Total Value to Paid-in Capital

A closed-ended fund returns money over years, holds what it has not sold yet, and cannot be marked to a market price. So "how is it doing?" needs a measure that counts both the cash already handed back and the value still sitting in the portfolio.

That is TVPI. It is the fund's investment multiple and, in the workbook's words, the fundamental metric in measuring private fund performance. It is commonly called the net multiple.

It can be built two ways and they give the same answer: divide (cumulative distributions + residual value) by paid-in capital, or simply add DPI and RVPI.

Because RVPI is an estimate of unsold assets, TVPI keeps moving until the fund is fully realised. The realised half of the number is fact; the unrealised half is an opinion.

The family of paid-in multiples fits together:

• PIC multiple = paid-in capital ÷ capital commitments. How invested the fund is. A high PIC means the fund is near the end of its drawdown phase.
• DPI, distributed to paid-in, the realisation multiple = cumulative distributions ÷ paid-in capital. How much money investors actually got back. Better for judging a fund late in life, when there are more distributions to measure.
• RVPI, residual value to paid-in, the unrealised multiple = residual (fair market) value ÷ paid-in capital. More representative of future returns early in a fund's life than DPI.
• TVPI = DPI + RVPI.

The workbook sets out how the three behave over a fund's life:

1. Before capital calls and the investing phase, TVPI is less than 1 — the corpus has been reduced by fees and expenses chargeable to it.
2. Through the vintage years and the growth cycle, value is mostly captured in RVPI.
3. As the fund harvests, DPI rises. When every investment has been exited, DPI is complete, RVPI is zero, and DPI = TVPI. Until then, DPI + RVPI = TVPI.

MOIC, the multiple on invested capital, divides total realised and unrealised value — the same numerator as TVPI — by total invested capital. When all capital calls have been met, total invested capital equals total paid-in capital, so TVPI equals MOIC. The workbook adds a warning: a consistently large MOIC-to-RVPI ratio should be a red flag prompting a revisit of the underlying asset valuations.

KS-PME takes the same TVPI arithmetic and compounds the capital calls and distributions forward at the market index return: market-adjusted TVPI above 1 means the AIF beat the market.

TVPI = (Cumulative distributions + Residual value of unrealised assets) / Paid-in capital

TVPI = DPI + RVPI

DPI  = Cumulative distributions / Paid-in capital
RVPI = Residual (fair market) value / Paid-in capital
PIC multiple = Paid-in capital / Capital commitments

MOIC = (Realised + unrealised value) / Total invested capital

Take the workbook's own figures. A fund has capital commitments of Rs 1,000 crore, of which Rs 800 crore has been paid in, so the PIC multiple is 0.80, or 80% — the fund is well into its drawdown phase.

Now measure performance on a paid-in capital of Rs 1,000 crore, with cumulative distributions of Rs 400 crore and residual value estimated at Rs 1,100 crore:

DPI  = 400  / 1,000 = 0.40
RVPI = 1,100 / 1,000 = 1.10
TVPI = (400 + 1,100) / 1,000 = 1.50   = DPI + RVPI = 0.40 + 1.10

A TVPI of 1.50 on Rs 1,000 crore means Rs 1,500 crore of total value — a gain of Rs 500 crore. But read where it comes from: only Rs 400 crore is cash in hand. The other Rs 1,100 crore is an estimate of what unsold holdings are worth.

Now run the fund forward. It exits everything, realising Rs 1,060 crore against the Rs 1,100 crore carried:

DPI  = (400 + 1,060) / 1,000 = 1.46
RVPI = 0
TVPI = 1.46          <- and now DPI = TVPI

The multiple fell from 1.50 to 1.46 without a single bad decision — the residual value was simply an estimate, and estimates settle. That is the double-edged sword the workbook warns about.

Chapter 6 (Risk and Return — Investor and Fund Perspective) works through the whole family at 6.6: the FIRR and MIRR first, then the PIC multiple at 6.6.3, DPI at 6.6.4, RVPI at 6.6.5, TVPI at 6.6.6 and KS-PME at 6.6.7. Expect computation questions using exactly these definitions, a question on the identity DPI + RVPI = TVPI, and a question on the life-cycle behaviour — when TVPI is below 1, when RVPI dominates, and when DPI equals TVPI.

• TVPI is a multiple, not a rate of return. It says nothing about how long the money was out. A TVPI of 1.5 over four years and over twelve years are very different investments — that is what IRR is for.
• The workbook states TVPI two ways that do not agree numerically. The narrative gives TVPI = 1.50 for the example above, while the displayed formula in section 6.6.6 writes it as [(cumulative distributions + valuation of unrealised assets) ÷ PIC − 1] × 100, which on the same figures gives 50%. Both are describing the same result — a multiple of 1.50 is a 50% gain — so read the "− 1 × 100" version as the percentage return and the plain ratio as the multiple, and answer in whichever form the question asks for.
• DPI = TVPI only when RVPI is zero, that is, once every investment is exited.
• TVPI equals MOIC only when all capital calls have been met, so that total invested capital equals total paid-in capital. Before that they differ.
• The denominator is paid-in capital, not commitments. Commitments are the denominator of the PIC multiple and nothing else here.
• At the investor level, DPI can differ from fund-level TVPI — because of the investor's status in the fund, any preferential rights, and the tax rate applicable to that investor.
• A TVPI below 1 early in a fund's life is normal, not a failure: fees and expenses have reduced the corpus before anything has been realised.