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Basic Concepts: Basic Assumptions: Present Value Essentials
College of Visual Arts, US has reference to this Academic Journal, Present Value Essentials Basic Assumptions: All cash payments (receipts) Certainty regarding: Amount of cash flows Timing of cash flows All cash flows are immediately reinvested at designated interest rate Basic Concepts: For Accounting almost always Present value. I.e.: Answer the question: Some amount of money is so that be paid or received in the future (or a series of payments), how much is it worth now, given a certain required rate of return
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Basic Concepts I: Time Value of Money: Invested money earns interest (if in bank) or some rate of return (if invested in something else) Compound interest: Money earned on investment is reinvested immediately at required rate of return (interest earned on interest received) Basic Concepts II: Interest; rate of return; discount rate: For PV analysis they mean the same. From now, only ?interest? will be used Future Value: Value of an investment after a designated period of time, given a specified interest rate Present Value vs. Future Value Present value is based on future value, specifically the compound interest formula. Therefore Future value discussion so that help you understand present value
Basic Future Value Concepts: Invested money earns more money $1,000 today is worth more than $1,000 one year from today because: $1,000 invested at 10% grows so that $1,100 in one year $1,100 is the future value of $1,000 @ 10% after one year Future Value Example: FV Example (alternate view): $ 1,000 @ 10% grows so that $1,100 in one year $1,210 in two years $1,331 in three years OR $1,000 * 1.1*1.1*1.1 = $1,331
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Future Value Example: Another way so that determine the future value of $100 invested so that earn 10%, interest compounded annually:Use the Compound interest formula: (1 +r)n Where r = interest rate/compounding period in addition to n = number of compounding periods (1 + .1)3 = 1.331 * 100 = $133.10 Compounding: Number of times per year interest is calculated May be annually, semi-annually, quarterly, etc. However: Interest rate is expressed on annual basis, unless stated so that be in consideration of another period. Therefore: if annual interest rate is 10% ? Compounding: Semi-annual: 5% twice a year Quarterly: 2.5% four times a year Monthly: 10/12% 12 times a year In other words: If more than one compounding period/year, interest rate is divided by # of periods. # of years multiplied by # of periods
Compounding: Why does it matter? Because interest adds up faster. E.g.: 10%, 3 years, semi-annual compounding: (1 + .1/2)3*2 = 1.34 > (1 +.1)3 = 1.31 Future Value Calculation: FV of r= 10%, annual compounding in addition to n= 3 years: FV (r, n) = FV (10%,3) = 1.331 $100 invested in consideration of 3 years at 10% = $100 * FV (10%, 3) = X $100 * 1.331 = X = $133.10 Present Value (PV): Accounting almost always wants so that know what something is worth now PV asks: If $133.10 will be received in 3 years, how much is it worth today if 10% is the appropriate discount rate? Use FV formula so that answer the question:
PV of $133.10 (to be paid or received in 3 years) X * FV(10%,3) = $ 133.10 X * 1.331 = $ 133.10 (X* 1.331)/1.331 = $133.10/1.331 = $100 PV = Reciprocal of FV OR 1/FV therefore: PV(10%,3) = 1/FV(10%,3) = 1/(1+.1)3 = .75132 PV of $133.10 (to be paid or received in 3 years (again)) $ 133.10 * PV(10%,3) = X $ 133.10 * .75132 = X = $100 This is the equation you must use Do not use the formula, use table instead (p. C10) Part II Annuities Basic PV used in consideration of single sum payments E.g. a note payable due in 5 years PV of Annuity used in consideration of questions relating so that a series of equal payments at regular intervals E.g. car payments, payments on a student loan
PV of 3 payments of $ 100 each? Payments made at end of each of the next three years, 10% interest rate: PVA $100 (10%,3) PV annuity (PVA) $100, 10%, 3 years: PV annuity (PVA) $100, 10%, 3 years: Option 2: Use simple algebra, factor out constant: Restated equation: $100 * (.9091 + .8264 + .7531) = X $100 * 2.4868 = X = $248.68
PV annuity (PVA) Present value of an annuity (PVA) 3 periods, 10% = (.9091 + .8264 + .7531) = 2.4868 Libby ordinary annuity table, page 748: PVA (10%,3) = 2.4869 Kimmel ordinary annuity table, Appendix C: PVA (10%,3) = 2.48685 PV annuity due (PVA due) Difference: 1st payment is at beginning of period compared so that at the end in consideration of an ordinary annuity Example: Rent or lease payments Libby does not have table in consideration of it However: not a big problem
PVA due: 3 payments, 10% PVA due: 3 payments, 10% Option 2: Calculate the factor: PVA due (10%,3) = 1 +PVA(10%,2) = 1 + 1.73554 = 2.73554 * $ 100 = $2.73.55 Compared so that ordinary annuity: 2.4868
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