please show all the sloutions (a-f) please

(a) Question 3 [12 points) Consider a VC fund which is set up for ten years with $100 million committed capital by limited partners. The fund has a management fee of 2% per year and carried interest of 80-20. Suppose at t=10 the final value (liquidation value) of the fund is $X. What is the investment capital of the fund? [1p) For questions (b) to (e), X=140 million. (b) What is the payoff of the limited partner? [2p] What is the payoff of the general partner (excluding fees)? [1p] For all subsequent questions, suppose there is also a hurdle rate of 10%. (d) What is the payoff of the limited partner? [3p) What is the payoff of the general partner (excluding fees)? [1p] Given the above compensation structure, suppose the LP wants to have a (total) return on committed capital of 100%. (f) What is the required final value X of the fund? [4p] (a) Question 3 [12 points) Consider a VC fund which is set up for ten years with $100 million committed capital by limited partners. The fund has a management fee of 2% per year and carried interest of 80-20. Suppose at t=10 the final value (liquidation value) of the fund is $X. What is the investment capital of the fund? [1p) For questions (b) to (e), X=140 million. (b) What is the payoff of the limited partner? [2p] What is the payoff of the general partner (excluding fees)? [1p] For all subsequent questions, suppose there is also a hurdle rate of 10%. (d) What is the payoff of the limited partner? [3p) What is the payoff of the general partner (excluding fees)? [1p] Given the above compensation structure, suppose the LP wants to have a (total) return on committed capital of 100%. (f) What is the required final value X of the fund? [4p]