Fundamentals of Financial Instruments. Sunil K. Parameswaran

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Fundamentals of Financial Instruments - Sunil K. Parameswaran


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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

normal upper P period normal upper V period equals StartFraction normal upper F Over left-parenthesis 1 plus r right-parenthesis Superscript upper N Baseline EndFraction

      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?

upper P equals StartFraction 25 comma 000 Over left-parenthesis 1.08 right-parenthesis Superscript 4 Baseline EndFraction equals dollar-sign 18 comma 375.75

      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

Year Cash Flow
1 2,500
2 5,000
3 8,000
4 10,000
5 20,000
Year Cash Flow Present Value Future Value
1 2,500 2,314.8148 3,401.2224
2 5,000 4,286.6941 6,298.5600
3 8,000 6,350.6579 9,331.2000
4 10,000 7,350.2985 10,800.0000
5 20,000 13,611.6639 20,0000.0000
Total Value 33,914.1293 49,830.9824

      While computing the present value of each cash flow we have to discount the amount so as to obtain the value at time “0.” Thus the first year's cash flow has to be discounted for one year, whereas the fifth year's cash flow has to be discounted for five years. On the other hand, while computing the future value of a cash flow we have to find its terminal value as at the end of five years. Consequently, the cash flow arising after one year has to be compounded for four years, whereas the final cash flow, which is received at the end of five years, does not have to be compounded.

normal upper F period normal upper V period equals normal upper P period normal upper V period left-parenthesis 1 plus r right-parenthesis Superscript upper N

      In this case

49 comma 830.9824 equals 33 comma 914.1293 times left-parenthesis 1.08 right-parenthesis Superscript 5

      Consider a deal where we are offered the vector of cash flows depicted in Table 2.4, in return for an initial investment of $30,000. The question is, what is the rate of return that we are being offered? The rate of return r is obviously the solution to the following equation.

30 comma 000 equals StartFraction 2 comma 500 Over left-parenthesis 1 plus r right-parenthesis EndFraction <hr><noindex><a href=Скачать книгу