Consider a project that runs over n + 1 periods with payments X0, X1, ..., Xn. The present value at some interest rate r > 0 is n PV (x, r) = i=0 Xi. +r Define the external rate of return r* (x) as the largest (!) interest rater 0 such that PV (x, r) = 0. (1) Find conditions on the set of projects X CR2+1 such that the external rate of return r* (x) exists and is unique. (2) Find conditions on the set of projects X CR2+1 such that the function is quasi-concave. * X R x > r* (x) Instructions: In (1) and (2), your conditions have to be as general as possible. Once you have written down some conditions and proved that these are sufficient, illustrate why it is difficult to make these conditions more general (e.g., with counterexamples). Show all the steps of your argument or reasoning! The conditions in (2) are very likely more restrictive than those you need for (1).