What is Present Value?

Most financial management decisions involve present values rather than future values. For example, a financial manager who is considering purchasing an asset wants to know what the asset is worth now rather than at the end of some future time period. 

The reason that an asset has value is that it will produce a stream of future cash benefits. To determine its value now in time period zero, we have to discount, or reduce, the future cash benefits to their present value. 

What is Present Value?

Discounting is an arithmetic process whereby a future value decreases at a compound interest rate over time to reach a present value.

Let’s illustrate discounting with a simple example involving an investment. Assume that a bank or other borrower offers to pay you $1,000 at the end of one year in return for using $1,000 of your money now. 

If you are willing to accept a zero rate of return, you might make the investment. Most of us would not jump at an offer like this! Rather, we would require some return on our investment. To receive a return of, say, 8 percent, you would invest less than $1,000 now. 

The amount to be invested would be determined by dividing the $1,000 that is due at the end of one year by one plus the interest rate of 8 percent. This results in an investment amount of $925.93 ($1,000 ÷ 1.08), or $926 rounded. 

Alternatively, the $1,000 could have been multiplied by 1 ÷ 1.08, or 0.9259 (when carried to four decimal places) to get $925.90, or $926 rounded.

How To Calculate A Present Value?

Let’s now assume that you will not receive the $1,000 for two years and the compound interest rate is 8 percent. What dollar amount (present value) would you be willing to invest? In word terms, we have,

Present value = Future value × {[1 ÷ (1 + Interest rate)] × [1 ÷ (1 + Interest rate)]}

For our two-year investment example, we get,

Present value = $1,000 × (1 ÷ 1.08) × (1 ÷ 1.08) = $1,000 × (0.9259) × (0.9259) = $1,000 × 0.8573 = $857.30

Thus, for a one-year investment, the present value would be $925.90 ($1,000 × 1 ÷ 1.08, or 0.9259). A two-year investment would have a present value of only $857.30 ($1,000 × 0.9259 × 0.9259).

The discounting concept can be expressed in equation form, as follows: 

PV = FVn ÷ (1 + r)n

Or

PV = FVn[1 ÷ (1 + r)n]

where the individual terms are the same as those defined for the future value equation. Notice that the future value equation has simply been rewritten to solve for the present value. For the $1,000, 8 percent, two-year example, we have,

PV = $1,000[1 ÷ (1 + 0.08)] = $1,000(1 ÷ 1.1164)

= $1,000(0.8573)

= $857.30

= $857 (rounded)

If we extend the time period to ten years, the $1,000 future value would decrease to,

PV = $1,000[1 ÷ (1 + 0.08)10] = $1,000(1 ÷ 2.1589)

= $1,000(0.4632)

= $463.20

= $463 (rounded)

Most financial calculators are programmed to readily find present values. As noted, financial calculators, typically, have a present value (PV) key, a future value (FV) key, a number of time periods (N) key, an interest rate (%i) key, and a compute (CPT) key. If you have a financial calculator, you can verify the present value result for the ten-year example. First, clear the calculator. 

Then, enter 1000 (or –1000 for some calculators, to find a positive PV) and press the FV key, enter 8 and press the %i key, and enter 10 and press the N key. 

Finally, press the CPT key followed by the PV key to calculate the present value of 463.19, which rounds to $463.

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