[Basic Finance] The Time Value of Money #1

Time Value of Money Concepts & Applications

The concept of compound interest or interest on interest is deeply embedded in time value of money(TVM) procedures. When an investment is subjected to compound interest, the growth in the value of the investment from period to period reflects not only the interest earned on the original principal amount but also on the interest earned on the previous period’s interest earnings — the interest on interest.

TVM applications frequently call for determining the future value(FV) of an investment’s cash flows as a result of the effects of compound interest. Computing FV involves projecting the cash flows forward, on the basis of an appropriate compound interest rate, to the end of the investment’s life. The computation of the present value(PV) works in the opposite direction—it brings the cash flows from an investment back to the beginning of the investment’s life based on an appropriate compound rate of return.

Being able to measure the PV and/or FV of an investment’s cash flows becomes useful when comparing investment alternatives because the value of the investment’s cash flows must be measured at some common point in time, typically at the end of the investment horizon(FV) or at the beginning of the investment horizon(PV).

Time Lines

It is often a good idea to draw a time line before you start to solve a TVM problem in your life like a loan payments. A time line is simply a diagram of the cash flows associated with a TVM problem. A cash flow that occurs in the present(today) is put at time zero. Cash outflows(payments) are given a negative sign, and cash inflows (receipts) are given a positive sign. Once the cash flows are assigned to a time line, they may be moved to the beginning of the investments period to calculate the PV through a process called discounting or to the end of the period to calculate the FV using a process called compounding.

Figure 1 illustrates a time line for an investment that costs $1,000 today(outflow) and will return a stream of cash payments(inflows) of $300 per year at the end of each of the next five years.

Figure 1 : Time Line

Please recognize that the cash flows occur at the end of the period depicted on the time line. Furthermore, note that the end of one period is the same as the beginning of the next period. For example, the end of the second year(t = 2) is the same as the beginning of the third year, so a cash flows at the beginning of Year 3 appears at time t = 2 on the time line. Keeping this convention in mind will help you keep things straight when you are setting up TVM problems.

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