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Let us assume you expect to obtain Rs.2000 yearly for the next three years. The receipt of Rs.2000 is evenly divided. One part that is: Rs.1000 is obtained at the beginning of the year and the remaining Rs.1000 is received on the end of the year. We are interested in understanding the present value while the discount rate is 10%. The cash flows declared above are of two types that are similar to annuity due and regular annuity. The present value of such cash flow is determined as follows:
a) Present value of Rs.1000 obtained at the end of each year for three years as Regular annuity.
Rs. 1000 (1/ 1.10) + Rs.1000 (1/ 1.10)2 + Rs.1000 (1/ 1.10)3
= (1000 * 09091) + (1000 * 08264) + (1000 + 0.7513)
= Rs.2479.
b) Present value of Rs.1000 obtained at the starting of each year for three yearas annuity due
= Rs. 1000 + Rs. 1000 (1/ 1.10) + Rs.1000 (1/ 1.10)2
= 1000 + (1000 * 09091) + (1000 + 08264)
= Rs.2735
The present value of such annuity = Rs. 2479+Rs.2735 = Rs. 5214.
Derivation of Formulas i) Future Value of an Annuity Future value of an annuity is FVA n = A(1 + k) n -1 + A (1 + k) n - 2 + .......A (1 + k) + A ............
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