1. 8-1 PowerPoint Presentation by Douglas Cloud Professor Emeritus of Accounting Pepperdine University © Copyright 2007 Thomson South-Western, a part of The Thomson Corporation. Thomson, the Star Logo, and South-Western are trademarks used herein under license. Task Force Image Gallery clip art included in this electronic presentation is used with the permission of NVTech Inc. Financial Accounting Information for Decisions 6 th edition Ingram and Albright F13 8 The Time Value of Money Financial Accounting A Bridge to Decision Making Ingram and Albright 6 th edition

2. 8-2ObjectivesObjectives Once you have completed this chapter, you should be able to—

3. 8-3 1.Define future and present value. ObjectivesObjectives 2.Determine the future value of a single amount invested at the present time. 3.Determine the future value of an annuity. 4.Determine the present value of a single amount to be received in the future. 5.Determine the present value of an annuity. 6.Determine investment values and interest expense or revenue for various periods.

4. 8-41 ObjectiveObjective Determine future and present value.

5. 8-5 Future Value The future value of an amount is the value of that amount at a particular time in the future.

6. 8-6 Future Value The present value of an amount is the value of that amount at a particular date prior to the time the amount is paid or received.

7. 8-7 Future Value Future Value = Present Value (1 + R) Interest Rate

8. 8-8 Future Value Future Value = Present Value (1 + R) Future Value = $1,000(1.05) If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value (the amount that will accumulate) by December 31, 2007? Future Value = $1,050

9. 8-9 2 2 Determine the future value of a single amount invested at the present time. ObjectiveObjective

10. 8-10 Compound Interest If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31, 2008, how much would the investment be worth at that time? FV = $1,050(1.05) FV = $1,102.50

11. 8-11 Compound Interest Interest earned in one period on interest earned in an earlier period is known as compound interest.

12. 8-12 Compound Interest Assume you invest $500 for three years at 8% interest. How much would your investment be worth at the end of three years? FV = PV(1 + R) t FV = $500(1.08)³ FV = $500(1.08)(1.08)(1.08) FV = $629.86

13. 8-13 To calculate a future value, a future value of a single amount table, such as the one in the next slide, can be used. Compound Interest

14. 8-14 Compound Interest 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Period Interest Rate 1.0101.0201.0301.0401.0501.0601.0701.0801.090 1.0201.0401.0611.0821.1031.2241.1451.6641.188 1.0301.0611.0931.1251.1581.1911.2251.2601.295 123123 Future Value of a Single Amount Note: Due to space limitations, the tables in this chapter have the table values rounded to three decimal places.

15. 8-15 Compound Interest 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Period 1.0101.0201.0301.0401.0501.0601.0701.0801.090 1.0201.0401.0611.0821.1031.2241.1451.6641.188 1.0301.0611.0931.1251.1581.1911.2251.2601.295 123123 Interest Rate 1.260 FV = $500 x 1.260 = $630 (rounded)

16. 8-16 Interest Table for an Investment of $500 for Three Years at 8% A B C D A B C D Value atInterest EarnedFV at Yearend YearBeginning of Year(B x Interest Rate)(B + C) 1500.0040.00540.00 2540.0043.20583.20 3583.2046.66629.86 Total 129.86 Total 129.86 Exhibit 1

17. 8-17 Exercise 8-2 Click the button to skip this exercise. If you experience trouble making the button work, type 20 and press “Enter.” Assume that you borrow $25,000 on April 1, 2007, at an annual rate of 7%. How much will you owe on March 31, 2008 if you make no payments until that date? Press “Enter” or left click the mouse for solution. FV = $25,000 x (1.07) = $26,750 1ContinuedContinued

18. 8-18 Exercise 8-2 How much will you owe on March 31, 2009 if you make no payments until that date? FV = $25,000 x (1.07) = $28,622.50 2ContinuedContinued Press “Enter” or left click the mouse for solution.

19. 8-19 Exercise 8-2 If you pay the interest incurred for the first year on March 31, 2008, how much will you owe on March 31, 2009 if you make no other payments until that date? FV = $25,000 x (1.07) = $26,750 1 If the interest incurred during the first year is paid off before the second year begins, interest will accrue only on the $25,000 during Year 2. Press “Enter” or left click the mouse for solution.

