Description: The amount of 1 [i.e., the amount that $ 1 is worth after 1 year] for an account earning a nominal interest r compounded n times annually is Pn[r,t], where t = [t1, . . . ,tn]. Note that Pn[r,t] is a polynomial in r of degree n. Now suppose that the n compounding periods have lengths T1, . . . ,Tn chosen at random. What can we say about Pn[r , T] , where T=[T1, . . . , Tn]? This depends of course on what is meant by choosing random lengths and we will consider two different natural possibilities that give rise to different answers to this question.

Description: Obsolescence of physical assets and processes is a major component of operational risk for some companies. A simulation experiment shows that managers, who consider the retirement and replacement of individual assets in isolation, have rational incentives, due to risk aversion and uncertainty, to defer the replacement of assets past a time that is optimal from the perspective of the shareholder who owns the entire portfolio of such assets. This results in measurable wealth destruction, —and a demonstrable opportunity to significantly enhance a company’s value. A practical decision model for the replacement timing of fixed, physical assets, which creates wealth by minimizing the long-term consumption of scarce resources, is provided.