Present Value (PV) formula refers to the exact numerical method to calculate present value of an asset or capital owned in future. The present value is often known as discounted value.

PV = \frac{CF}{(1+r)^ {n}}

Where PV = Present Value, CF is Cash Flow at period 1, r is the rate of interest or return, and n is the number of periods.

The conception of idea of present value arises from the classic concept of Time Value of Money. In its simplest form, this theory states that a dollar today is worth more than a dollar from future, which means the value of money decreases as we move ahead in time. So, we can deduce that present value of a certain sum of capital is more than the Present Value of the same sum of capital.

The decrease in worth of assets has many reasons and inflation remains the prime factor for it. We can look into this fact in a way that 1 dollar which is currently owned by us can be invested to earn some return from it. This potential of readily available for investment increases the present value of money. This fact is of such huge importance for investors that they have more liking in receiving a certain amount of capital today rather than having it after 2 years.

Note: The widespread use of present value formula shall not put anyone in this misconception that this formula determines that exact present value of a future asset. As a matter of fact, it cannot take into consideration the inflation, changing interest rates, and fluctuations in currency which are impossible to determine exactly. The reason for this is that these events are yet to happen.

Uses of Present Value Formula

Present Value formula has many applications and uses in financial world. Some of them are described briefly below:

  • Present Value serves as the meter to determine chances of future benefits, risks, and liabilities in any financial endeavours.
  • The Present Value formula has extensive use in stock pricing, bond pricing, financial modelling and etc.
  • It is used in pension fund evaluation, and lottery pay outs.
  • The concept of Present Value is also used in banking and insurance

Examples of Present Value Formula

Mrs. David wants to invest $30,000 after 1 year in an online business opportunity. If her bank is offering 5% interest rate on deposits, then find the amount that she needs to deposit now in order to withdraw the desired amount from bank after a year.

  • Cash Flow in future = CF = $ 30, 000
  • Interest Rate = r = 5 % = 0.05
  • Number of Periods = n = 1

Let’s use the formula of Present Value to calculate it:

PV = \frac{CF}{(1+r)^ {n}}

Substituting all the values:

PV = \frac{30,000}{(1+0.05)^ {1}} PV = \frac{30,000}{(1.05)^ {1}} PV = \frac{30,000}{(1.05)}

PV = \$28,571.4

So, Mrs. David needs to deposit $28,571.4 in her bank in order to withdraw 30,000 after a year for her online business investment.

Travis has $ 20,000 cash, but he needs $ 28,000 to invest in a movie project after 1 year. Find the interest rate that he needs to get from bank in order to accumulate desired amount at the end of year.

  • Cash Flow in future = CF = $ 28, 000
  • Present Value = PV = $ 20, 000
  • Number of Periods = n = 1
20,000 = \frac{28,000}{(1+r)^ {1}}

1+r = \frac{28,000}{20,000}

r = \frac{28,000}{20,000} -1 r = \frac{28,000- 20,000}{20,000} r = \frac{8,000}{20,000}

r = 40\%

So, he needs to get an interest rate of 40% in order to get his desired investment after a year. This interest is pretty high and banks rarely offer such rates.

Alternative Formulas

Sometime the term Future Value (FV) is used instead of Cash Flow (CF) in Present Value formula, so it modifies the formula as follows:

PV = \frac{FV}{(1+r)^ {n}}