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Homework answers / question archive / Suppose that EastCapital (EC), a venture capital firm, raises $250 million of committed capital

Suppose that EastCapital (EC), a venture capital firm, raises $250 million of committed capital

Finance

Suppose that EastCapital (EC), a venture capital firm, raises $250 million of committed capital. Over the 11-year life of the fund, $50 million of this committed capital is used to pay EC's management fee. As is typical in the venture capital industry, EC only invests $200 million (committed capital less lifetime management fees). At the end of 11 years, the investments made by the fund are worth $810 million. EC also charges 20% carried interest on the profits of the fund (final fund value minus intial investment net of management fees). The proceeds from the investments are collected at the end of the 11-year fund life. (a) Calculate the IRR on the investments made by EastCapital. The IRR on the investments is %. (round to 2 decimals) (b) Calculate the IRR on the investment of a limited partner into East Capital net of all management fees and expenses. The IRR for the limited partner is %. (round to 2 decimals) (c) Suppose that the limited partner has a cost of capital of 15%. Which value (net of carried interest) must the fund at the end of ${col} years have that the IRR for the limited partner is 15%? (Hint: define the profit to the limited partner in the same way as is done in (b)) The fund must have a value of $ million. (round to the nearest million, no comma as thousand separator) 8 6 7 9 10 2 5 11 4 3

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Solution

(a) Calculate the IRR on the investments made by EastCapital.

Initial net investment = $200 million

Fund value at the end of 11 years = $810 million

Carried interest = ($810- $200)*20% = $ 122 million

So, total cumulative value = $810 + $122 = $ 932 million

Assuming the IRR = R we get:

$932=$200∗(1+R)^11

Solving for R we get

Or, R =15.02%

The IRR on the investments is 15.02%

(b) Calculate the IRR on the investment of a limited partner into EastCapital net of all management fees and expenses.

Considering the management fees the IRR will be :

(1+R)=(982/200)^1/11=1.1556

Or,R=15.56%

(c) Suppose that the limited partner has a cost of capital of 15%. Which value (net of carried interest) must the fund at the end of 11 years have that the IRR for the limited partner is 15%?

We assume the final fund value (including interest + fees) = FV

So, FV=200∗(1+15%)^11

=$930.48

So value (net of carried interest = V then,

V+(V−200)∗20%+50=930.48

Or,1.2V=930.48+200∗20%−50=920.48

Or, V=920.48/1.2=$767.07 million