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Time Value of Money Measurement of recording of liabilities are based on the concept of the time value of money Time value of money compound interest Compound vs simple interest o Earns interest on the principle invested Compound interest previously earned interest Four Time Value Money Cases 1 Future Value of a lump sum 2 Present Value of a lump sum 3 Future Value of annuity 4 Present Value of annuity earns interest on bot principal invested as well as all o In each of these you need to use table factors Number of periods n Interest rate i In the future value of a lump sum case we know the value of some amount today and we want to know the value at some point in the future o FV PV FV factor Example 1 Compounding frequency with which interest is added to the principal o If ever different then being compounded annually must adjust interest rate and number of periods o i of compounds per year o n of compounds per year These adjustments must be made in all time value money cases FV factors can be calculated by 1 i n o Use table factors provided in the present value of a lump sum case we know the value of some amount in the future and we want to know the value today PV FV PV factor Example 2 discounting Key Point o Figuring out how much a future amount is worth today is called o The PV of a lump sum and the FV are reciprocals opposites of each other they can be used interchangeably to solve problems o As compounding frequency increases FV increases and PV decreases The more frequent the compounding the more interest earned on interest Annuity Lump sum single payment payment having the same time interval between them a series of equal payments either received or paid with each o A series of equal annual payments o A series of equal semi annual payments An annuity with payments occurring at the end of each period is known as an ordinary annuity An annuity with payments occurring at the beginning of each period is known as annuity due In the FV of an ordinary annuity case we want to know the value of a series of equal cash flows occurring at the end of each period at the same point in the future FV of annuity payment FV annuity factor Key Points 1 The payment in the above formula represents the amount of each individual equal payment do not add these payments together 2 The FV and PV of annuities are NOT reciprocal to each other and therefore can not be used interchangeably to solve problems Example 4 o To find the FV of an annuity due table factor multiply the ordinary annuity factor by 1 i PV of an ordinary annuity payment PV annuity factor Key Points 1 The payment in the above formula represents the amount of each individual equal payment Do not add these together 2 The FV and PV at annuities are NOT reciprocal to each other and therefore can not be used interchangeably to solve problems Example 5 o To find the pV of an annuity due table factor multiply the ordinary annuity factor by 1 i Example 6 Adequately evaluate different alternatives you must be able to compare each option at the same point in time o It is always easiest to compare alternatives using PV rather than FV Example 7 Example 8


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