Fundamentals of Financial Instruments. Sunil K. Parameswaran
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Название: Fundamentals of Financial Instruments
Автор: Sunil K. Parameswaran
Издательство: John Wiley & Sons Limited
Жанр: Ценные бумаги, инвестиции
isbn: 9781119816638
isbn:
The expression (1 + r)N is the amount to which an investment of $1 will grow at the end of N periods, if it is invested at a rate r. It is called the FVIF (Future Value Interest Factor). It depends only on two variables, namely the periodic interest rate, and the number of periods. The advantage of knowing the FVIF is that we can find the future value of any principal amount, for given values of the interest rate and time period, by simply multiplying the principal by the factor. The process of finding the future value given an initial investment is called compounding.
EXAMPLE 2.11
Shelly Smith has deposited $25,000 for four years in an account that pays interest at the rate of 8% per annum compounded annually. What is the future value of her investment?
The factor in this case is given by
Thus, the future value of the deposit is
Note 3: Remember that the value of N corresponds to the total number of interest conversion periods, in case interest is being compounded more than once per measurement period. Consequently, the interest rate used should be the rate per interest conversion period. The following example will clarify this issue.
EXAMPLE 2.12
Simone Peters has deposited $25,000 for four years in an account that pays a nominal annual interest of 8% per annum with quarterly compounding. What is the future value of her investment?
8% per annum for four years is equivalent to 2% per quarter for 16 quarterly periods. Thus the required factor is FVIF(2,16) and not FVIF(8,4).
Thus the future value of
Note 4: The FVIF is given in the form of tables in most textbooks, for integer values of the interest rate and number of time periods. If, however, either the interest rate or the number of periods is not an integer, then we cannot use such tables and would have to rely on a scientific calculator or a spreadsheet.
PRESENT VALUE
Future value calculations entailed the determination of the terminal value of an initial investment. Sometimes, however, we may seek to do the reverse. That is, we may have a terminal value in mind, and seek to calculate the quantum of the initial investment that will result in the desired terminal cash flow, given an interest rate and investment horizon. Thus, in this case, instead of computing the terminal value of a given principal, we seek to compute the principal that corresponds to a given terminal value. The principal amount that is obtained in this fashion is referred to as the present value of the terminal cash flow.
The Mechanics of Present Value Calculation
Take the case of an investor who wishes to have $F after N periods. The periodic interest rate is r%, and interest is compounded once per period. Our objective is to determine the initial investment that will result in the desired terminal cash flow. Quite obviously
where P.V. is the present value of $F.
EXAMPLE 2.13
Patricia wants to deposit an amount of $P with her bank in order to ensure that she has $25,000 at the end of four years. If the bank pays 8% interest per annum compounded annually, how much does she have to deposit today?
The expression 1/(1 + r)N is the amount that must be invested today if we are to have $1 at the end of N periods, if the investment were to pay interest at the rate of r% per period. It is called the PVIF (Present Value Interest Factor). It too depends only on two variables, namely the interest rate per period and the number of periods. If we know the PVIF for a given interest rate and time horizon, we can compute the present value of any terminal cash flow by simply multiplying the quantum of the cash flow by the factor. The process of finding the principal corresponding to a given future amount is called discounting and the interest rate that is used is called the discount rate. Quite obviously, there is a relationship between the present value factor and the future value factor, for assumed values of the interest rate and the time horizon. One factor is simply a reciprocal of the other.
HANDLING A SERIES OF CASH FLOWS
Let us assume that we wish to compute the present value or the future value of a series of cash flows, for a given interest rate. The first cash flow will arise after one period, and the last will arise after N periods. In such a situation, we can simply find the present value of each of the component cash flows and add up the terms in order to compute the present value of the entire series. The same holds true for computing the future value of a series of cash flows. Thus present values and future values are additive in nature.
EXAMPLE 2.14
Let us consider the vector of cash flows shown in Table 2.3. Assume that the interest rate is 8% per annum, compounded annually. Our objective is to compute the present value and future value of the entire series.
TABLE 2.3 Vector of Cash Flows
| Year | Cash Flow |
|---|---|
| 1 | 2,500 |
| 2 | 5,000 |
| 3 | 8,000 |
| 4 | 10,000 |
|
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