Private Equity puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 22
- Topics
- 12
- Hard
- 30
070A Rs 1,000 crore fund charges a 2% management fee on commitments for its first five years, then 1.5% on invested capital of Rs 800 crore for the next five. What are total management fees over the fund's life?Secondaries and fund of funds
Try it first
Total management fees over ten years?
Show the worked solution
Rs 160 crore, or 16% of commitments. In years one to five the fee is 2% of Rs 1,000 crore, Rs 20 crore a year, Rs 100 crore in all. In years six to ten it is 1.5% of the Rs 800 crore invested, Rs 12 crore a year, Rs 60 crore in all. The early fees are charged on the full commitment, whether or not the money has been invested yet.
Why does the base change halfway through?
Think of a gym that charges full membership from the day you sign, even before you start going, and then a lower fee once you only use part of the facilities. During the investment period, fees are charged on what investors have promised, because the manager is busy finding deals; afterwards they usually drop to what is actually invested, because the job shifts to managing what was bought. The rates and bases differ from fund to fund, so read the agreement rather than assuming.
The fund charges Rs 20 crore a year for five years on Rs 1,000 crore of commitments and Rs 12 crore a year for five more on Rs 800 crore invested, a total of Rs 160 crore, 16% of commitments. The relationship2% x 1,000 the annual fee on commitments in years 1 to 5 1.5% x 800 the annual fee on invested capital in years 6 to 10 What it says in wordsAdd the fees of each phase: rate times base times the years it applies.Why does an investor in the fund care about this number?
Because fees come out of the investors' money before any profit is shared. Rs 160 crore of fees on Rs 1,000 crore of commitments means the investments must earn back 16% before the investors are even whole on what they put in. The early fees bite hardest: if only Rs 200 crore were invested in year one, an illustrative figure, the Rs 20 crore fee would be 10% of the money actually at work. That is why investors care about the fee base as much as the rate.
Where candidates lose it
The common slip is applying 2% to the full Rs 1,000 crore for all ten years and answering Rs 200 crore. The question gives a step-down in both rate and base; using it is the whole point.
The second is computing the second phase as 1.5% of 1,000. After the investment period the base is the Rs 800 crore invested, not the original promise.
What the interviewer asks next
- If the fund also charges 20% carry over an 8% hurdle, what else must you know to estimate total cost?
- How would fee offsets from portfolio company charges change the total?
- Why do investors push for fees on invested rather than committed capital?
072An investor in a fund has paid in 800, received distributions of 600, and still holds a net asset value of 700. What are the DPI, RVPI and TVPI, and which of them is cash?Secondaries and fund of funds
Try it first
Which ratio tells you how much cash the investor has actually got back?
Show the worked solution
DPI is 0.75x, RVPI is 0.875x and TVPI is 1.625x; only DPI is cash. All three divide by the 800 paid in. DPI counts the 600 distributed, RVPI the 700 still held at estimated value, and TVPI adds them, 1,300 over 800. On paper the fund is well ahead, but in cash the investor has 600 back on 800 and is still short of break-even.
What does each ratio measure?
Imagine lending a friend Rs 800 to start a business. She has paid you back Rs 600 and says your share of the shop is worth Rs 700 more. Rs 600 is in your wallet; Rs 700 is her estimate. DPI counts the cash back, RVPI counts the estimated value still held, and TVPI adds the two, all measured against the money paid in. In fund language: distributions to paid-in, residual value to paid-in, total value to paid-in.
Against 800 paid in, the investor has 600 back in cash and 700 still held as net asset value, so DPI is 0.75x, RVPI is 0.875x and TVPI is 1.625x, and only the DPI part is money in the bank. The relationshipDPI distributions over paid-in capital RVPI residual value, the NAV, over paid-in capital TVPI total value over paid-in capital What it says in wordsTotal value to paid-in is the cash already returned plus the value still held, each divided by the money paid in.Why does the difference between DPI and TVPI matter so much?
Because NAV is a valuation made by the manager, and it only becomes cash when the holdings are sold. A fund with a high TVPI and a low DPI is telling you it is worth a lot on paper, and investors have learnt to ask how much of that has actually come home. Here more than half the reported value, 700 of 1,300, is still an estimate. A buyer of this fund stake on the secondary market would price that 700 at whatever discount it thinks the estimate deserves, which is exactly why the split matters.
Where candidates lose it
The common slip is quoting TVPI as the return, 1.625x, and saying the investor has made 62.5%. That mixes cash with an estimate.
The second is dividing by commitments instead of paid-in capital, or adding NAV to paid-in. All three ratios share one denominator, the money actually called and paid.
What the interviewer asks next
- What would DPI be if the fund sold the remaining holdings at a 20% discount to NAV?
- Why might two funds with the same TVPI have very different IRRs?
- A secondary buyer offers 90% of NAV. What is the seller's TVPI after the sale?