An entrepreneur has a project which generates the following (sure) cash flow stream:

t=1 t=2 t=3
$10 $20 $40

in million dollars. The initial investment costs (at t=0) are $20 millions. In addition, the entrepreneur has to incur the following operating costs (in million dollars) to run the business in the subsequent periods:

t=1 t=2 t=3
$12 $10 $3

The entrepreneur can borrow and save any amount at any date at the one period interest rate r=10% from a bank.

(a) Should the entrepreneur undertake the project?

(b) Suppose a private equity firm wants to buy the whole project (at t=0). Once the private equity firm owns the project it has to finance all costs (setup cost and operating costs) itself. What is the minimum price it has to pay so that the entrepreneur accepts the offer? What is the maximum price the private equity firm is willing to pay?