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

Серия:

isbn: 9781119816638

isbn:

СКАЧАТЬ alt="upper F upper V left-parenthesis 0.012 comma 20 comma comma negative 20000 right-parenthesis equals dollar-sign 25 comma 388.69"/>

      The Present Value Function in Excel

       Rate

       Nper

       Pmt

       Fv

       Type

      Fv stands for the future value. The other parameters have the same meaning as specified for the FV function.

      EXAMPLE 2.25

      Sharon Oliver wants to accumulate $25,000 in her bank account after five years. The bank agrees to pay 5.40% per annum compounded quarterly. How much should she deposit today?

upper P upper V left-parenthesis .0135 comma 20 comma comma negative 25000 right-parenthesis equals dollar-sign 19 comma 118.99

      EXAMPLE 2.26

      Allegra is offering an instrument that promises to pay $4,000 per year for 10 years, beginning one year from now. If the annual rate of interest is 5.40%, and interest is paid annually, what is the present value of the annuity?

      We can use the PV function in Excel. The parameters are: Rate = 0.054, Nper = 10, Pmt = –4,000. There is no need to input parameters for Fv and Type. This is because there is no lump-sum terminal cash flow, and so there is no need to input a value for the future value. Type needs to be input only for annuities due.

upper P upper V left-parenthesis 0.054 comma 10 comma negative 4000 right-parenthesis equals dollar-sign 30 comma 295.65

      The future value of this annuity may be computed using the FV function.

upper F upper V left-parenthesis .054 comma 10 comma negative 4000 right-parenthesis equals dollar-sign 51 comma 260.92

      Now assume that the above annuities are annuities due. The present and future values may be computed as follows.

StartLayout 1st Row 1st Column Blank 2nd Column upper P upper V left-parenthesis 0.054 comma 10 comma negative 4000 comma comma 1 right-parenthesis equals dollar-sign 31 comma 931.62 2nd Row 1st Column Blank 2nd Column upper F upper V left-parenthesis 0.054 comma 10 comma negative 4000 comma comma 1 right-parenthesis equals dollar-sign 54 comma 029.01 3rd Row 1st Column Blank 2nd Column 31 comma 931.62 equals 30 comma 295.65 times 1.054 EndLayout

      And

54 comma 029.01 equals 51 comma 260.92 times 1.054

       Rate

       Nper

       PV

       FV

       Type

      The values for PV and FV should have opposite signs.

      For the first period, upper P upper M upper T left-parenthesis 0.048 comma 8 comma negative 500 comma 000 right-parenthesis equals dollar-sign 76 comma 736.66 period

      Now consider the second period. There are two ways in which the PMT function can be invoked. We can specify the same set of parameters as for the first period. Or we can specify the Nper as 7, and the PV as the outstanding balance, which is $447,263.34.

upper P upper M upper T left-parenthesis 0.048 comma 8 comma negative 500000 right-parenthesis equals upper P upper M upper T left-parenthesis 0.048 comma 7 comma negative 447263.34 right-parenthesis equals dollar-sign 76 comma 736.66

      Now consider the interest and principal components of each installment. We can use a function in Excel called IPMT to compute the interest component of an installment and another function called PPMT to compute the principal component of the installment. The parameters, for both, are

       Rate: This is the periodic interest rate.

       Per: This stands for period.

       Nper: This represents the total number of periods.

       Pv: This is the present value.

       Fv: This is the future value.

       Type: This has the usual meaning.

      IPMT left-parenthesis 0.048 comma 1 comma 8 comma negative 500000 right-parenthesis equals dollar-sign 24 comma 000. While computing the interest component of the second installment, we can invoke IPMT as IPMT(0.048,2,8,–500000) or as IPMT(0.048,1,7,–447263.94). Both will return a value of $21,468.64. Similarly, the principal component of the first installment is PPMT left-parenthesis 0.048 comma 1 comma 8 comma negative 500000 right-parenthesis equals dollar-sign 52 comma 736.66. For the second period,

PPMT left-parenthesis 0.048 comma 2 comma 8 comma negative 500000 right-parenthesis equals PPMT left-parenthesis 0.048 comma 1 comma 7 comma negative 447263.94 right-parenthesis equals dollar-sign 55 comma 268.02 period

      IPMT and PPMT can be used with two sets of parameters. We can keep the total number of periods at the initial value, specify the present value as the initial loan amount, and keep changing Per to compute the interest and principal components. For the first installment, Per = 1, and for the nth installment, it is equal to n. The alternative is to re-amortize the outstanding amount at the beginning of each period over the remaining number of periods. Remember that each time we re-amortize, we are back to the first period. Thus, after every payment, we are back to the first period of a loan whose life is equal to the remaining time to maturity, and whose principal amount is equal to the remaining outstanding balance.

      1 1 To rephrase a famous Microsoft claim, in this case “What СКАЧАТЬ