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Chapter 6 Time Value of Money Concepts Time Value of Money Time value of money money invested today will grow to a larger dollar amount in the future Simple versus Compound Interest Interest the rent paid for the use of money for some period of time In dollar terms it s the amount of money paid or received in excess of the amount o of money borrowed or lent Simple interest computed by multiplying an initial investment times both the applicable interest rate and the period of time for which money is used Compound interest results in increasingly larger interest amounts for each period of the investment o The reason is that interest is now being earned not only on the initial investment amount but also on the accumulated interest earned in previous periods More rapid compounding has the effect of increasing the actual rate which is called the effective rate at which money grows per year Interest is typically stated as an annual rate regardless of the length of the o compounding period involved In situations when the compounding period is less than a year the interest rate per compounding period is determined by dividing the annual rate by the number of periods Valuing a Single Cash Flow Amount Future Value of a Single Amount Future Value FV a single amount is the amount of money that a dollar will grow at some point in the future 1 i n FV I w h ere FV Future value of t h e invested amount I Amount invested at t h e beginning of t h e period i Interest rate n Number of compounding periods The future value can be determined by using Table 1 o The table contains the future value of 1 invested for various periods of time n and at various rates i o Use this table to determine the future value of any invested amount simply by multiplying the table value at the intersection of the column for the desired rate an the row for the number of compounding periods FV I FV factor Present Value of a Single Amount Present value PV the present value of a single amount is today s equivalent to a particular amount in the future The computation for future value can be revered to find the present value of a future amount to be the future amount divided by 1 i n o Substitute PV for I invested amount in the future value formula above 1 i n FV PV 1 i n PV FV o While the calculation of future value of a single sum invested today requires the inclusion of compound interest present value problems require the removal of compound interest Solving for Other Values when FV and PV are Known There are 4 variables in the process of adjusting single cash flow amounts for the time value of money the present value PV future value FV the number of compounding periods n and the interest rate i If you know any 3 of these the 4th can be determined Preview of Accounting Applications of Present Value Techniques Single Cash Amount Many assets and most liabilities are monetary in nature Monetary assets include money and claims to receive money the amount of which is fixed or determinable o Examples include cash and most receivables Monetary liabilities obligations to pay amounts of cash the amount of which is fixed or determinable o Most liabilities are monetary Monetary receivables and payables are valued based on the fixed amount of cash to be received or paid in the future with proper reflection of the time value of money In other words we value most receivables and payables at the PV of future cash flows reflecting an appropriate time value of money Expected Cash Flow Approach Because of its increased importance the FASB issued statement of Financial Accounting Concepts No 7 Using Cash Flow Information and Present Value in Accounting Measurements o This statement provides a framework for using future cash flows as the basis for accounting measurement and assets that the objective in valuing an asset or liability using present value is to approximate the fair value of that asset or liabilities Key to that objective is determining the PV of future cash flows associated with the asset or liability taking into account any uncertainty concerning the amounts and timing of the cash flows Lease payments are provided in the contract between lessor and lese o On the other hand the future cash flows to be paid to settle a pending lawsuit may be highly uncertain Traditionally the way uncertainty has been considered in PV calculations has ben by discounting the best estimate of future cash flows applying a discount rate that s been adjusted to reflect the uncertainty or risk of those cash flows With the approach described by SFAC No 7 though the adjustment for uncertainty or risk of cash flows is applied to the cash flows not the discount rate specific probabilities of cash flows in the analysis The discount rate used to determine PV when applying the expected cash flow approach should be the company s credit adjusted risk free rate of interest This new expected cash flow approach incorporates o Other elements of uncertainty are incorporated in the determination of the probability weighted expected cash flows In the traditional approach elements of uncertainty are incorporated into a risk adjusted discount rate The FASB expects that the traditional approach to calculating PV will continue to be used in many situations particularly those where future cash flows are contractual o The board also believes that the expected cash flow approach is more appropriate in more complex situations BASIC ANNUITIES Financial instruments frequently involve multiple receipts or payments of cash If the same amount is to be received or paid each period the series of cash flows is referred to as an annuity A common annuity encountered in practice is a loan on which periodic interest is paid in equal amounts An agreement that creates an annuity can produce either an ordinary annuity or an annuity due situation o The first cash flow receipt or payment of an ordinary annuity is made one compounding period after the date on which the agreement begins o The final cash flow takes place on the last day covered by the agreement The first payment of an annuity due is made on the first day of the agreement and the last payment is made on period before the end of the agreement Future Value of an Annuity Future Value of an Ordinary Annuity In the future value of an ordinary annuity the last cash payment will not earn any interest Future Value of an Annuity Due In the future value of an annuity due the last cash payment will earn interest Present Value of an Annuity

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