$latex TVPI=\frac{(\text{Distributions}+\text{Residual Value})}{\text{Paid In Capital}} $
Often, returns for an LP investor are measured using the above formula, Total Value to Paid In Capital, its an expression of the ratio of the Net Asset Value of a fund to the cost of the LPs investment. Essentially, it expresses how much each invested LP dollar is returning. Distributions are the liquid assets returned to LPs, Residual Value is the value remaining in illiquid assets that the fund holds, and Paid In Capital is the money invested by the LP
Where this formula gets interesting is at the end of the fund life. Typically TVPI tends to decline as funds reach year 8 or 9, so, in order to preserve their capital, it’s in the best interests of a LP to sell their investment. Let’s say hypothetically the LP invested $100 in a fund, has received $80, and the GP claims that there is $50 in residual value.
[latex]\begin{aligned}
\text{Distributions} = \$80 \
\text{Residual Value} =\$50 \
\text{Paid In Capital} = \text{\$100} \
\end{aligned}[/latex]
Right now the TVPI of this investment would be 1.3x, or in other words, for every $1 invested, $1.30 in total value exists.
[latex]\text{TVPI} = \frac{80+50}{100} = 1.3[/latex]
And because our hypothetical fund is in its 8th year, this LP realizes that over time this TVPI metric will decline, they decide that it’s in their best interest to sell their stake in the fund. A secondaries investor offers to buy their stake at 30% discount to the GP’s estimated residual NAV, or in other words, they offer $35 for the LPs stake.
[latex]\text{LP Proceeds} = \$80\ + \$35\ =\ \$115[/latex]
In exchange for liquidity and short term returns, the LP takes a haircut on their already pretty low returns. While the secondaries investor already enters with a relatively high hypothetical TVPI of 1.6x.
[latex]\text{Secondary TVPI} = \frac{50}{30}=1.66
Even if the fund continues to “underperform” and the assets sell for 80% of the residual NAV predicted by the GP in 3 years, the Secondary investor will still exit with a 1.33x ROIC and a IRR of around 15%. The best part is that the LP doesn’t even underperform that much by exiting early. Selling at year 8 yields an IRR of 2.45%, while waiting to receive the distributions yielded to the secondary buyer through the sale, yields an IRR that is only marginally higher at 2.99%. Both IRRs are abysmal for Private Equity, so they are much better off getting liquidity and redeploying the capital.
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