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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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