Concept of Present Value of Money
The two aspects of time value of money are present value and future value. Present value refers to today’s value of money which will received in the future. Determining the present value of money is very important in making financial decisions.
Let’s say, you want $5,000 after 3 years at 10% interest, how much money do you need to deposit in the bank today? It can be found by determining the present value of money.
Process of Calculation of Present Value
Formula: PV = FV ÷ (1+i)n
Detail,
PV = Present Value
FV = Future Value
i = Interest Rate
n = Number of Period
Example: 01
After 5 years Smith needs $10,000. XYZ Bank pays interest at the rate of 10% per annum on their savings accounts. How much money must Smith deposit in XYZ Bank to have a total of $10,000 after 5 years?
FV = 10,000
i = 10%
n = 5 years
PV = ?
Present Value (PV) = FV ÷ (1+i)n
PV = FV ÷ (1+i)n
= 10000 ÷ (1+.10)5
= 10000 ÷ 1.61051
Present Value (PV) = $6,209.21
Example: 02
What is the present value of $10,000, 4 years from now if the interest rate is 5%?
FV = 10,000
i = 5%
n = 4 years
PV = ?
PV = FV ÷ (1+i)n
= 10000 ÷ (1+.05)4
= 10000 ÷ 1.2155
Present value = 8,227.06
Why Present Value Important?
Investment decisions can be made by applying the concept of present value of money.
Let’s illustrate the point with an example:
A and B are two projects. Project A will receive $100,000 after 1 year, and Project B will receive $105,000 after one and a half years. Using the present value of money, the investment amount and the profit amount for these two projects can be calculated.
Project A: Present Value (PV) = 100,000 ÷ (1 + 0.1)1
= 100,000 ÷ 1.1
= $90,909.09
Project B: Present Value (PV) = 105,000 ÷ (1+0.1)2
= 105,000 ÷ 1.21
= $86,776.85
Profit from project A = 100,000 – 90,909 = $9,091
Profit from project B = 105,000 – 86,776 = 18,224
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