Question

Suppose that EastCapital (EC), a venture capital firm, raises $250 million of committed capital. Over the 15-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 15 years, the investments made by the fund are worth $850 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 15-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 EastCapital 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 15 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)

Answer 1

Part a)

Investment in EC by investor/limited partner = $ 250 million

For calculating IRR of EC, we have to calculate

i) Investment made by EC net of management fees as cash outflow (this is the actual investment made by EC)

Investment made by EC = Total Money raised from limited partner - Management Fees

= $ 250 million - $ 50 million = $ 200 million

=> cash Flow at time 0 i.e. CF₀ = - $200 million ---(1)

ii) Cash Inflow at the end of 15 year (CF₁₅) = Total value of fund = $850 million ---- (2)

Using IRR formula which is based on the fact that NPV of the investment = 0

=> 0 = CF₀ + (CF₁₅/ (1+IRR)¹⁵)

Replace CF₀ and CF₁₅ from (1) and (2) respectively

(1+IRR)¹⁵ = 850 / (- (-200))

IRR = (4.25)^(1/15) - 1

= 1.1013 - 1

= 0.1013

= 10.13%

Part b

For calculating IRR of Limited Partner, we have to calculate

i) Investment made by limited partner as cash outflow

Investment made by Limited Partner = Committed capital raised

= $ 250 million

=> cash Flow at time 0 i.e. CF₀ = - $250 million ---(1)

ii) Cash Inflow at the end of 15 year (CF₁₅) = Final value of fund - carried Interest

Carried Interest = 20% * (850 - (250 - 50)) = 20%* (850 - 200)

= 20%* (650) = $130 million

Hence CF₁₅ = $ 850 million - $ 130 million = $ 720 million ---- (2)

Using IRR formula which is based on the fact that NPV of the investment = 0

=> 0 = CF₀ + (CF₁₅/ (1+IRR)¹⁵)

Replace CF₀ and CF₁₅ from (1) and (2) respectively

(1+IRR)¹⁵ = 720 / (- (-250))

IRR = (2.88)^(1/15) - 1

= 1.0731 - 1

= 0.0731

= 7.31%

Part c

From Part b

i) CF₀ = - $250 million ---(1)

Suppose that the final fund value at the end of 15 years is $ x million

ii) Cash Inflow at the end of 15 year (CF₁₅) = Final value of fund - carried Interest

Carried Interest = 20% * (x - (250 - 50)) = 20%* (x - 200)

= 0.2 x - 40

Hence CF₁₅ = x - (0.2x - 40) = 0.8x + 40  ---- (2)

Using IRR formula which is based on the fact that NPV of the investment = 0

=> 0 = CF₀ + (CF₁₅/ (1+IRR)¹⁵)

Replace CF₀ and CF₁₅ from (1) and (2) respectively

IRR = 15% (given)

CF₁₅ = -CF₀ *((1+IRR)¹⁵)

0.8x +40 = - (-250) * (1.15)¹⁵

x = (2034.265 - 40)/ 0.8

= $ 2493 million