Risk Averse VC (p17)

Suppose a venture capitalist (VC) is not fully risk neutral and has an ex post utility function given by `u(c_i) = c_i^0.8` where `c_i` is the VC's level of consumption in dollars in state `i`. The VC initially has $200,000 and is considering offering the contract just discussed in class: the VC would pay the founder $30,000 to undertake the biofuels project, and if the project succeeds, the founder would give the VC $300,000 of the payoff. As a reminder, if the founder undertakes the project, it has a 20% chance of success.

1. Please draw the VC's decision tree.
2. Evaluate it by calculating: (a) the EV and (b) the expected utility (EU) to the VC of offering the contract (you may assume the founder accepts if the contract is offered). Indicate (c) whether the VC offers the contract.
3. Finally, calculate (d) the certainty equivalent (CE) to the VC of the contract and (e) VC's risk premium. Note that 1/0.8 = 1.25.