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Chapter 11

Chapter 11. Time Value of Money. Adapted from Financial Accounting 4e by Porter and Norton. Time Value of Money. Prefer payment now vs. in future due to interest factor. Applicable to both personal and business decisions. 18. Simple Interest. I = P x R x T. Dollar amount of

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Chapter 11

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

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

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

  4. 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. 20

  5. 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. P x R x T $ 3,000 x .10 x 2 = $ 600 21

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

  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.

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

  9. Period Beginning Interest 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 Example of Compound Interest

  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

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

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

  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? Yr. 1 Yr. 2 Yr. 3 + Interest @ 10% per year

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

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

  16. Future Value of $1 (n) 2% 4% 6% 8%10% 1 1.020 1.040 1.060 1.080 1.10 2 1.040 1.082 1.124 1.166 1.210 3 1.061 1.125 1.191 1.260 1.331 4 1.082 1.170 1.262 1.360 1.464 5 1.104 1.217 1.338 1.470 1.611 6 1.126 1.265 1.419 1.587 1.772 7 1.149 1.316 1.504 1.714 1.949 8 1.172 1.369 1.594 1.851 2.144

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

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

  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 Yr. 1 Yr. 2 Yr. 3 Discount @ 10%

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

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

  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

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

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

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

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

  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 2 2.020 2.040 2.060 2.080 2.100 2.120 3 3.060 3.122 3.184 3.246 3.3103.374 4 4.122 4.246 4.375 4.506 4.641 4.779 5 5.204 5.416 5.637 5.867 6.105 6.353

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

  29. Periods 1 2 3 4 $0 $500 $500 $500 $500 Discount Present Value ? Present Value of an Annuity

  30. Yr. 1 Yr. 2 Yr. 3 Yr. 4 $0 $4,000 $4,000 $4,000 $4,000 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 ??

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

  32. Present Value of Annuity of $1 (n) 2% 4% 6% 8% 10% 1 0.980 0.962 0.943 0.926 0.909 2 1.942 1.886 1.833 1.783 1.735 3 2.884 2.775 2.673 2.5772.487 4 3.808 3.630 3.465 3.312 3.170 5 4.713 4.452 4.212 3.992 3.791

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

  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?

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

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

  37. Present Value of an Annuity Table (n) 10% 11% 12% 15% 1 0.909 0.901 0.893 0.870 2 1.736 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%. 53

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