Present Value and Discounting

Consider an investment in a $100 U.S. Government savings bond paying 4% interest, compounded annually, over the next six years. Consider that the bond will pay $100 at the end of the sixth year, but no separate interest payments will be made. What amount should one pay for that bond today to receive 4% compounded annually when you redeem that bond for $100 at the end of year six ? Consider this question differently, expressed in time value of money terms: What is the present value of the right to receive $100 six years from now if one needs to receive 4% on that money to be appropriately compensated for the investment they are making ?

This seemingly simple idea has profound implications for financial decision making since it typifies the time value of money process by which all investments are valued. Mathematically, the formula for determining the present value factor in this calculation is:


Notice that the denominator of that fraction is compounded future value of 4% for 6 years, which when divided into 1 gives the discounted present value of the right to receive the future cash flow it is multiplied by. In this case, 1/(1.04)^6=.7903 multiplied by $100 equals $79.03. Thus the investor in this savings bond can pay no more than $79.03 in order to earn at least 4%, annually compounded, over the next six years on their investment.

Here we see present value and discounting as the obverse of future value and compounding. The methods used to make the calculation can be algebraic, as indicated above, or in the pre-computed present value tables. Financial mode line calculators and computer spreadsheet programs are the preferred methods for discounted present value calculations because they permit the simple solving of such complicated discounting problems at the time necessary at the discounted rate, or the discounted rate necessary to achieve a specific price. These rigorous calculations are an integral part of a wide variety of financial calculations including the valuation of stocks, bonds and real estate.

Discounting has many applications in the banking business as well. Frequently a manufacturer of goods will deliver those goods to a wholesaler and take back a note, say for $100,000, in payment, then take the note to its bank and "discount it" for cash, say $95,000. The manufacturer has immediate cash, the bank collects the note for $100,000 in due course, earning its interest on the advance to the manufacturer. This is a present value transaction since the present value of the note the bank is willing to advance represents the price the manufacturer pays for the early cash and the interest the bank must earn on that advance. In addition, the payments we make on our car loans and home mortgages are the equal payments necessary at the required interest to "amortize" or "pay off" the present value of the remaining obligations on those loans.

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