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1 Chapter 11 Time Value of Money Adapted from Financial Accounting 4e by Porter and Norton

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2 18 Time Value of Money Prefer payment now vs. in future due to interest factor Applicable to both personal and business decisions

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3 Simple Interest I = P x R x T Principal amount Dollar amount of interest per year Time in years Interest rate as a percentage

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4 20 Example of Simple Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years Calculate interest on the note.

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5 21 Example of Simple Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years Calculate interest on the note. Px R x T $ 3,000 x.10 x 2 = $ 600

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6 22 Compound Interest Interest is calculated on principal plus previously accumulated interest Compounding can occur annually, semi-annually, quarterly, etc.

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7 Example of Compound Interest Given following data: principal amount = $ 3,000 annual interest rate = 10% term of note = 2 years semiannual compounding of interest Calculate interest on note.

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8 Compound Interest Periods Year 1Year 2 10% annually 5% + 5% semiannually 5% + 5% semiannually 4 periods @ 5% semi-annual interest

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9 Example of Compound Interest Period BeginningInterest Ending Principal at 5% Balance 1 $ 3,000 $ 150 $ 3,150 2 3,150 158 3,308 3 3,308 165 3,473 4 3,473 174 3,647

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10 Comparing Interest Methods Simple annual interest: $3,000 x.10 x 2 = $ 600 Semiannual compounding: 1 $ 150 2 158 3 165 4 174 Total $ 647

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11 Compound Interest Computations Present value of an annuity Future value of an annuity Present value of a single amount Future value of a single amount

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12 Future Value of Single Amount Known amount of single payment or deposit Future Value + Interest =

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13 Future Value of a Single Amount Example If you invest $10,000 today @ 10% compound interest, what will it be worth 3 years from now? invest $10,000 Future Value? + Interest @ 10% per year Yr. 1Yr. 2Yr. 3

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14 Future Value of a Single Amount Example - Using Formulas n FV = p (1 + i) 3 = $10,000 (1.10) = $13,310

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15 FV = Present Value x FV Factor = $ 10,000 X (3 periods @ 10%) Future Value of a Single Amount Example - Using Tables FV?? $10,000 PV Yr. 1Yr. 2Yr. 3

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16 (n) 2% 4% 6% 8% 10% 11.020 1.0401.0601.0801.10 21.0401.082 1.124 1.1661.210 3 1.0611.1251.1911.260 1.331 41.0821.1701.2621.3601.464 51.1041.2171.3381.4701.611 61.1261.2651.4191.5871.772 71.1491.3161.5041.7141.949 81.1721.3691.5941.8512.144 Future Value of $1

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17 FV = Present Value x FV Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X 1.331 = $ 13,310 Future Value of a Single Amount Example - Using Tables FV = $13,310 $10,000 PV Yr. 1Yr. 2Yr. 3

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18 34 Present Value of Single Amount Discount Known amount of single payment in future Present Value

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19 Present Value of a Single Amount Example If you will receive $10,000 in three years, what is it worth today (assuming you could invest at 10% compound interest)? Present Value? $ 10,000 Discount @ 10% Yr. 1Yr. 2Yr. 3

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20 Present Value of a Single Amount Example - Using Formulas -n PV = payment x (1 + i) -3 = $10,000 x (1.10) = $7,513

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21 PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 10%) Present Value of a Single Amount Example - Using Tables FV=$10,000 PV ?? Yr. 1Yr. 2Yr. 3

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22 Present Value of $1 (n) 2% 4% 6% 8% 10% 1.9804.9615.9434.9259.9090 2.9612.9246.8900.8573.8265 3.9423.8890.8396.7938.7513 4.9238.8548.7921.7350.6830 5.9057.8219.7473.6806.6209

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23 PV = Future Value x PV Factor = $ 10,000 X (3 periods @ 10%) = $ 10,000 X.7513 = $ 7,513 Present Value of a Single Amount Example - Using Tables FV=$10,000 PV = $7,513 Yr. 1Yr. 2Yr. 3

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24 Periods Future Value? +Interest Future Value of an Annuity 1 2 3 4 $0 $3,000$3,000$3,000 $3,000

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25 If we invest $3,000 each year for four years at 10% compound interest, what will it be worth 4 years from now? Future Value of Annuity Example $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV ??

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26 $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV ?? FV = Payment x FV Factor = $ 3,000 x (4 periods @ 10%) Future Value of Annuity Example

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27 Future Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 12% 1 1.000 1.000 1.000 1.000 1.000 1.000 22.020 2.040 2.060 2.080 2.100 2.120 3 3.060 3.122 3.184 3.246 3.310 3.374 4 4.122 4.246 4.375 4.506 4.641 4.779 55.204 5.416 5.637 5.867 6.105 6.353

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28 FV = Payment x FV Factor = $ 3,000 x (4 periods @ 10%) = $ 3,000 x 4.641 = $ 13,923 $0 $3,000 $3,000 $3,000 $3,000 Yr. 1Yr. 2Yr. 3Yr. 4 FV = $13,923 Future Value of Annuity Example

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29 Present Value of an Annuity Periods 12341234 Present Value ? Discount $0 $500 $500 $500 $500

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30 Present Value of an Annuity Example What is the value today of receiving $4,000 at the end of the next 4 years, assuming you can invest at 10% compound annual interest? PV ?? Yr. 1Yr. 2 Yr. 3 Yr. 4 $0 $4,000 $4,000 $4,000 $4,000

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31 Present Value of an Annuity Example Yr. 1Yr. 2 Yr. 3 Yr. 4 PV ?? $0 $4,000 $4,000 $4,000 $4,000 PV = Payment x PV Factor = $ 500 x (4 periods @ 10%)

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32 Present Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 10.980 0.962 0.943 0.926 0.909 21.942 1.886 1.833 1.783 1.735 3 2.884 2.775 2.673 2.577 2.487 4 3.808 3.630 3.465 3.312 3.170 54.713 4.452 4.212 3.992 3.791

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33 Present Value of an Annuity Example Yr. 1Yr. 2 Yr. 3 Yr. 4 P.V. = $12,680 $0 $4,000$4,000 $4,000 $4,000 PV = Payment x PV Factor = $ 4,000 x (4 periods @ 10%) = $ 4,000 x 3.170 = $ 12,680

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34 Solving for Unknowns Assume that you have just purchased a new car for $14,420. Your bank has offered you a 5-year loan, with annual payments of $4,000 due at the end of each year. What is the interest rate being charged on the loan?

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35 Solving for Unknowns Yr. 1Yr. 2 Yr. 3 Yr. 4 Yr. 5 discount discount discount discount discount PV = $14,420 PV = Payment x PV factor PV factor = PV / Payment rearrange equation to solve for unknown

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36 Solving for Unknowns Yr. 1Yr. 2 Yr. 3 Yr. 4 Yr. 5 discount discount discount discount discount PV = $14,420 PV factor = PV / Payment = $14,420 / $4,000 = 3.605

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37 53 Present Value of an Annuity Table (n) 10% 11% 12% 15% 10.909 0.901 0.893 0.870 21.736 1.713 1.690 1.626 32.487 2.444 2.402 2.283 43.170 3.102 3.037 2.855 5 3.791 3.696 3.605 3.352 PV factor of 3.605 equates to an interest rate of 12%.

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