1. Electronic Presentation by Douglas Cloud Pepperdine University
Chapter F8
The Time Value of Money
Electronic Presentation by Douglas Cloud Pepperdine University

2. Once you have completed this chapter, you should be able to:
Objectives
1. Define future and present value.
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.
Once you have completed this chapter, you should be able to:

3. Objective 1
Determine future and present value.

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

5. Present Value
The present value of an amount is the value of that amount on a particular date prior to the time the amount is paid or received.

6. Future Value = Present Value (1 + R)
Interest Rate
If $1,000 is invested on January 1, 2004, at 5% interest, what will be the future value (the amount that will accumulate) by December 31, 2004?
Future Value = $1,000(1.05)
Future Value = $1,050

7. Objective 2
Determine the future value of a single amount invested at the present time.

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

9. Compound Interest
If the accumulated amount ($1,050 from Slide 6) is left in the savings account for a second year, until December 31, 2005, how much would the investment be worth at that time?
$1,050(1.05) =
$1,102.50

10. 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 = $629.86

11. Compound Interest
Recall that the future value of an amount is the value of that amount at a particular time in the future.

12. Compound Interest
You can use Excel to determine the future value of $500 that earns 8% interest compounded annually for three years.

13. Insert =500*(1.08^3) in a cell and press Enter.
Compound Interest
Insert =500*(1.08^3) in a cell and press Enter.

14. Compound Interest
The amount shown in the cell represents the future value, which is $

15. Compound Interest
Excel also contains built-in functions for calculating present and future values.

16. Compound Interest
When you see USING EXCEL in the margin of the textbook, follow the instructions to learn how to use the built-in function.

17. Compound Interest
To calculating a future value, a future value of a single amount table, such as the one in the next slide, can be used.

18. Compound Interest Interest Rate Period 1 2 3

19. Compound Interest Interest Rate Period
0.08 1 2 3

20. Compound Interest FV = $500 x 1.260 = $630 (rounded) Interest Rate
Period
0.08 1 2 3
1.260
FV = $500 x = $630 (rounded)

21. Interest Table for an Investment of $500 for Three Years at 8%
Exhibit 1
A B C D
Value at Interest Earned FV at End
Year Beginning of Year (B x Interest Paid) (B + C)
Total

22. Objective 3
Determine the future value of an annuity.

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

24. Future Value of an Annuity
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?

25. Future Value of an Annuity
Interest Rate
Period 1 2 3
3.246
FVA = Amount invested (A) x Interest factor (IF)
FVA = $500 x (rounded to three decimal places)
FVA = $1,623 (rounded)

26. Interest Table for an Annuity of $500 at End of Each Year for Three Years at 8%
Exhibit 2
A B C D E
Value Interest Earned Amount FV at
at Beginning (Column B x Invested at End of
Year of Year Interest Rate) End of Year Year
,040.00
3 1, ,623.20
Total ,500.00

27. 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.

28. Future Value of an Annuity
Interest Rate
Period
0.08 1 2 3
1.000
2.080 3
3.184
FVA = Amount invested (A) x Interest factor (IF)
$1,000 = A x (rounded to three decimal places)
A = $1,000 ÷ 3.184
A = $314 (rounded)

29. Future Value of an Annuity
We can calculate the amount of the payment in Excel using the payment function. Insert =PMT(0.06,3,,1000) in a cell and press Enter.

30. Objective 4
Determine the present value of a single amount to be received in the future.

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

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

33. Present Value of a Single Amount
Interest Rate
Period
0.08 1 2 3
0.926
0.857 3
0.794
PV = FV x IF
PV = $3,000 x (rounded to three decimal places)
PV = $2,382 (rounded)

34. Interest Table for a Present Value of $2,381.49 for Three Years at 8%
Exhibit 3
A B C D
Present Value at Interest Earned Value at End
Year Beginning of Year (B x Interest Rate) (B + C)
1 2, ,572.01
2 2, ,777.77
3 2, * 3,000.00
Total
*Adjusted due to rounding

35. Objective 5
Determine the present value of an annuity.

36. Present Value of an Annuity
Assume that you are considering the purchase of an investment that would pay $1,000 at the end of each year for three years. The investment is expected to earn a return of 8%.
How much would you have to invest now?

37. Present Value of an Annuity
Present Value at
Beginning of Year 1
$ = $1.000 x (1.08)¹ (table value of )

38. Present Value of an Annuity
Present Value at
Beginning of Year 1 $
= $1,000 ÷ (1.08)² (table value of .= )

39. Present Value of an Annuity
Present Value at
Beginning of Year 1 $
857.34
= $1,000 ÷ (1.08)³ (table value of )

40. Present Value of an Annuity
Present Value at
Beginning of Year 1 $
857.34
793.83
$2,577.10
Required investment now

41. Present Value of an Annuity
Present Value at
Beginning of Year 1 $
857.34
793.83
$2,577.10
Required investment now
$3, Total amount received over three years
2, Present value of total investment
$ Interest earned over three years

