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Time Value of Money In accounting (and finance), the phrase time value of money indicates a relationship between time and money—that a dollar received today is worth more than a dollar promised at some time in the future. Nature of Interest Payment for the use of money; Excess cash received or repaid over the amount borrowed (principal). Principal Amount borrowed or invested Interest Rate A percentage Time The number of years or portion of a year that the principal is outstanding Simple Interest Interest computed on the principal only. Compound Interest Computes interest on the principal and any interest earned that has not been paid or withdrawn. any interest earned that has not been paid or withdrawn. number of years x the number of compounding periods per year. Compounding Period Interest Rate annual rate divided by the number of compounding periods per year. FVF = (1+i)^n Formula to determine the future value factor (FVF) for 1 Fundamental Variables to Compound Interest Rate of Interest Fundamental Variables to Compound Interest Number of Time Periods Fundamental Variables to Compound Interest Present Value Fundamental Variables to Compound Interest Future Value Future Value of a Single Sum FV = PV (FVF) FV future value PV present value (principal or single sum) FVF future value factor for n periods at i interest PV = FV (PVF) present value of a single sum Annuity requires Periodic payments or receipts (called rents) of the same amount, Annuity requires Same-length interval between such rents Annuity requires Compounding of interest once each interval. Ordinary annuity - rents occur at the end of each period. Annuity Due rents occur at the beginning of each period Future Value of an Ordinary Annuity Rents occur at the end of each period; No interest during 1st period FVF-OA future value factor of an ordinary annuity Future Value of an Annuity Due Rents occur at the beginning of each period; Interest will accumulate during 1st period; Annuity Due has one more interest period than Ordinary Annuity. Factor = multiply future value of an ordinary annuity factor by 1 plus the interest rate. Present Value of an Ordinary Annuity Present value of a series of equal amounts to be withdrawn or received at equal intervals; Periodic rents occur at the end of the period. Present Value of an Annuity Due Present value of a series of equal amounts to be withdrawn or received at equal intervals; Periodic rents occur at the beginning of the period Deferred Annuities Rents begin after a specified number of periods Future Value of deferred annuities Calculation same as the future value of an annuity not deferred Present Value off Deferred Annuities Must recognize the interest that accrues during the deferral period Valuation of Long-Term Bonds Two Cash Flows Periodic interest payments (annuity) and Principal paid at maturity (single-sum). Concepts Statement No. 7 introduces an expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows. Three Components of Interest pure rate Three Components of Interest expected inflation rate Three Components of Interest credit risk rate Risk-free rate of return FASB states a company should discount expected cash flows by the risk-free rate of return.