WHAT
The time value of money (TVM) is the concept that a sum of money is worth more now than the same sum will be at a future date due to its earnings potential in the interim. Money can grow only through investing.
A sum of money in the hand is worth more now than the same sum in the future. This is a core principle of finance. An investment delayed is an opportunity lost. The time value of money is also referred to as present discounted value.
WHY
Why money today is worth more than money tomorrow?
Today's dollar is worth more than tomorrow's because of inflation (on the side that's unfortunate for you) and compound interest (the side you can make work for you). Inflation increases prices over time, which means that each dollar you own today will buy more in the present time than it will in the future, i.e. the decline of purchasing power of a given currency over time.
Inflation is a measure of the rate of rising prices of goods and services in an economy. It can occur when prices rise due to increases in production costs, such as raw materials and wages. A surge in demand for products and services can cause inflation as consumers are willing to pay more for the product.
In this context which happens most of the time (based on history so far), investors prefer to receive money today rather than the same amount of money in the future because a sum of money, once invested, grows over time.
HOW
For example, money deposited into a savings account earns interest. Over time, the interest is added to the principal, earning more interest. That's the power of compounding interest.
PV = FV
( 1 + r )
PV = present time value
FV = future value
r = rate of interest
Example: You have $1,000 on hand (PV), and interest rate is 1% per annum (r= 0.01).
FV = PV x ( 1 + r ) = 1,000 x (1.01) = $1,010 a year later if you have deposited the PV amount in the bank which promised the interest of 1% per annum.
If it is not invested, the value of the money erodes over time. If you hide $1,000 in a mattress for three years, you will lose the additional money it could have earned over that time if invested. It will have even less buying power when you retrieve it because inflation has reduced its value.
As another example, say you have the option of receiving $10,000 now or $10,000 two years from now. Despite the equal face value, $10,000 today has more value and utility than it will two years from now due to the opportunity costs associated with the delay.
In other words, a payment delayed is an opportunity missed.
Formula:
Generally, it considers 1) the amount of money, 2) its future value, 3) the amount it can earn, and 4) the time frame.
For savings accounts, the number of compounding periods is an important determinant.
FV = PV x [ 1 + (i / n) ] (n x t)
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Assume a sum of $10,000 is invested for one year at 10% interest compounded annually. The future value of that money is:
FV = $10,000 x [1 + (10% / 1)] ^ (1 x 1) = $11,000
The formula can be rearranged to find the value of the future sum in present day dollars. For example, the present day dollar amount compounded annually at 6% interest that would be worth $5,000 one year from today is:
PV = $5,000 / [1 + (6% / 1)] ^ (1 x 1) = $4,717
Effect of Compounding Periods on Future Value
Taking
the $10,000 example above, if the number of compounding periods is
increased to quarterly, monthly, or daily, the ending future value
calculations are:
Quarterly Compounding: FV = $10,000 x [1 + (6% / 4)] ^ (4 x 1) = $10,614
Monthly Compounding: FV = $10,000 x [1 + (6% / 12)] ^ (12 x 1) = $10,617
Daily Compounding: FV = $10,000 x [1 + (6% / 365)] ^ (365 x 1) = $10,618
Hence,
TVM
depends not only on the interest rate and time horizon but also on
how many times the compounding calculations are computed each year.
Why is TVM important?
It can help guide investment decisions. Read on how TVM is being applied to property investment: property valuation math
