Valuation Made Simple: No Uncertainties, Just Time

Abstract

Finance deals with time and uncertainty. This chapter introduces the very basics of financial economics in a deterministic setting. Leaving aside any consideration of risk is obviously restrictive, yet important lessons are to be learned in this simplified context. We start from the time value of money. Typical computations involve the future value of a given sum of money today, and the present value of a certain amount of money to be received in the future. To compute these values properly requires the notions of compounding and discounting. Both of them involve the use of the interest rate, which can be made alternatively on a discrete- and continuous-time basis. We frame this discussion in the context of annuity contracts with pre-specified cash flows over time. Next we move to situations in which future cash flows are not exogenously given, but are the direct result of decisions by (project) managers. Optimal management and (project) value maximization thus naturally arise as the two faces of a single coin. At this stage we introduce dynamic programming through two simple examples. Then we provide the formal exposition under a finite time horizon. This opens the way to more complex settings in the coming chapters.