Consider a project that has the following cashflow: 20 = 1.25,21 = -3,22 = -3,23 = 8. (a) Define the present value PV(x,r) of this project as a function of an interest rate r. Produce 1-2 plots showing PV(x,r) as a function of r to illustrate its shape. (10 marks] (b) Find the internal rate of return and prove that it is unique. [25 marks) (c) Prove that the internal rate of return is quasi-concave for projects 20, 21, ..., X'n with 20 > 0. Explain what statement needs to be proved, and modify the proof presented in the lecture to cover cases such as the one above. [25 marks] Consider a project that has the following cashflow: 20 = 1.25,21 = -3,22 = -3,23 = 8. (a) Define the present value PV(x,r) of this project as a function of an interest rate r. Produce 1-2 plots showing PV(x,r) as a function of r to illustrate its shape. (10 marks] (b) Find the internal rate of return and prove that it is unique. [25 marks) (c) Prove that the internal rate of return is quasi-concave for projects 20, 21, ..., X'n with 20 > 0. Explain what statement needs to be proved, and modify the proof presented in the lecture to cover cases such as the one above. [25 marks]