To work out how much you will have in the future if you invest for t year at an interest rate r, multiply the inial investement by (1 + r). to find the present value of a future payment, run the process in reverse and divide by (1 + r)Present valuers are always calculates using compound interest. Whereas the ascending lines in Figure 1.4 showed future value of $ 100 a critical with compound interest, when we calculate present values we move back along the lines from future to present.Thus the present values decline, other things equal, when future cash payments are delayed. the longer you have to wait for money, the less it is worth today, as we see in Figure 1.5. Notice how very small variations in the interest rate can have a powerful effect on the value of distant cash flows. At an interest rate increases to 15 percent, the value of the future payment falls by about 60 percent to $ 6.The present value formula is sometimes written differently. Instead of dividing the future payment by (1 + r), we could equally well multiply it by 1/(1 + r)The expression 1/(1 + r) is called the discount factor. It measures the present value of $ 1 received in year t.The simplest way to find the discount factor is to use a calculator, but financial managers sometimes find it convenient to use tables of discount factors. For example, table 1.7 shows discount dactors for a small range of years and interest rates. Table a. 2 at the end of the marerial provides a set of discount factors a wide range of years and interest rates
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