# The Importance of Time Value of Money

The term “Time value of money” can in easy words be defined as; the dollar that you have today holds more value than the dollar you get tomorrow. The whole concept revolves around two main perspectives: the investment and the consumption perspective. The investment angle depicts how today’s \$1 is worth more than tomorrow’s \$1; while the consumption perspective indicates how you can buy less stuff tomorrow with \$1 than today due to the factor of inflation.

Inflation tends to erode the value of money with time thus, gradually reducing the purchasing power of money. Thus, giving us an idea of how money received today holds more value than the same amount in the future; due to the potential of it being invested and earning interest over it.

##### What does time value of money have to do with Financial management?

Considering that we are aware of the primary objective of financial management– to maximize the firm’s stocks intrinsic value. Financial managers need to stay informed and well aware of the stock values as they depend on the timings of the cash flow. The time value of money influences consumer, business, and government finance as it is an outcome of interest. Interest can be earned over an investment in terms of simple or compound interest; while the periods could be in months, quarters, semi or years. Lets have a look how interest is calculated using these two methods and what they depict.

##### Simple Interest

The interest calculated on the beginning principal – giving X% on the initial investment.

Formula: I= P * R* T

“I” as the interest

“P” as the principal amount

“R” as the rate

“T” as the time

##### Compound Interest

Interest is not only calculated on the principal amount but is compounded timely and is accumulated.

Formula: FVn= P * (1+ R)^n

“FVn” being future value

“P” as the principal amount

“R” as the rate

“n” as the time

The future value of the investment depends upon the number of years you tend to keep it for and the rate of return. We can also use the same formula to find the Present value through discounting if P is made the subject. This shows how much you need to invest today to receive the FVn required.

P = FVn/(1+R)^n

Also indicating a negative relationship of interest rates and time period with Present value.

Thus, we can see that compound interest gives you more returns compared to simple interest as in compound interest; interest is calculated on the principal amount as well as the accumulated addition to it.

###### The 4 important factors when compounding:
• A higher interest rate means more FV and vice versa.
• A larger present value means more FV and vice versa.
• A longer time period means more FV and vice versa.
• If the frequency of interest compounded increases (semiannual compounding than rather annual), more FV.

Eventually showing that more compounding means more future value.

Another important topic which is included when referring to the time value of money and its importance is annuities.

##### Annuities

Equal payments made at fixed intervals of time are known as annuities.

Future value of annuities

If the payment is made at the end of each period, it is an ordinary annuity.

FVAn=  (PMT*[( 1+I)^n-1])/I

While if the payment is made at the start of each period, it is known as an annuity due.

FVA(due) = FVAn *(1+I)

A good example to understand annuities is the pension system as a fixed amount is received by individuals per month.

Present value of annuities

Another type of annuity is a perpetuity whose payments could go on endlessly. As the payments may go on forever, most of the step by step approaches fail here; however, the PV of the perpetuity can be found using the formula:

PV of perpetuity = PMT/I

###### An overview of time value of money –

We have discussed interests, annuities and perpetuity above to give an idea of how value of money varies with time and; how we can calculate the future values as well as discount to find the present ones. In depth calculations and practice can help you master the art of valuing money with time; however uncertain factors will always exist thus they must be considered. You may use financial analysis and your own intuitions to make decisions; but the risk factor is always present as currencies,inflation and the whole economy may go through uncertainties at anytime.

Related article if you want to know about financial analysis : Financial Statement Analysis of a Company