Definition of Present Value

Present Value

The present value of future payments discounted at the rate R is defined to be the current bank balance in an account paying interest at the rate R that would be required to replicate those future payments.

All these words are best understood in terms of a simple example. Suppose banks take deposits and make loans at the rate R, which is now 10%. Suppose a pure discount bond pays $110 in one year. The present value of that bond is $100 because a current bank deposit of $100 will replicate next year's bond payment of $110.

This notion of present value is driven by powerful market forces. Suppose the bond described above sold for $95. You could borrow $100 from a bank, buy the bond for $95, and put a $5 arbitrage profit in your pocket. In a year, the bond payment is just the right amount to pay off your bank loan.

If the current bond price is $105, bond issuers could sell bonds for $105, put $100 in the bank at 10% interest, and put a $5 arbitrage profit in their pockets. The bank deposit would be sufficient to pay off the bondholder next year.

The only bond price that shuts off these arbitrage profits is the present value of $100. Calculating the present value of a security's payment stream thus yields the price for that security that rules out arbitrage profits.

The mortgage/bond calculator illustrates the present value calculations for a variety of fixed-income streams. The present value calculator performs the calculations for payment streams that might increase over time (with inflation, for example).

The Classic Economic Models also includes two models useful for a money and banking course: Utility-Based Valuation of Risk and Mean-Variance Analysis: Risk vs. Expected Return.

This glossary supports the EconModel applications known as the Classic Economic Models. That collection includes 16 of the most important models from microeconomics and macroeconomics. Check out the 10-day free trial.