The time value of money (TVM) is the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also sometimes referred to as present discounted value.
Investor’s Rationale with the help of Illustration
The time value of money draws from the idea that rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. For example, money deposited into a savings account earns a certain interest rate and is therefore said to be compounding in value.
Further illustrating the rational investor's preference, assume you have the option to choose between receiving Rs 1,000 now versus Rs 1,000 in two years. It's reasonable to assume most people would choose the first option. Despite the equal value at the time of disbursement, receiving the Rs 1,000 today has more value and utility to the beneficiary than receiving it in the future due to the opportunity costs associated with the wait. Such opportunity costs could include the potential gain on interest were that money received today and held in a savings account for two years.
Time Value and Purchasing Power
The time value of money is also related to the concepts of inflation and purchasing power. Both factors need to be taken into consideration along with whatever rate of return may be realized by investing the money.
It is really important because inflation constantly erodes the value, and therefore the purchasing power, of money. It is best exemplified by the prices of commodities such as gas or food. If, for example, you were given a certificate for Rs 100 of free gasoline in 1990, you could have bought a lot more gallons of gas than you could have if you were given Rs 100 of free gas a decade later.
Inflation and purchasing power must be factored in when you invest money because to calculate your real return on an investment, you must subtract the rate of inflation from whatever percentage return you earn on your money. If the rate of inflation is actually higher than the rate of your investment return, then even though your investment shows a nominal positive return, you are actually losing money in terms of purchasing power. For example, if you earn a 10% on investments, but the rate of inflation is 15%, you’re actually losing 5% in purchasing power each year (10% – 15% = -5%).
Understanding the formula of TVM
Depending on the exact situation, the time value of money formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
Effect of compounding periods on Future Value
The number of compounding periods can have a drastic effect on the TVM calculations. Taking the Rs 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 = Rs 10,000 x [1 + (10% / 4)] ^ (4 x 1) = Rs 11,038
Monthly Compounding: FV = Rs 10,000 x [1 + (10% / 12)] ^ (12 x 1) = Rs 11,047
Daily Compounding: FV = Rs 10,000 x [1 + (10% / 365)] ^ (365 x 1) = Rs 11,052
This shows TVM depends not only on interest rate and time horizon, but also on how many times the compounding calculations are computed each year.