In accounting, most measures are documented at their fair value, which is the cash or cash equivalent amount a buyer pays for a good or service in an open market, namely, a good's fair market value. Fair market value is considered a reliable measure because it's an objective one set by market forces and one that reflects estimated cash flows.

When the fair market value (FMV) can be determined, accountants must use it; there is no need to analyze a good's present value or its expected cash flow. But when the FMV is not available, the latter is used.

## FV and PV of Future Cash Flows

"Fair value" represents the economic characteristics of an asset or a liability. The present value measurement, which estimates a fair value, estimates the future cash flow or a series of cash flows.

Fair value provides a CPA with the most complete and faithful measurement of the economic characteristics of an asset or liability. The present value measurement, which estimates fair value, would incorporate the following:

- An estimate of future cash flows or a series of cash flows,
- Market expectations about the possible variation in the timing or amount of the cash flows,
- The time value of money,
- The price of bearing the uncertainty that's inherent in an asset or liability and
- Other factors, such as a lack of liquidity.

## Present Value (PV) and Future Sums

A present value of future cash flows represents the current value of a future sum of cash or a future cash flow, assuming a certain rate of return. To calculate a present value, a discount rate is applied to the future cash flow. The higher the discount rate, the lower the present value of the cash flow.

The present value methodology infers that the current value of a future sum of cash is of greater value than is the future cash sum. To value the future cash flow, care must be taken when selecting a discount rate.

## The Present Value (PV) Concept

According to the present value theory, the $5,000 you might receive today has a greater value than does the $5,000 you might receive three years from today due to the time value of money. The reason being is that the PV concept assumes that you will invest the $5,000 you have in hand today and earn interest for the next three years.

In contrast, if you must wait five years to receive the $5,000, you incur an opportunity cost in the form of the interest that you could have otherwise earned on the principal for three years.

## The PV Concept in Practice

Assume that you receive $5,000 today and you invest it for three years and earn a compound interest of 5 percent per annum. This means that you will earn 5 percent interest on the principal amount of $5,000 each year for three years.

As the following example demonstrates, if you waited three years to receive the $5,000, there would be an opportunity cost of $788.13, or the 5 percent rate of return on the $5,000 principal for the three-year term:

- $5,000 multiplied by 0.05 percent equals $250, the interest earned for year one of the investment.
- $5,000 plus the $250 interest for year one equals $5,250, the principal and interest for year one of the investment.
- $5,250 multiplied by 0.05 percent equals $262.50, the interest for year two of the investment.
- $5,250 plus the $262.50 interest for year two equals $5,512 .50, the principal plus interest for year two of the investment.
- $5,512.50 multiplied by 0.05 percent equals $275.62, the interest earned for year three of the investment.
- $5,512.50 plus $275.62 interest equals $5,788.13, the principal plus interest for year three of the investment.
- $5,788.13 the principal plus interest for the three-year investment minus $5,000 the original principal equals $788.13, the total interest earned for years one, two and three.

## Present Value Discount Rate

The discount rate used to calculate a present value represents the investment rate of return a person foregoes on a fixed dollar value when she elects to accept that dollar value in the future, rather than today. The choice to use a certain discount rate is a subjective one.

The discount rate might represent a risk-free rate of return, or "hurdle rate," which is the rate of return an investment must earn to be worthwhile. For instance, the U.S. Treasury bond rate can serve as the discount rate in the PV calculation. For example, an investor might decide he must earn at a minimum a 2 percent yield for each of two years to justify an investment's associated risk.

## Using the Present Value Formula

Assume that you're given a choice of $3,000 in cash today or $3,300 one year from today. To identify your best option, you must either calculate the present value of $3,300 or the future value of $3,000.

### The Present Value Formula

Present value equals FV/(1+r )n, where FV is the future value, r is the rate of return and n is the number of periods. Using the example, the formula is $3,300/(1+.10)1, where $3,300 is the amount you expect to receive, the interest rate is 10 percent and the term is one year.

To calculate the present value of $3,300, divide $3,300 by 1.0 plus 10 percent for one period, or $3,000. So, $3,000 is the minimum amount you must receive today to have $3,300 one year from today. If you are paid $3,000 today, based on a 10 percent interest rate, the amount is enough to give you $3,300 in one year's time. Alternatively, the future value of $3,000 in one year's time equals $3,000 multiplied by 1.10 percent, or $3,300.