Present Value

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Present value (PV) is the current worth of future cash given an established rate of return and a time period, usually in years.

Formula

The PV formula is the basic formula behind all aspects of time value of money. The PV formula is comprised of four variables as listed in the following and is commonly represented as:

\[PV=\frac{FV}{{{\left( 1+i \right)}^{n}}}\]

  • Present value (PV) is the value of an investment today, at time zero;
  • Future value (FV) is the value of today’s investment at a future point of time;
  • ‘n’ is the amount of periods, often in years, in the future; and
  • ‘i’ is the assumed interest rate an investment is projected to earn.

Example

Any of these variables can be solved if one knows values for the other three. For example, what is the present value of $105,000 which can be garnered one year from now at an interest rate of 5%?

\[PV=\frac{\$105,000}{{{\left(1+0.05\right)}^{1}}}=\$100,000\]

It is easiest for us to use pre-established tables which resolve for most of the more common combinations of years and interest. An abbreviated PV table is included as Table 1.

Present value Table

Table 1 Present value Table

Example 2

If you had won the lottery and had an option to receive an established sum of money today compared to 1 or $10,000 is too low. Since money today is worth more than money tomorrow, anything close to $500,000 today would be an easy decision to forego the payment in the future. The present value of this example is resolved as follows:

\[PV=\frac{\$500,000}{{{\left(1+0.03\right)}^{10}}}=\$370,000\]

Or using table 1,

\[\$500,000\times\frac{74}{100}=\$370,000\]

Any sum greater than 370,000 dollars would result in choosing today’s money versus 500,000 dollars ten years from now. Any sum less than 370,000 dollars would result in foregoing today’s payment and taking the 500,000 dollars ten years from now.

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