Page 46 - DMGT409Basic Financial Management

Unit 3: Time Value of Money

Illustration 8 (Quarterly compounding): Suppose a fi rm deposits ` 50 lakhs at the end of each Notes
year, for 4 years at the rate of 6 per cent interest and compounding is done on a quarterly basis.
th
What is the compound value at the end of the 4 year.
Solution:
×
⎛ 0.06⎞ 44
FV = ` 50,000,000 1 + ⎟
⎜
4 ⎝ 4 ⎠
= ` 50,00,000 [FVIF ]
3y….8y
= ` 50,00,000 × 1.267 = ` 63,35,000
Calculation of the Compound Growth Rate

Compound growth rate can be calculated with the following formula:
g = V (1 + r) = V
n
r o n
where,
g = Growth rate in percentage.
r
V = Variable for which the growth rate is needed (i.e., sales, revenue,
o
dividend at the end of year ‘0’).
V = Variable value (amount) at the end of year ‘n’.
n
(1 + r) = Growth rate.
n
Illustration 9: From the following dividend data of a company, calculate compound rate of
growth for period (1998 – 2003).
Year 1998 1999 2000 2001 2002 2003
Dividend per share (` ) 21 22 25 26 28 31
Solution:
21 (1 + r) = 31
5
5
(1 + r) = 31/21 = 1.476
Note: See the compound value one rupee Table for 5 years (total years – one year) till you fi nd
the closest value to the compound factor, after finding the closest value, see first above it to get

the growth rate.
Compounded/Future Value of Series of Cash Flows [Annuity]

Illustration 10: Mr. Bhat deposits each year ` 5000, ` 10000, ` 15000, ` 20000 and ` 25000 in his
savings bank account for 5 years at the interest rate of 6 per cent. He wants to know his future
value of deposits at the end of 5 years.
Solution:
CV = 5000(1+0.06) +10000(1+0.06) +15000(1+0.06) +20000(1+0.06) +25000(1+0.06)
1
2
0
3
4
n
CV = 5000(1.262)+10000(1.191)+15000(1.124)+20000(1.050)+25000(1.00)
5
= 6310 + 11910 + 16860 + 21000 + 25000 = ` 81,080/-

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