20. 8-20 3 3 Determine the future value of an annuity. ObjectiveObjective

21. 8-21 An annuity is a series of equal amounts received or paid over a specified number of equal time periods. Future Value of an Annuity

22. 8-22 If $500 is invested at the end of each year for three years, how much would the investment be worth at the end of three years if the interest earned is 8% per year? Future Value of an Annuity

23. 8-23 Future Value of an Annuity End of Year 1 End of Year 2 End of Year 3 FV at End of Year 3 Invested for 2 years ($500 x 1.08²) $ 583.20 Invested for 1 years ($500 x 1.08¹) 540.00 Invested for 0 years 500.00 Future value of total investment$1,623.20 Total amount invested over 2 years1,500.00 Interest earned over 2 years$ 123.20

24. 8-24 Future Value of an Annuity 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period 1.000 1.0001.0001.0001.0001.0001.0001.0001.000 2.0102.0202.0302.0402.0502.0602.0702.0802.090 3.0303.0603.0913.1223.1533.1843.2153.2463.278 3.246 FVA = Amount invested (A) x Interest factor (IF) FVA = $500 x 3.246 (rounded to three decimal places) FVA = $1,623 (or $1,623.20 if a four-decimal table is used)

25. 8-25 A B C D E A B C D E Value Interest EarnedAmountFV at at Beginning(Column B xInvested atEnd of at Beginning(Column B xInvested atEnd of Year of YearInterest Rate)End of YearYear 10.000.00500.00500.00 2500.0040.00500.001,040.00 31,040.0083.20500.001,623.20 Total 123.201,500.00 Total 123.201,500.00 Interest Table for an Annuity of $500 at the End of Each Year for Three Years at 8% Exhibit 2

26. 8-26 Future Value of an Annuity How much would you need to invest each year to accumulate $1,000 at the end of three years to take a trip to Mexico after you graduate from college? Assume you can earn 6% on your investment.

27. 8-27 Future Value of an Annuity 1.000 1.0001.0001.0001.0001.0001.0001.0001.000 2.0102.0202.0302.0402.0502.0602.0702.0802.090 3.0303.0603.0913.1223.1531.1911.2251.2601.295 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3 0.08 1.000 2.080 3.184 FVA = Amount invested (A) x Interest factor (IF) $1,000 = A x 3.184 (using three decimal places) A= $1,000 ÷ 3.184 A= $314 (or $314.11 if 3.1836 is used)

28. 8-28 Exercise 8-5 Click the button to skip this exercise. If you experience trouble making the button work, type 32 and press “Enter.” Optimism, Inc. anticipates the need for factory expansion four years from today. The firm has determined that it will have the necessary funds for expansion if it puts $400,000 per year into a stock portfolio expected to earn 9% per year. Deposits will be made at the end of the year. ContinuedContinued

29. 8-29 Exercise 8-5 a)How much is the company planning to raise toward factory expansion with this plan? Press “Enter” or left click the mouse for solution. ContinuedContinued FV of an annuity = Amount x Interest Factor = $400,000 x 4.57313 = $1,829,252 9%, 4 years

30. 8-30 Exercise 8-5 b)What amount would the company expect to raise if it could invest $400,000 per year for seven years? FV of an annuity = Amount x Interest Factor = $400,000 x 9.20043 = $3,680,172 9%, 7 years Press “Enter” or left click the mouse for solution. ContinuedContinued

31. 8-31 Exercise 8-5 c)Why is the answer to part b more than twice as large as the answer to part a even though the length of the annuity is less than twice as long? The future value of an annuity grows from the contribution of additional deposits and by the compounding of interest on the existing balances. In short, interest on interest contributes substantially to the annuity’s future value. Press “Enter” or left click the mouse for solution.

32. 8-32 4 4 Determine the present value of a single amount to be received in the future. ObjectiveObjective

33. 8-33 Present Value of a Single Amount A company offered to sell you an investment that pays $3,000 at the end of three years. You want to earn 8% return on your investment. How much would you be willing to pay for the investment?

