Discounted Present Value

BIBLIOGRAPHY

Discounted present value is a concept in economics and finance that refers to a method of measuring the value of payments or utility that will be received in the future. Most people would agree that receiving $1,000 today is better than receiving $1,000 in a year, because $1,000 today can be used for consumption or investment. This feature is referred to as time value of money—a given amount of money today is better than the same amount of money in the future. Discounted present value allows one to calculate exactly how much better, most commonly using the interest rate as an input in a discount factor, the amount by which future payments are reduced in order to be comparable to current payments.

There are two ways to think about discounted present value—transferring money from the future to the present via borrowing or transferring money from the present to the future via lending. In both cases the interest rate at which one can borrow or lend is a crucial part of the formula.

Suppose a firm is scheduled to receive a payment of $1,000 in a year. To understand how much this payment is worth to the firm today, we can calculate how much the firm can borrow today against that payment:

x · (1 + i ) = 1000,

where i is the interest rate. Then, x = 1000/(1 + i ). The factor 1/(1 + i ) by which we multiply the future payment is called a discount factor.

If the payment is scheduled to arrive in two years instead, we can use a two-step approach. Assuming the interest rate is the same for two years, a year from today the value of the payment will be 1000/(1 + i ), which today is worth

(1000/(1 + i )).1/(1 + i ) = 1000/(1 + i )².

Thus, for discounting the payments far in the future the compound interest rate is used.

To calculate the discounted present value (DPV) of a stream of future payments, one has to discount each payment appropriately and then add them up. If we denote the payment in each future year by y_t, where t is the year, then:

The formula above makes a set of assumptions that are important for the result: (1) interest accrues and is compounded annually; (2) the interest rate is constant over time; (3) the payments occur for T years, starting one year from today. Altering each of these assumptions would lead to different results. To properly calculate the discounted present value of future payments, one also has to use the most appropriate interest rate in calculations.

In addition, individuals might be simply impatient and prefer to receive their utility today instead of waiting for the future payment, even if interest will accrue. This impatience is measured with the individual discount factor, which can be multiplied by the market discount factor described above to measure the discounted present value of future utility in terms of today’s utility.

The concept of discounted present value is commonly used in all areas of finance, including decisions individuals commonly make—taking a mortgage credit for purchase of a house, financing the purchase of the car, and the like. Every firm uses the discounted present value of their future cash flow to assess the value of their projects. Investors use discounted present value to estimate the return on their investment. Lawyers use discounted present value in lawsuits to calculate the value of settlement in cases when damage to a client’s health deprives him or her of future income.

SEE ALSO Finance; Interest Rates; Loans; Time Orientation; Time Preference; Utility Function