Concept of annuity
Investment lump sum at T0 and get lump sum at Tn = Future value; process is “compounding”. This is called future value of a single stream.
Suppose we are given a future value and want to know how much should be invested at present. We use the process that is converse of compounding and this is called “discounting”. In order to get lump sum after a given period, we should invest the present value at the beginning, again a lump sum. This is called the present value of a single stream.
Invest lump sum at T0 in a project and get annual returns. The returns will not be equal to each other. To determine the present value of the future returns to determine Net Present Value = Present value; process is “discounting”. This is the example of present value of multiple streams.
Annuity refers to “multiple stream” of cash flows but which are equal to each other and occurring annually. The cash flows could either be in flows or out flows. This means that the following alternatives are available to us when we are talking of “annuity”.
¨ We invest at the beginning one lump sum amount and get returns over a period of time that are equal to each other. The cash in flows that are equal to each other are called “annuity”. Herein we use what is known as Present Value Interest Factor Annuity (PVIFA). We multiply the Annuity by this factor and get the present value of the future cash flows in one shot. Then we compare this present value with our proposed investment at T0 taking decision on investment. We invest provided the Present value of future annuities is at least equal to our investment at T0.
¨ We invest in equal installments over a period of time and get one lump sum at the end of the period. The cash outflows that are equal to each other are called “annuity”. Herein we use what is known as Future Value Interest Factor Annuity (FVIFA) .We multiply the Annuity by this factor and get the future value of the cash out flows in one shot.
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