42. Present Value of an Annuity
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.

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

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

45. Present Value of an Annuity
Interest Rate
Period
0.08 1 2 3
0.926
1.783 3 3
2.577
PVA = FV x IF
PVA = $1,000 x (table value read to three decimal places)
PVA = $2,577 (rounded)

46. Interest Table for an Annuity of $1,000 Each Year for Three Years at 8%
Exhibit 4
A B C D E
Present Value Interest Earned Total Amount Value at
at Beginning (Column B x Invested End of
Year of Year Interest Rate) (B + C) Year
1 2, , ,783.27
$2, – $1,000.00

47. Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%
Exhibit 4
A B C D E
Present Value Interest Earned Total Amount Value at
at Beginning (Column B x Invested End of
Year of Year Interest Rate) (B + C) Year
1 2, , ,783.27
2 1, ,
$1, – $1,000.00

48. Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%
Exhibit 4
A B C D E
Present Value Interest Earned Total Amount Value at
at Beginning (Column B x Invested End of
Year of Year Interest Rate) (B + C) Year
1 2, , ,783.27
2 1, , ,
Total

49. Objective 6
Determine investment values and interest expense or revenue for various periods.

50. Loan Payments and Amortization
You negotiate with a dealer to purchase a car for $5,000, which you arrange to borrow from a local bank.

51. Loan Payments and Amortization
What approach should I use?
The bank charges 12% interest on the loan, which is to be repaid in two years in equal monthly payments.

52. Loan Payments and Amortization
Of course, the present value of an annuity.
How much will the payment be each month?

53. Loan Payments and Amortization
If the annual interest rate is 12 percent, then interest is 1 percent per month.
Interest Rate
Period
0.01
0.01 1 2 3 3

54. Loan Payments and Amortization
If the annual interest rate is 12 percent, then interest is 1 percent per month.
Interest Rate
Period
0.01
0.01 1 2 3 3

55. Loan Payments and Amortization
There are 24 monthly periods in two years.
Interest Rate
Period
0.01
0.01 1 2 3 3

56. Loan Payments and Amortization
PVA = A x IF
$5,000 = A x
A = $5,000 ÷
A = $235.37 1 2 3
Interest Rate
Period
0.01

57. Loan Payments and Amortization
Insert =PMT(.01,24,5000) in the cell and press Enter.
How do I determine the monthly car payment by using the payment function in Excel?

58. Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5
A B C D E
Present Value Interest Incurred Value at
at Beginning (Column B x Amount End of
Month of Year Interest Rate) Paid) Month
1 5, ,814.63
$5, – ($ – $50.00)

59. Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5
A B C D E
Present Value Interest Incurred Value at
at Beginning (Column B x Amount End of
Month of Year Interest Rate) Paid) Month
1 5, ,814.63
2 4, ,627.41
$4, – ($ – $48.15)

60. Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5

61. Loan Payments and Amortization
On April 1, 2004, you borrow the necessary $5,000 from the bank by issuing a note payable.

62. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
4/1 Notes Receivable 5, Cash -5,000
Bank’s Books

63. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
4/1 Cash 5, Notes Payable 5,000
Customer’s Books

64. Loan Payments and Amortization
On April 30, 2004, the first payment of $ is made. Interest of $50 is included ($5,000 x 1%) in the payment.

65. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
4/30 Cash
Notes Receivable –185.37
Interest Revenue
Bank’s Books

66. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
4/30 Notes Payable –185.37
Interest Expense –50.00
Cash –235.37
Customer’s Books

67. Loan Payments and Amortization
In the last month of the loan (March 2006), the bank records would reflect that the note has been fully paid by the customer.

68. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
3/31 Cash
Notes Receivable –232.97
Interest Revenue
Bank’s Books
Click this button to review the amortization table.

69. Loan Payments and Amortization
ASSETS =
LIABILITIES
+ OWNERS’ EQUITY
Cash
Other Assets
Contributed
Capital
Retained
Earnings
Date Accounts
3/31 Cash –235.30
Notes Payable –232.97
Interest Expense –2.33
Customer’s Books

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

71. Unequal Payments $700 Four Years x 1.19102 (6%, 3 periods) $ 833.71$
$800
Three Years
x (6%, 2 periods)
898.88
$900
Two Years
x (6%, 1 period)
954.00
$1,000
One Year x
1,000.00
Total $3,686.59

72. Unequal Payments
How much would she have to invest to receive $200, $300, and $400 at the end of the next three years if she earned 7%?

73. Amounts Received at End of Each Year
Unequal Payments
PV at Beginning of Year
Amounts Received at End of Each Year
$186.92
One Year x
$200
Two Years
262.03 x
$300
326.52
Three Years x
$400
$775.47
Total

74. Future and Present Value Concepts
Exhibit 6

75. CHAPTER F8
THE END

78. Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5
A B C D E
Present Value Interest Incurred Value at
at Beginning (Column B x Amount End of
Month of Year Interest Rate) Paid) Month
1 5, ,814.63
2 4, ,627.41
3 4, ,438.32
23 463,
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