1. Introduction

By now, we are well familiar with the concept of Future Values: When we receive a cash flow at time t (Ct), we can easily compute its value at a future point in time T, assuming the investment earns a constant return of R at the end of each investment period:

 

\( FV_T = C_t \times (1+R)^{(T-t)} \)

 

Oftentimes, however, we want to travel in the opposite direction. We want to know how valuable a specific investment proposal is from today's perspective. For example, we want to know whether the future cash flows of a specific investment project justify today's purchase price. The so-called Present Value provides the answer.

 

The present value (PV) indicates how valuable a future cash flow (or a string of future cash flows) is from today's perspective. More formally speaking, the present value indicates how much money we have to invest today into an alternative asset with identical risk to generate the exact same cash flows as the investment project in question. 

  

The following graph illustrates the basic logic of the present values:

  

Present Value Illustration  

The present value is arguably the most important tool in the toolbox of finance professionals. This section explain the basic concept of present values and how to apply that concept to specific valuation situations. It also briefly discusses the key assumptions we make when working with present values. 

  

The ability to compute (and understand) present values is an extremely powerful and useful instrument in the toolbox of investors and financial managers. Most investment projects involve a trade-off between investing money today and receiving payouts in the future. To understand whether such investment proposals make financial sense, we need to make cash flows comparable across time. That's what the present value does.

 

In this section, we cover the following topics:

  • First, We start with a simple example to show how present values work. Thereby, we get to know discounting, i.e., the mechanism that converts future cash flows into present values. We also talk about the crucial assumptions we make when discounting future cash flows: We need an alternative investment opportunity with identical risk and whose expected return we can estimate.
     
  • Second, we get to know the so-called discount factors, that allow us to quickly convert future cash flows into present values.
     
  • Third, we discuss how to handle different compounding frequencies and how to use the effective annual rate to compute present values.
     
  • Fourth, we show how to extend the idea of present values to investment proposals with multiple cash flows.
     
  • Finally, we go through an additional example to practice the important tools from this section.