34. 8-34 Present Value of a Single Amount FV=PV(1+R) t $3,000=PV(1+R)³ PV=$3,000 x 1/(1.08)³ PV=$3,000 ÷ (1.08)³ PV=$2,381.50 $3,000=PV(1.08)³

35. 8-35 Using Excel, the present value of an investment that pays $3,000 at the end of three years at 8% can be calculated by entering =3000*(1/(1.08^3)) in a cell. Present Value of a Single Amount

36. 8-36 The present value of a single amount table also could be used to determine the present value of the $3,000. Present Value of a Single Amount

37. 8-37 0.9900.9800.9710.9620.9520.9430.9350.9260.917 0.9800.9610.9430.9250.9070.8900.8730.8570.842 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 3 0.08 0.926 0.857 PV = FV x IF PV = $3,000 x 0.794 (rounded to three decimal places) PV = $2,381.49 Present Value of a Single Amount 0.794

38. 8-38 Interest Table for a Present Value of $2,381.49 for Three Years at 8% A B C D A B C D Present Value atInterest EarnedValue at End YearBeginning of Year(B x Interest Rate)(B + C) 12,381.49190.522,572.01 22,572.01205.762,777.77 32,777.77222.233,000.00 Total 618.51 Total 618.51 Exhibit 3

39. 8-39 Exercise 8-10 Click the button to skip this exercise. If you experience trouble making the button work, type 41 and press “Enter.” Assume that you received a loan on July 1, 2007. The lender charges annual interest of 6%. On June 30, 2012, you owe the lender $802.93. Assuming that you made no payments for principal or interest on the loan during the five years, how much did you borrow? Press “Enter” or click the left mouse button for solution.

40. 8-40 Exercise 8-10 The present value of $802.93 at 6% for five years is $802.93 x 0.74726 = $600. 6%, 5 years You borrowed $600.

41. 8-41 5 5 Determine the present value of an annuity. ObjectiveObjective

42. 8-42 Present Value of an Annuity Assume that you could purchase an investment that would pay $1,000 at the end of each year for three years, and you expect to earn a return of 8%. How much would you be willing to pay for the investment?

43. 8-43 $ 925.93 = $1,000 ÷ (1.08)$1,000 Present Value of an Annuity 1 Present Value at Beginning of Year 1 End of Yr. 1

44. 8-44 $ 925.93 857.34= $1,000 ÷ (1.08)$1,000 Present Value of an Annuity Present Value at Beginning of Year 1 End of Yr. 2 2

45. 8-45 Present Value of an Annuity Present Value at Beginning of Year 1 End of Yr. 3 3 $ 925.93 857.34 793.83= $1,000 ÷ (1.08)$1,000

46. 8-46 Present Value of an Annuity Present Value at Beginning of Year 1 $3,000.00 Total amount received over three years 2,577.10Present value of total investment $422.90Interest earned over three years $ 925.93 857.34 793.83 $2,577.10 Present value of total investment You would be willing to pay $2,577.10.

47. 8-47 The PV function in Excel can be used to calculate the present value of an annuity. The function can be entered in the pop-up box or directly into the cell. Present Value of an Annuity

48. 8-48 If you purchase an investment that paid $1,000 each year for three years at 8% interest, type =PV(0.08,3,–1000) in a cell and press Enter. Present Value of an Annuity

49. 8-49 Present Value of an Annuity Or, you can use the present value of an annuity table.

50. 8-50 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 3 Present Value of an Annuity 2.577 PVA = FV x IF PVA = $1,000 x 2.577 (table value read to three decimal places) PVA = $2,577 ($2,577.10 if five decimal places used) 0.9900.9810.9710.9620.9520.9430.9350.9260.917 1.9701.9421.9131.8861.8591.8331.8081.7831.759

51. 8-51 A B C D F A B C D F Present Value Interest EarnedTotal AmountValue at at Beginning(Column B xInvestedEnd of at Beginning(Column B xInvestedEnd of Year of YearInterest Rate)(B + C)Year 12,577.10206.172,783.271,783.27 Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8% Exhibit 4 $2,783.27 – $1,000.00 Note: Column E was omitted because of limited space.

52. 8-52 A B C D F A B C D F Present Value Interest EarnedTotal AmountValue at at Beginning(Column B xInvestedEnd of at Beginning(Column B xInvestedEnd of Year of YearInterest Rate)(B + C)Year 12,577.10206.172,783.271,783.27 21,783.27142.661,925.93925.93 Exhibit 4 $1,925.93 – $1,000.00 Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%

53. 8-53 A B C D F A B C D F Present Value Interest EarnedTotal AmountValue at at Beginning(Column B xInvestedEnd of at Beginning(Column B xInvestedEnd of Year of YearInterest Rate)(B + C)Year 12,577.10206.172,783.271,783.27 21,783.27142.661,925.93925.93 3925.9374.071,000.000.00 Total 422.90 Total 422.90 Exhibit 4 Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%

54. 8-54 Exercise 8-13 Click the button to skip this exercise. If you experience trouble making the button work, type 57 and press “Enter.” A wealthy uncle has offered to give you either of two assets: (a) an asset that pays $500 at the end of three years or (b) an asset that pays $100 at the end of each year for five years. Assume that both assets earn a 7% annual rate of return. Which asset should you choose? Press “Enter” or left click the mouse for solution.

