Page 31 - DMGT405_FINANCIAL%20MANAGEMENT

Unit 2: Time Value of Money

PV of annuity of 4,80,000 ( n =10, i =20%) = 480,000 × 4.19247 20,12,386 Notes

PV of 6,00,000 at the end of 10 years = 600,000 × 0.16151 96,906
Total present value of Project A cash inflows 21,09,292
The problem can be broken down into two separate annuities, one with receipts of 4,50,000 per
year for 15 years and the other with payments of 50,000 for 4 years. The present value of the two
annuities can be found by computing the present value of 4,50,000 for 15 years at 20 per cent
minus an annuity of 50,000 for 4 years at 20 per cent.
PV of annuity of 4,50,000 ( n=15, i=20 per cent) = 450,000 × 4.67547 21,03,961
PV of annuity of 50,000 ( n=4, i=20 per cent) = 50,000 × 2.58873 (1,29,437)
Total present value of project B cash inflows 19,74,524

By discounting each project at the company’s required rate of return, we find the Project A
cash inflows have a present value of 12,09,292 and Project B cash inflows have a present value
of 19,74,524. Since the asking price of each project is 20,00,000, project B should not be
accepted. The value of project A is greater than the asking price, therefore the company should
acquire Project A.

Task Calculate the present value of cash flows of 700 per year for ever (in perpetuity)

1. Assuming an interest rate of 7%
2. Assuming an interest rate of 10%

Self Assessment
Fill in the blanks:

10. An annuity that goes on for ever is called a……………...
11. The present value of a perpetuity of C amount is given by the simple formula: C/i where
i is the………………..

12. Many business problems are solved by use of compound interest and ……………….tables.
2.5 Calculation of the Compound Growth Rate

Compound growth rate can be calculated with the following formula:
n
gr = Vo(1 + r) = V n
where,
gr = Growth rate in percentage.
Vo = Variable for which the growth rate is needed (i.e., sales, revenue, dividend at
the end of year ‘0’).
V n = Variable value (amount) at the end of year ‘n’.
(1 + r) n = Growth rate.
Illustration:
From the following dividend data of a company, calculate compound rate of growth for period
(1998-2003).

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