###### Binomial Option Valuation Model

One-Period Binomial Option Valuation Model In the one-period binomial model, we start today... **Read More**

Consider the following information:

- Management fee: 2%
- Carried interest: 20%
- Committed capital: 200
- The first total return method is applied.

All amounts are given in $ millions.

Calculate:

- Management fees.
- Carried interest.
- NAV before distributions.
- NAV after distributions.
- Distributed to paid in (DPI).
- Residual value to paid-in (RVPI).
- Total value to paid-in (TVPI).

$$\small{\begin{array}{c|c|c|c|c|c}\textbf{Year}&{\textbf{Capital Called Down}\\ }&{\textbf{Paid-in Capital}\\ }&{\textbf{Management Fees}\\ }&{\textbf{Operating Results}\\}&{\textbf{NAV Before Distributions}\\ }&{\textbf{Carried Interest}\\}&{\textbf{Distributions}\\}&{\textbf{NAV After Distributions}\\}\\ \hline\text{2015} & 80 & 80 & 1.6 & -8 & 70.4&0&&70.4 \\ \hline \text{2016} & 25 & 105 & 2.1 & -24 & 69.3&0&&69.3 \\ \hline \text{2017} & 20 & 125 & 2.5 & 41 & 127.8&0&&127.8 \\ \hline\text{2018} & 40 & 165 & 3.3 & 73 & 237.5&7.5&40&190\\ \hline \text{2019} & 25& 190& 3.8& 89 & 300.2&12.5&75&212.7 \\ \hline\text{2020} & 10 &200 &4 & 170 & 388.7&17.7&125&246\\ \end{array}}$$

**Paid-in capital** is the cumulative total of all capital called down.

$$\text{Paid-in capital in 2017}=$80+$25+$20=$125 \text{ million}$$

$$\text{Management fees}=\text{Management fee (%)}\times \text{Paid-in capital for each year.}$$

For 2020, management fee is \(2\text{%}\times $200 \text{ million} = $4 \text{ million}\).

**Carried interest** is paid when the NAV before distributions is greater than the committed capital.

In 2018, the NAV before distributions exceeded the committed capital for the first time and was calculated as follows:

$$\text{2018 carried interest}=20\text{%}\times($237.5-$200)=$7.5 \text{ million}$$

In subsequent years, it is calculated using the increase in the NAV before distributions as follows:

$$\text{2019 carried interest}=20\text{%}\times($300.2-$237.5)=$12.5 \text{ million}$$

$$\text{NAV before distributions =NAV after distribution in prior years+Capital called down}-\text{Management fees+Operating results}$$

$$\text{NAV after distribution in 2018}=($127.8+$40-$3.3+$73)=$237.50 \text{ million}$$

$$\text{NAV after distributions =NAV before distribution}-\text{Carried interest}-\text{Distributions}$$

E.g..

$$\text{NAV after distribution in 2018}=($237.5-$7.5-$40)=$190 \text{ million}$$

$$\text{DPI}=\frac{\text{Cumulative distributions pasid to the LPs}}{\text{Cumulative capital invested}}=\frac{($40+$75+$125)}{$200}=1.2X$$

$$\text{RVPI}=\frac{\text{Value of LP’ s holdings in the fund}}{\text{Cumulative capital invested}}=\frac{$246}{$200}=1.23X$$

The NAV after distributions is the net non-distributed value of the fund.

$$\text{TVPI}=\text{DPI}+\text{RVPI}= 1.2+1.23=2.43X$$

## Question

Gatsby LTD is interested in verifying carried interest, management fees, and the NAV of EVP. The following information is provided about yearly capital class, annual distribution, and operating results.

- Management fee: 3%
- Carried Interest: 15%
- Committed cap: 105
$$\small{\begin{array}{l|c|c|c}\textbf{Calls, Operating Results, and Distributions (Millions)}&{\textbf{}\\ }&{\textbf{}\\ }&{\textbf{}\\ }&{\textbf{}\\}\\ \hline & \bf{2011}& \bf{2012}& \bf{2013}& \bf{2014} \\ \hline\textbf{Called down} & 40 & 20 & 15 & 30 \\ \hline \textbf{Realized Results} & 0 & 5 & 15& 20 \\ \hline \textbf{Unrealized Results} & -2 & -5 & 10& 15 \\ \hline\textbf{Distributions} & 0 & 0 & 15 & 35 \end{array}}$$

The carried interest in 2012 is

closestto:

- $0.
- $7,440,00.
- $7.44.
## Solution

The correct answer is B.$$\small{\begin{array}{l|c|c|c|c|c|c}\textbf{Year}&{\textbf{Capital Called Down}\\ }&{\textbf{Paid-in Capital}\\ }&{\textbf{Management Fees}\\ }&{\textbf{Operating Results}\\}&{\textbf{NAV Before Distributions}\\ }&{\textbf{Carried Interest}\\}&{\textbf{Distributions}\\}&{\textbf{NAV After Distributions}\\}\\ \hline\text{2011} & 40 & 40 & 1.2 & -2 & 36.8&0&&36.8 \\ \hline \text{2012} & 20 & 60 & 1.8& 0& 55&0&&55 \\ \hline \text{2013} & 15 & 75 & 2.25& 25 & 92.75&0&15&77.75 \\ \hline\text{2014} & 20 & 105 & 3.15 & 35 & 154.6&7.44&35&112.16 \end{array}}$$

In 2012 the carried interest was 0 because interest is only paid when NAV before distribution is more than the committed cap of 105.

B is incorrect.This is the credit interest of the year 2014.

C is incorrect.$7.44 should be expressed in millions since the entire calculation is in millions.

Reading 38: Private Equity Investments

*LOS 38 (i) Calculate management fees, carried interest, net asset value, distributed to paid in (DPI), residual value to paid-in (RVPI), and total value to paid in (TVPI) of a private equity fund.*