Why Does Money Have A Time Value

QUESTION 4

Why does money have a time value? Your answer must be supported with examples and academic citations.

Money that one has on hand right now, will most likely be worth more in the future because the money on hand today can be invested to earn interest to yield more value of the money (in whatever denomination it may be, in the future. The time value of money quantifies its value through time. This usually depends on the interest rate which can be earned on the money invested.

The concepts of the time value of money can either be its future value and its present value.  Its future value describes the process of finding what an investment today will grow to in the future while the present value describes the process of determining what a cash flow to be received in the future is worth in today's dollars.

For example, if a person deposited HK$100 today in a bank account to earn an interest rate of 10% compounded annually, this deposit will grow to $110 in one year. This can be shown as follows: 100 (1 + 0.1).  As one leaves the deposit and allows it to grow through the years, each year, the interest earned will also increase as it is compounded.  This is where the concept of compound interest comes from. 

Under compound interest, interest is earned not only on the initial principal but also on the accumulated interest. Interest begins to be earned on the accumulated interest as soon as it is paid, which occurs at the end of each compounding period.  Therefore, the future value of an initial investment at a given interest rate compounded annually at any point in the future can be found using the following equation:

where

• FV_t = the Future Value at the end of year t,
• CF₀ = the initial investment,
• r = the annually compounded interest rate, and
• t = the number of years.

Using the aforementioned example, if one leaves the deposit there for a decade, the future value of the initial HK$100 deposit becomes,

FV (in ten years) = 100 (1 + 0.1)¹⁰ = 259.37

The present value describes the process of determining what a cash flow to be received in the future is worth in today's money.  This means that the present value of a future cash flow represents the amount of money today which, if invested at a particular interest rate, will grow to the amount of the future cash flow at that time in the future. The process of finding present values is called discounting and the interest rate used to calculate present values is called the discount rate. For example, the present value of HK$100 to be received one year from now is $90.91 if the discount rate is 10% compounded annually.

Reference: Foundations and Applications of the Time Value of Money by Pamela Drake and Frank Fabozzi, 2009.