55. 8-55 Exercise 8-13 a. $500 x 0.81630 (from Table 3) = $408.15 7%, 3 years b. $100 x 4.10020 (from Table 4) = $410.02 7%, 5 years ContinuedContinued

56. 8-56 Exercise 8-13 The annuity (b) has a slightly higher present value. The alternatives are approximately the same, however. (Note: One consideration may be expected investment opportunities at the end of three years. Since there is little difference between a. and b., a. may be the better choice since the $500 could be reinvested sooner than in b.)

57. 8-57 6 6 Determine investment values and interest expense or revenue for various periods. ObjectiveObjective

58. 8-58 Loan Payments and Amortization You negotiate with a dealer to purchase a car for $5,000, which you arrange to borrow at the bank.

59. 8-59 The bank charges 12% interest on the loan, which is to be repaid in two years in equal monthly payments. Loan Payments and Amortization How much will your payments be each month?

60. 8-60 We are looking for the present value of multiple payments (an annuity), therefore, Table 4 can be used to solve this problem. Loan Payments and Amortization

61. 8-61 0.990100.980390.970870.961540.95238 1.970401.941561.913471.886091.85941 2.940992.883882.828612.775092.72325 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 Period 2421.2433918.9139316.9355415.2469613.79864 3 0.01 0.99010 1.97040 2.94099 0.01 0.99010 1.97040 2.94099 If the annual interest rate is 12 percent, then interest is 1 percent per month. Loan Payments and Amortization 21.24339

62. 8-62 Loan Payments and Amortization 2421.2433918.9139316.9355415.2469613.79864 21.24339 0.990100.980390.970870.961540.95238 1.970401.941561.913471.886091.85941 2.940992.883882.828612.775092.72325 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 Period 3 0.01 0.99010 1.97040 2.94099 0.01 0.99010 1.97040 2.94099 24 21.24339 18.91393 16.93554 15.24696 13.79864 There are 24 monthly periods in two years. 21.24339

63. 8-63 Loan Payments and Amortization PVA = A x IF (Table 4) $5,000= A x 21.24339 A= $5,000 ÷ 21.24339 A= $235.37 2421.2433918.9139316.9355415.2469613.79864 21.24339 0.990100.980390.970870.961540.95238 1.970401.941561.913471.886091.85941 2.940992.883882.828612.775092.72325 123123 Interest Rate 0.01 0.02 0.03 0.04 0.05 Period 3 0.01 0.99010 1.97040 2.94099 0.01 0.99010 1.97040 2.94099 24 21.24339 18.91393 16.93554 15.24696 13.79864 21.24339

64. 8-64 Loan Payments and Amortization Thus, the answer to the question (How much would you pay each month?) is $235.37.

65. 8-65 Enter =PMT(.01,24,5000) in the cell and press Enter. How would you determine the monthly car payment by using the payment function in Excel? Loan Payments and Amortization

66. 8-66 Loan Payments and Amortization How much interest will you pay over the two years? To answer this question, let’s walk through Exhibit 5 (p. 296) from the textbook.

67. 8-67 A B C D F A B C D F Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month 15,000.0050.00235.374,814.63 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 $5,000.00 – ($235.37 – $50.00) Note: Column E was omitted because of limited space.

68. 8-68 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 $4,814.63 – ($235.37 – $48.15) A B C D F A B C D F Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month

69. 8-69 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 Total 648.815,648.81 Total 648.815,648.81 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 34,627.4146.27235.374,438.32 23463,704.64235.37232.97 24232.972.33235.300.00 A B C D F A B C D F Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month

70. 8-70 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 Total 648.815,648.81 Total 648.815,648.81 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 34,627.4146.27235.374,438.32 23463,704.64235.37232.97 24232.972.33235.300.00 A B C D E A B C D E Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month The total interest incurred over the life of the loan is $648.81.

