Page 29 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Personal Financial Planning

Notes Illustration 6
Given the time value of money as 10% (i.e. the discounting factor), you are required to find out
the present value of future cash inflows that will be received over the next four years.

Year Cash flows (`)
1 1,000
2 2,000
3 3,000
4 4,000
Solution:
Present Value of Cash flows

1 2 3 4(2x3)
Year Cash flows Present Value Present
Factor at 10% Value
1 1,000 0.909 909
2 2,000 0.826 1,652
3 3,000 0.751 2.253
4 4,000 0.683 2,732
Present value of series of Cash flows 7,546

2.4.2 Present Value of an Annuity

In the above case there was a mixed stream of cash inflows. An individual or depositor may
receive only constant returns over a number of years. This implies that, the cash flows are equal
in amount. To find out the present value of annuity either, we can find the present value of each
cash flow or use the annuity table. The annuity table gives the present value of an annuity of Re.
1 for interest rate ‘r’ over number of years ‘n’.
Illustration 7
Calculate the present value of annuity of ` 500 received annually for four years, when the
discounting factor is 10%.
Solution:
Present value of annuity of ` 500

1 2 3 4(2x3)
Year Cash flows Present Value Present
Factor at 10% Value
1 500 0.909 454.50
2 500 0.827 413.50
3 500 0.751 375.50
4 500 0.683 341.50
3.170
Present value of series of Cash flows ` 500 1,585.00
This basically means to add up the Present Value Factors and multiply with ` 500.
i.e. 3.170× 500 = ` 1,585.

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