Time Value of MoNey - business applications Present value of 1, future value of 1, present value of ordinary annuity (or annuity due), future value of ordinary annuity (or annuity due)

What is the time value of money and why is it important? Compensate for risk, delay in payment/receipt, and inflation Values of some items on financial reports – determined by TVM Lendors and other creditors use in determining pay back on loans, etc. Investors expect returns to tie up their funds with a company Discounting – converting future cash flows to the present value Compounding – converting current period cash flows to the future value Examples – investing in PPE using loans or mortgages, estimating fair values of assets/liabilities, valuing certain assets/liabilities known for future cash flows

Types of Interest – simple versus compound Simple interest Compound interest Only calculated on original principal received or paid No matter how many periods, no interest is accrued on from the past interest Beneficial if borrowing Detrimental if investing Principal X interest rate (usually annual*) X time Time – if note expressed in days, time will be days/360 or days/365 Example – 2 year $1000 note with 10% interest………… $1000 X .10 X 24/12 = 200 Calculated on original principal received or paid plus interest previously accrued Beneficial if investing Detrimental if borrowing (Principal + accumulated interest) X rate* X time Time – if note expressed in days, time will be days/360 or days/365 Example – 2 year $1000 note with 10% interest... … 1st year $1000 X .10 X 12/12 = $100, 2nd year 1100 X .10 X 12/12 = 110, interest is $210 Example – if compounded semi-annually, above note would be: $1000 X .10 X 6/12 = $50 (1st 6 months), $1050 X .10 X 6/12 = $52.50 (2nd 6 months), $1102.50 X .10 X 6/12=55.13 (3rd 6 months) and finally 1157.13 X .10 X 6/12 (4th 6 months) = $57.86, interest is $215.49

Future value versus present value of a single sum Future value (FV) Present value (PV) One amount in the present plus compound interest on future periods until a specified time period is reached Example -- $1000 now with 4% interest and how much is there in three years (3 periods)? 1st year 1000 X 1.04 = 1040 2nd year (1000 X 1.04) X 1.04 = 1081.60 3rd year (1000 X 1.04) X 1.04 X 1.04 = 1124.86 FV = PV X (1 + i) n n=number of periods, i=interest rate Future value of 1 table based on equation Factor table amount (3,4%) = PV X (1.04)3 = 1.124864 1000 * 1.124864 = 1124.86 One amount in the future at a specified period of time brought back to the present Example -- $1124.86 three years from now – how much is it worth in today’s dollars? PV = FV X 1/(1 + i)n Present value of 1 Table based on equation Factor table amount = FV X 1/(1.04)3 Factor table amount = 1/1.1245864 =.8892158

Future value Ordinary Annuity (FVOA) versus Future value annuity Due (FVAD) Future value ordinary annuity – determined immediately after the last cash flow in the series Annuity – series of equal cash flows (rents-- deposits, receipts, payments or withdrawals) Ordinary annuity –cash flow occurs at end of period Fvo = C X [(1+i)^n – 1)/i] C = cash flow FV? R R R R ---------/--------/---------/-------/ Future value annuity due – Determined one period after the last cash flow in the series Annuity – series of equal cash flows (rents-- deposits, receipts, payments or withdrawals) Annuity due – cash flow occurs at the beginning of period Fvad = C X ((1+i)^n – 1)/i) X (1+i) FVOA earns one extra interest period R R R R FV? /---------/--------/---------/-------/

Present value ordinary annuity (PVOA) versus present value of annuity due (PVAD) Present value of ordinary annuity – the 1st rent occurs one period after the beginning of the problem PVo = C X [(1-1/(1+i)n)/i] Table approach –present value of ordinary annuity of 1 --example for 10 periods, 5% interest [1-1/(1.05)10 /.05 = 7.721735 PV? R R R R ---------/---------/----------/----------/ Present value of annuity due – the 1st rent occurs right away at the beginning of the problem PVD = C X [1- 1/(1+i)n-1 /i + 1] Table approach- present value of annuity due of 1 – example for 10 periods, 5% [1-1/(1.05)9 /.05 + 1] PV? R R R R /----------/----------/---------/