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Effective Rates of Interest and Discount
The effective rate of discount is used in computing the present values of certain types of annuities. Assuming as the rate of interest per annum, an investor who deposits Re 1 at the beginning of the year would receive Re (1 + i) at the end of the year. If he demands the interest payment in the beginning of the period, as money has time value, he would obviously get an amo

APPENDIX 2-A
This Appendix further develops some aspects of application of compounding and discounting techniques. Those not interested in the detailed treatment of these aspects may skip over the Appendix.
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EXAMPLE 2.11
Company XYZ is establishing a sinking fund 10 retire Rs 5.00,000, 8 per cent debentures, 10 years from today. The company plans to put a fixed amount into the fund each year for 10 years. The first payment will be made at the end of the current year. The company anticipates that the funds will earn 6 per cent a year. What equal annual contributions must be made to accumulate Rs 5,00:000, 10 years fro

PRACTICAL APPLICATIONS OF COMPOUNDING AND PRESENT VALUE TECHNIQUES
In the preceding’ sections we have outlined compounding and discounting techniques. These values have a number of important applications, relevant to the task of the financial manager and investors. Some of these are illustrated here.
1. A financial manager is often interested in determining the size of annual payments to accumulate a future

Present Value of an Infinite Life Annuity (Perpetuities)
An annuity that goes on for ever is called a perpetuity. The present value of a perpetuity of Rs C amount is given by the formula:
C/i
This is because as the length of time for which the annuity is received increases. the annuity discount factor also increases but if the length goes on extending, this increase in the annuity factor slows down. In fact. as

Present Value of a Mixed Stream of Cash flows
Table 2.7
Present Value of a Mixed Stream of Cash flows
Long Method for Finding Present Value of an Annuity of Rs 1,000 for Five Years.
Table 2.8
Long Method for Finding Present Value of an Annuity of Rs 1,000 for Five Years
Table 2.8 shows the long way of determining the present value of annuity. This method is the same as the one adopted for mixed stream. This proc

Present Value of Uneven Cash Inflows Having Annuity
Table 2.9
Present Value of Uneven Cash Inflows Having Annuity
It may be noted that the present values (PV) of Rs 2,00,000 and Rs 1.50,000 (uneven cash flows) received at the end of the first and second years respectively are to be determined will reference 10 Table A-3. ,The present value of subsequent "ash inflows of Rs. 1,00,000 each for 8 years is
found in T

EXAMPLE 2.6
In order to solve this problem, the present value or each individual cash now discounted at 10 percent for the appropriate number or years is to be determined. The sum of all these individual values is then calculate to get the present value of the total stream. The present value factor 5 required for he purpose are obtained from Table A-3. The results are summarized in Table 2.7.
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Present Value of a Series or Cash Flows.
So far we have considered only the present value of a single receipt at some future date. In many instances, .especially in capital budgeting decisions, we may be interested in the present value of a series of receipts received by a firm at different time periods. Like compounding, in order to determine the present value of such a mixed. stream of cash inflows, all tha

EXAMPLE 2.5
Mr X wants to find the present value of Rs 2,000 to be received 5 years from now, assuming 10 per cent rate of interest. We have to look in the 10 per cent column of the fifth year in Table A·3. The relevant PVIF as per Table A-3 is 0.621.
Therefore, present value = Rs 2,000 (0.621) = Rs 1,242
Some points may be noted with respect to present Values. First, the expression (or the present value factor