Time Value of Money Concepts BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction. If the interval between periods is constant and the amount is always the same, this is called an annuity. Because an annuity is a stream of payments over a period of time, our previous discussion of the time value of money would indicate that there must be an interest factor involved. In the language of annuities, the payments are called Rents (the symbol R is used to designate the amount of Rents). If the rent is paid at the end of each period the annuity is called an Ordinary Annuity. If the rent is paid at the beginning of each period the annuity is called an Annuity Due. FUTURE VALUE OF AN ORDINARY ANNUITY An example of an ordinary annuity is contributions to a 401-k retirement plan. At the end of each month a certain sum is deducted from the employee’s paycheck (or paid by the employer) and placed in an investment account. The algebraic formula for the future value of an ordinary annuity is: FVOA=R*[FVOA, n, i]Let’s assume that Spencer Company has agreed to contribute $60,000 to an employee retirement plan at the end of each year. The investment yields a 12% annual return. If we assume that contributions will be made for 10 years then the following reflects the Future Value of the retirement plan contributions. FVOA=R*[FVOA, n, i]FVOA=60,000*[FVOA, n=10, i=12%]FVOA=60,000*17.54874FVOA=1,052,924PRESENT VALUE OF AN ORDINARY ANNUITY The algebraic formula for the present value of an ordinary annuity is: PVOA=R*[PVOA, n, i]In many cases business enterprises offer some kind of long-term benefits to employees after they retire. If Spencer Company has agreed to make semiannual contributions of $60,000 to a post-retirement medical insurance plan for 10 years and the investment vehicle earns 5% per annum what is the present value of this contribution schedule? Using the above formula we can calculate the present value of this ordinary annuity as follows: PVOA=R*[PVOA, n, i]PVOA=60,000*[PVOA, n=20, i=2.5%]PVOA=60,000*15.58916PVOA=935,3501
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