Discounting 101 (2024)

Suppose you can earn a guaranteed return of 3% per year by putting $1 in a bank account. That $1 will grow to be worth $1.03 in one year ($1*(1+3%)=$1.03). If we divide both sides of this equation by (1+3%), we have $1=$1.03/(1+3%), which relates the present value ($1) to the future value ($1.03) and the discount rate (3%). Then we say that, using a discount rate of 3%, the present value of $1.03 received in one year is $1 today.

If the $1 is in the bank for more than one year, the investment yields compound interest (the interest on the interest). For a two-year investment, the value would be $1.0609 ($1*(1+3%)*(1+3%)=$1*(1+3%)^2=$1.0609). As before, using a discount rate of 3%, the present value of $1.0609 received in 2 years is $1.

Compound interest accounts for why the investment grows by 6.09 cents rather than just 6.0 cents (3 cents per year for two years). Over long time periods, compounding of interest can have significant effects on the calculation results.

Leaving the bank account example behind, the general relationship between the present value (PV), the future value (FV), the discount rate (r), and the duration of the investment (t) is described by the following formula:

PV = FV/(1+r)^t

Because t, which represents the number of years in the future until the payment is received, appears in an exponential form, small changes in the discount rate can have large effects on present values. For example, consider a payment of $1,000 received in 200 years. Using a 3% discount rate, the present value can be calculated as follows:

$1,000/(1+3%)^200 = $2.71.

At a slightly higher discount rate of 4%, the present value is calculated to be only $0.39, which is about 7 times smaller.