Page 30 - DMGT515_PERSONAL_FINANCIAL_PLANNING

Unit 2: Time Value of Money

Formula for calculation of the present value of an annuity can be derived from the formula for Notes
calculating the present value of a series of cash flows :

C C C C
PVA = 1 1 + 2 2 + 3 3 + n n
n
(1i+ ) (1i+ ) (1i+ ) (1i+ )
⎛ 1 1 1 1 ⎞
= C ⎜ + + + n ⎟
⎝ (1i+ ) 1 (1i+ ) 2 (1i+ ) 3 (1i+ ) ⎠
⎛ n Ct ⎞
= C ⎜∑ n ⎟
⎝ t1 ( + ) ⎠
1i
=
Where,
PVA = Present value of an annuity having a duration of ‘n’ periods.
n
A = value of single instalment.

i = Rate of interest.
However, as stated earlier, a more practical method of computing the present value would be to
multiply the annual instalment with the present value factor.

PVA = A × ADF
n
Where ADF denotes Annuity Discount Factor. The PVA in the above example can be calculated
n
as 500 × 3.170 = ` 1,585.
The figure of 3,170 has been picked up directly from the Annuity Table for present value.
Illustration 8
Find out the present value of an annuity of ` 5,000 over 3 years when discounted at 5%.
Solution:

PVA = A × ADF
n
= 5000 × 2.773
= 13,865

Present Value of a Perpetual Annuity

A person may like to find out the present value of his investment, in case he is going to get a
constant return year after year. An annuity of this kind which goes on for ever is called a
‘perpetuity’.
The present value of a perpetual annuity can be ascertained by simply dividing ‘A’ by interest or
discount rate ‘i’, symbolically represented as A/i.
Illustration 9
Mr. Bharat, principal, wishes to institute a scholarship of ` 5,000 for an outstanding student
every year. He wants to know the present value of investment which would yield ` 5,000 in
perpetuity, discounted at 10%.

Solution:
A 5000
P = = = 50,000
1 .10

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