Part A: Basic Concepts

1. Time Value of Money
   1. The  time value of money means that money can be invested today to earn interest and grow to a larger dollar amount in the future.
   2. Interest is the amount of money paid or received in excess of the amount borrowed or lent.
      1. Simple interest is computed by multiplying an initial investment times both the applicable interest rate and the period of time for which the money is used.
      2. Compound interest includes interest not only on the initial investment but also on the accumulated interest in previous periods.
          Illustration
   
   
2. Valuing a Single Cash Flow Amount
   1.  The future value of a single amount (FV) is the amount of money that a dollar will grow to at some point in the future.
      1. The future value of a single amount can be calculated by multiplying the initial investment (I) times (1 + i)ⁿ
         

         where:	i	=	interest rate
         	n	=	number of compounding periods

      2. The future value also can be determined by using  Table 1, Future Value of $1.
   2.  The present value of a single amount (PV) is today's equivalent of a particular amount in the future.
      1. The present value of a single amount can be calculated by dividing the future value by (1 + i)ⁿ.
      2. As with future value, we can use a table, Table 2, Present Value of $1, to  determine present value.
   3.  Solving for other values when PV and FV are known
      1. There are four variables in the process of adjusting single cash flow amounts for the time value of money: the present value (PV), the future value (FV), the number of compounding periods (n), and the interest rate (i).
      2. If you know any three of these, the fourth can be determined.
   
   
3. Accounting Applications of Present Value Techniques - Single Cash Amount
   1. Most receivables and payables are valued at the present value of future cash flows, reflecting an appropriate time value of money.
   2. While most notes, loans, and mortgages explicitly state an interest rate that will properly reflect the time value of money, there can be exceptions.  Here is an example.
   
   
4. Expected Cash Flow Approach
   1. SFAC No. 7 provides a framework for using future cash flows as the basis for accounting measurement and asserts that the objective in valuing an asset or liability using present value is to approximate the fair value of that asset or liability.
   2. Traditionally, the way uncertainty has been considered in present value calculations has been by discounting the best estimate of future cash flows applying a discount rate that has been adjusted to reflect the uncertainty or risk of those cash flows. SFAC No. 7 offers an alternative method called the expected cash flow approach. This approach adjusts for uncertainty or risk of cash flows by incorporating specific probabilities of cash flows into the analysis.
       Illustration

Part B: Basic Annuities

1.  Ordinary Annuity and Annuity Due
   1. An annuity is a series of equal-sized cash flows occurring over equal intervals of time.
   2. In an ordinary annuity cash flows occur at the end of each period.
   3. In an annuity due cash flows occur at the beginning of each period.
   
   
2. Future Value of an Annuity
   1. The future value of an annuity can be determined by summing the future value of each of the individual cash payments or by using the appropriate annuity table, Table 3, Future Value of an Ordinary Annuity, or Table 4, Future Value of an Annuity Due.
   2. In the future value of an ordinary annuity (FVA), the last cash payment will not earn any interest.
       Illustration
   3. In the future value of an annuity due (FVAD), the last cash payment will earn interest.
       Illustration
   
   
3. Present Value of an Annuity
   1. The present value of an annuity can be determined by summing the present value of each of the individual cash payments or by using the appropriate annuity table, Table 5, Present Value of an Ordinary Annuity, or Table 6, Present Value of an Annuity Due.
   2. In the present value of an ordinary annuity (PVA) the first cash flow takes place at the end of the first compounding period.
       Illustration
   3. In the present value of an annuity due (PVAD) the first cash flow takes place at the beginning of the first compounding period.
       Illustration
   4. In the present value of a  deferred annuity, the first cash flow occurs more than one period after the date the agreement begins.
   
   
4. Solving for Unknown Values in Present Value Situations
   1. In present value problems involving annuities, there are four variables: present value of an annuity (PVA or PVAD), the amount of each annuity payment, the number of periods (n), and the interest rate (i).
   2. If you know any three of these, the fourth can be determined.  Here is an example.
   
   
5. Accounting Applications of Present Value Techniques – Annuities
   1. Because financial instruments typically specify equal periodic payments, accounting applications incorporating the time value of money concept quite often involve annuity situations.
   2. Three examples are:
      1. The valuation of long-term bonds.
      2. The valuation of certain  long-term leases.
      3. The valuation of  pension obligations.
   
   
6.  Summary of Time Value of Money Concepts

 Here is a quiz to test your understanding of this chapter.