year from a NAV the GP itself set.

Where candidates lose it

The common loss is comparing the roll with NAV instead of with the sale proceeds reinvested. The question is not whether the assets are worth Rs 550 crore; it is whether they will be worth Rs 1,026 crore in four years, because that is what Rs 495 crore earns elsewhere at 20% a year.

The second is forgetting that the roll starts from the discounted price while the assets grow from NAV, and that the new vehicle's carry takes a fifth of the gain. Both raise the bar the roll must clear.

What the interviewer asks next

  • The secondary buyer raises its price to NAV. How does the rolling LP's break-even change?
  • The GP offers rolling LPs no carry on the rolled portion. What growth rate does rolling now need to beat selling?
  • Why might an LP roll even when the numbers favour selling?
  • What would you want to know about how the Rs 400 crore NAV was set?

Company names and figures are illustrative.