71. 8-71 Loan Payments and Amortization Now let’s determine the transactions that the bank and the borrower would record each month.

72. 8-72 Loan Payments and Amortization The first transaction on April 1 records the amount of the loan. The second transaction, dated April 30, records the amount received from you, the customer, and the amount earned for the first month, $50 ($5,000 x.12 x 1/12).

73. 8-73 Loan Payments and Amortization Journal Journal Date Accounts Debits Credits Apr. 1Notes Receivable5,000.00 2007Cash5,000.00 Apr. 30Cash235.37 2007Notes Receivable185.37 Interest Revenue50.00 Click this button or type “88” and press “Enter” to review the amortization table. Bank’s Books

74. 8-74 Loan Payments and Amortization Bank’s Books Effect on Accounting Equation Effect on Accounting Equation A = L + 4/1Notes Receivable+5,000.00 Cash–5,000.00 4/30Cash235.37 Notes Receivable–185.37 Interest Revenue+50.00 OE CC + RE

75. 8-75 Loan Payments and Amortization Customer’s Books Journal Journal Date Accounts Debits Credits Apr. 1Cash5,000.00 2007Notes Payable5,000.00 Apr. 30Notes Payable185.37 2007Interest Expense50.00 Cash235.37 Click this button or type “89” and press “Enter” to review the amortization table.

76. 8-76 Loan Payments and Amortization Customer’s Books Effect on Accounting Equation Effect on Accounting Equation A = L + 4/1Cash+5,000.00 Notes Payable+5,000.00 4/30Notes Payable–185.37 Interest Expense–50.00 Cash–235.37 OE CC + RE

77. 8-77 Loan Payments and Amortization In the last month of the loan (March 2009), the bank records would reflect that the note has been fully paid by the customer.

78. 8-78 Journal Journal Date Accounts Debits Credits Mar. 31Cash235.30 2009Notes Receivable232.97 Interest Revenue2.33 Loan Payments and Amortization Bank’s Books Click this button or type “90” and press “Enter” to review the amortization table.

79. 8-79 Loan Payments and Amortization Bank’s Books Effect on Accounting Equation Effect on Accounting Equation A = L + 3/31Cash+235.30 Notes Receivable–232.97 Interest Revenue+2.33 OE CC + RE

80. 8-80 Unequal Payments Jill Johnson invested a portion of her salary at the beginning of each year for four years. The amounts she invested in those years were $700, $800, $900, and $1,000, respectively.

81. 8-81 Unequal Payments How much would her investments be worth at the end of four years if she earned 6% per year?

82. 8-82 $ 833.71 $800898.88 $900 954.00 $1,000 1,000.00 $700 Four Years x 1.19102 (6%, 3 periods) Three Years x 1.12360 (6%, 2 periods) Two Years x 1.0600 (6%, 1 period) Unequal Payments x 1.0000 x 1.0000 Total $3,686.59 Year 1 2 3 End of 4

83. 8-83 You can purchase an investment that is expected to pay $200, $300, and $400 at the end of the next three years. You expect to earn 7% interest. How much should you pay for the investment? Unequal Payments

84. 8-84 $200 $186.92One Year x 0.93458 Two Years 262.03 $300 x 0.87344 $400 326.52 Three Years x 0.81630 $775.47Total PV at Beginning of Year Amounts Received at End of Each Year Unequal Payments

85. 8-85 Future and Present Value Concepts Exhibit 6

86. 8-86 T HE E ND C HAPTER 8

87. 8-87

88. 8-88 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 34,627.4146.27235.374,438.32 23463,704.64235.37232.97 24232.972.33235.300.00 A B C D E A B C D E Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month Click this button or type 73 and press “Enter” to return to Slide 73.

89. 8-89 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 34,627.4146.27235.374,438.32 23463,704.64235.37232.97 24232.972.33235.300.00 A B C D E A B C D E Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month Click this button or type 75 and press “Enter” to return to Slide 75.

90. 8-90 Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month Exhibit 5 15,000.0050.00235.374,814.63 24,814.6348.15235.374,627.41 34,627.4146.27235.374,438.32 23463,704.64235.37232.97 24232.972.33235.300.00 A B C D E A B C D E Present Value Interest IncurredValue at at Beginning(Column B xAmountEnd of at Beginning(Column B xAmountEnd of Monthof YearInterest Rate)Paid)Month Click this button or type 78 and press “Enter” to return to Slide 78.