Case 045Fund, LP and portfolio analyticsHard

Take-home: four deals with dated cash flows. Compute each deal's MOIC and IRR, then the pooled IRR of the four together, and explain why the pooled IRR is not the average of the deal IRRs.

Bain CapitalBoston · 2024

The situation

Sthira Partners Fund II made four investments. All amounts are Rs crore and dated to the end of the year shown, with year 0 the fund's first close.

Deal A, Nirjhar Water: invested 100 in year 0, received 300 in year 3.

Deal B, Vidyankur Schools: invested 200 in year 0, received 400 in year 5.

Deal C, Tejasvi Logistics: invested 50 in year 1, received 100 in year 2.

Deal D, Mridang Retail: invested 150 in year 2, received 120 in year 6.

The fund's marketing deck quotes the average of the four deal IRRs.

Your task

Compute each deal's MOIC and IRR, the pooled IRR and pooled MOIC, and explain the gap between the pooled IRR and the average the deck quotes.

Quick check

The four deal IRRs average about 38%. Where will the pooled IRR land?

Worked solution

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

30-second answerThe answer to give first

The deals return 3.0x and 44.2%, 2.0x and 14.9%, 2.0x and 100%, and 0.8x and -5.4%; pooled, the fund earns 1.84x and 19.8%. The simple average of deal IRRs is 38.4%, because it counts a Rs 50 crore one-year flip at 100% as a full quarter of the result. The pooled IRR weights every rupee by size and by how long it was invested.

Step 1What does each deal return on its own?

For a single buy and single sale, both numbers fall out directly. MOIC is cash out over cash in; IRR is the yearly rate that turns one into the other over the holding period, so a deal that triples in three years earns 3 to the power of a third, less 1, 44.2%. Deal B doubles in five years, 14.9%. Deal C doubles in one year, 100%. Deal D returns 0.8x over four years, -5.4% a year.

DealInvestedReturnedYears heldMOICIRR
A, Nirjhar Water10030033.0x44.2%
B, Vidyankur Schools20040052.0x14.9%
C, Tejasvi Logistics5010012.0x100.0%
D, Mridang Retail15012040.8x-5.4%
Pooled fund5009200 to 61.84x19.8%
Rs crore. The four deals range from -5.4% to 100% on their own, while the fund as a whole returns 1.84x and 19.8% once their cash flows are combined by date.
Step 2How do you pool them, and what comes out?

Add every deal's cash by year, then solve one IRR on the combined strip. Year 0 is -100 and -200, -300; year 1 is Deal C's -50; year 2 is C's +100 and D's -150, a net -50; year 3 is A's +300; year 5 is B's +400; year 6 is D's +120. The pooled strip returns Rs 920 crore on Rs 500 crore, 1.84x, at an IRR of 19.8%. On paper, find it by trial: at 20% the strip's present value is just below zero, at 19% just above, so the answer sits a shade under 20%.

Four deals and the fund, as dated cash, Rs croreY0Y1Y2Y3Y4Y5Y6Nirjhar Water-100+300IRR 44.2%Vidyankur Schools-200+400IRR 14.9%Tejasvi Logistics-50+100IRR 100.0%Mridang Retail-150+120IRR -5.4%Pooled fund-300-50-50+300+400+120IRR 19.8%
Laid out by date, the four deals combine into one fund strip of -300, -50, -50, +300, +400 and +120, whose IRR of 19.8% sits far below Deal C's 100% and Deal A's 44.2% because most of the money was in the slower, larger deals.
Step 3Why is the pooled IRR not the average of the deal IRRs?

A cricket team's batting average is runs over dismissals, not the average of each player's average; a tail-ender who scored 50 once is not worth the same as an opener who scored 5,000. The simple average gives each deal one vote, so a Rs 50 crore deal held for one year counts as much as a Rs 200 crore deal held for five; the pooled IRR gives each rupee one vote for each year it was invested. Weighting by capital alone brings the average down from 38.4% to 23.2%; weighting by time as well brings it to the pooled 19.8%. Drop Deal C and the simple average of the other three is 17.9%, which shows how much one quick flip moves it.

Same four deals, three different 'average' IRRsSimple average of deal IRRs38.4%Average weighted by capital23.2%Pooled IRR of all the cash19.8%Pooled money multiple 1.84x: Rs 920 crore back on Rs 500 crore.
The same four deals average 38.4% if each deal counts equally, 23.2% if weighted by capital and 19.8% when pooled by date and size, which is the number that matches the fund's 1.84x money multiple.

Close with what to report and why. The pooled IRR is the fund's actual return on its investors' money; the average of deal IRRs is a statistic about deals that flatters any fund with a few quick wins. A careful analyst shows pooled IRR and pooled MOIC together, notes that a high IRR on small, short deals adds little money, and checks the loss ratio: here one deal in four lost money, Rs 30 crore on Rs 150 crore. The limit of the pooled figure is that it still ignores fees and carry; the investors' own net IRR would be several points lower.

Where candidates lose it

The usual loss is averaging the four IRRs and reporting about 38%. It is the number the deck wants you to quote and the one the take-home is built to catch.

The second miss is pooling by netting each deal's MOIC instead of by date. Pooling means adding the cash in each year and solving one IRR, which is why year 2 nets Deal C's exit against Deal D's entry.

What the interviewer asks next

  • Deal D is still held and marked at Rs 120 crore. How does that change the confidence you place in the pooled IRR?
  • What would the pooled IRR be if Deal B had exited in year 4 for the same Rs 400 crore?
  • Why do investors ask for both IRR and MOIC rather than one of them?

Asked at Bain Capital, Leveraged Buyouts, Boston, 2024 (Wall Street Oasis): Wasn't a full LBO but effectively a bunch of number crunching on MOIC and IRR across investments

Company names and figures are illustrative.