Time Value of Money

Accompanying Files
Study exercises problems
Study exercises answers


Managers and investors use time value of money techniques to estimate:

  • the value of operating assets;
  • the value of financial assets;
  • the value of liabilities such as stocks and bonds.

Cash that is available today is worth more than the same amount of cash that will be available later because today's cash can be invested to earn income.  The financial approach to these valuation problems is based on the assumption that real and financial assets are valued for the free cash flows that they provide. Valuing these cash flows is difficult because they occur at different points in time and with varying degrees of uncertainty. For that reason, companies must use time value of money techniques to estimate the value of an asset. Operating and financial managers in manufacturing and service companies use time value of money techniques when they evaluate investment proposals and consider alternative ways of financing their company's assets. Similarly, time value of money techniques are used by investment and portfolio managers  to estimate the values of stock and bonds in order to decide which to buy or sell. 


By the end of this workshop participants should be able to demonstrate an understanding of the fundamental theoretical justifications for using time value of money techniques in analyzing investment decisions. More specifically, participants should be able to compute:

  • future value of single cash flow;
  • present value of future single cash flow;
  • present value of n future cash flows;
  • present value of annuity;
  • present value of annuity with growth;
  • present value of perpetuity;
  • present value of perpetuity with growth g < i;
  • net present value.