This topic relates to capital budgeting. The starting point is an explanation of why investment analysis is important in managerial economics, and the different types of investment and investment decision. Cash flow analysis and the principles involved in identifying and measuring relevant cash flows is discussed. The concept of risk and types of risk, stand-alone risk, within-firm risk and market risk, are discussed. The security market line (SML), beta coefficients and the capital asset pricing model (CAPM) are explained. The cost of capital is examined, explaining the calculation of the cost of debt, the cost of equity and the weighted average cost of capital (WACC). Methods of evaluation of individual projects are discussed, with a focus on net present value (NPV) and internal rate of return (IRR). There is a discussion of the determination of the optimal capital budget for a firm, in terms of the investment opportunity schedule (IOS) and the marginal cost of capital (MCC), with the distinction between mutually exclusive projects and independent projects. Case studies include two resource-heavy situations: the HS2 rail link and 5G telecommunications.

As engineering and the sciences become increasingly data- and computation-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from the signal and data acquisition to modeling, analysis, and prediction.

In this chapter, we present an application of compressive sensing to a crucial problem in modern wireless (radio) communication: How can cognitive radios efficiently identify available spectrum? We will see that this problem can be cast as one of recovering the support of a sparse signal, in the presence of noise. We will see how the methods and algorithms described in this book will allow us to break theoretical limits of conventional approaches, and, once properly implemented in hardware, they can significantly advance the state of the art, by enabling better tradeoffs between energy consumption and scan time. Besides its practical importance, this application is very interesting as it is kind of dual to the situation in the magnetic resonance imaging that we studied in the preceding chapter. In MRI, the measurements are the Fourier transform of the image of interest and the sparse patterns are in the image domain; whereas for spectrum sensing, the sparse patterns are in the Fourier domain which we do not measure directly.

In the previous chapter, we saw many problems for which the goal is to find a sparse solution to an underdetermined linear system of equations y = Ax. This problem is NP-hard in general. However, we also observed that certain well-structured instances can be solved efficiently: in experiments, when y = Axo and xo was sufficiently sparse, tractable ℓ1 minimization

In this chapter, we will branch out from sparse signals to a broader class of models: the low-rank matrices. Similar to the problem of recovering sparse signals, we consider how to recover a matrix

This final chapter does not cover any new principles; instead it presents case studies that have a huge global impact in terms of both managerial and government decision making. These case studies relate to: the role of big tech firms in the economy and the opportunities and threats that they present; the problems that the Covid-19 pandemic has posed for governments at the global level; and the problems that climate change is posing for both governments and firms, again at the global level. The last two cases involve geopolitical issues that go beyond the scope of the text, but it is important for managers to have a general appreciation of these issues in order to anticipate government policy and respond appropriately. The questions at the end of the case studies are intended to prompt students to utilize principles explained throughout the text to develop an understanding of the relevant issues and determine optimal courses of action.