Page 45 - DMGT409Basic Financial Management

Basic Financial Management

Notes 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 4: 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
Illustration 5: Mr. Nandan intends to have a return of ` 10,000 p.a. for perpetuity, Incase the
discount rate is 20%, calculate the present value of this perpetuity.

Solution:
A 10,000
P = = = 50,000
i .20
This means that, Mr. Nandan should invest ` 50,000 at 20% to get an annual return of ` 10,000
for perpetuity.

3.5 Practical Implications of Compounding and Discounting
Value Concepts

Compound Interest

Illustration 6: Suppose you have ` 10,00,000 today, and you deposit it in a fi nancial institute,
which pays you 8 per cent compound interest annually for a period of 5 years. Show how the
deposit would grow.
Solution:
C = P (1 + I) n
v
n o
5
FV = 10,00,000(1+0.08) = 10,00,000 (1.469)
5
FV = ` 14,69,000
5
Note: See the compound value for one rupee Table for 5 years at 8 per cent rate of interest.
Variable Compounding Periods

Illustration 7 (Semi annual compounding): How much does a deposit of ` 40,000 grow in 10
years at the rate of 6 per cent interest and compounding is done semi-annually. Determine the
amount at the end of 10 years.
Solution:
×
⎛ 0.06⎞ 210
CV = ` 40,000 1 + ⎟
⎜
10y ⎝ 2 ⎠
= ` 40,000 [1.806] = ` 72,240
Note: See the compound value for one rupee Table for year 20 and at 3 per cent interest rate.

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