Fundamentals of Financial Instruments. Sunil K. Parameswaran

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is called the Present Value Interest Factor Annuity (PVIFA). PVIFA(r,N) is the present value of an annuity that pays $1 at periodic intervals for N periods, computed using a discount rate of r%. Thus, like the factors that we studied earlier, it too depends on the interest rate and the number of periods. The present value of any annuity that pays $A per period can therefore be computed by multiplying A by the appropriate value of PVIFA.

      EXAMPLE 2.16

      Alpha Technologies is offering a financial instrument to Alfred that promises to pay $2,500 per year for 25 years, beginning one year from now. Alfred requires an annual rate of return of 8%. The question is, what is the maximum price that he will be prepared to pay?

      . Thus the value of the payments is:

      Future Value

      Similarly, we can compute the future value of a level annuity that makes N payments, by compounding each cash flow until the end of the last payment period.

      Therefore,

       is called the Future Value Interest Factor Annuity (FVIFA). This is the future value of an annuity that pays $1 per period for N periods, where interest is compounded at the rate of r% per period. The advantage once again is that if we know the factor, we can calculate the future value of any annuity that pays $A per period.

      EXAMPLE 2.17

      Paula Baker expects to receive $2,500 per year for the next 25 years, starting one year from now. Assuming that the cash flows can be reinvested at 8% per annum, how much will she have at the point of receipt of the last cash flow?

       Thus the future value is:

ANNUITY DUE

The difference between an annuity and an annuity due is that in the case of an annuity due the cash flows occur at the beginning of the period. An N period annuity due that makes periodic payments of $A may be depicted as follows

FIGURE 2.2 Timeline for an Annuity Due

      Present Value

      Therefore,

      The present value of an annuity due that makes N payments is obviously greater than that of a corresponding annuity that makes N payments, because in the case of the annuity due, each of the cash flows has to be discounted for one period less. Consequently, the present value factor for an N period annuity due is greater than that for an N period annuity by a factor of (1 + r).

      An obvious example of an annuity due is an insurance policy, because the first premium has to be paid as soon as the policy is purchased.

      EXAMPLE 2.18

      David Mathew has just bought an insurance policy from MetLife. The annual premium is $2,500, and he is required to make 25 payments. What is the present value of this annuity due if the discount rate is 8% per annum?

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