Suppose that EastCapital (EC), a venture capital firm, raises $250 million of committed capital. Over the 12-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 12 years, the investments made by the fund are worth $820 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 12-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 ${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)