2. Kimmel Accounting, Second Edition
Appendix C
Time Value of Money
Kimmel Accounting, Second Edition

3. Study Objectives Distinguish between simple and compound interest.
Solve for future value of a single amount.
Solve for future value of an annuity.
Identify the variables fundamental to solving present value problems.
Solve for present value of a single amount.
Solve for present value of an annuity.
Compute the present value of notes and bonds.
1. On the topic, “Challenges Facing Financial Accounting,” what did the AICPA Special Committee on Financial Reporting suggest should be included in future financial statements?
Non-financial Measurements (customer satisfaction indexes, backlog information, and reject rates on goods purchases).
Forward-looking Information
Soft Assets (a company’s know-how, market dominance, marketing setup, well-trained employees, and brand image).
Timeliness (no real time financial information)

4. Basic Time Value Concepts
Time Value of Money
In accounting (and finance), the term indicates that a dollar received today is worth more than a dollar promised at some time in the future.

5. Basic Time Value Concepts
Nature of Interest
Payment for the use of money.
Excess cash received or repaid over the amount borrowed (principal).
Variables involved in financing transaction:
Principal (p) - Amount borrowed or invested.
Interest Rate (i) – An annual percentage.
Time (n) - The number of years or portion of a year that the principal is outstanding.

6. Simple Interest FULL YEAR Interest computed on the principal only.
ILLUSTRATION:
On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the annual interest cost.
Principal $20,000
Interest rate x %
FULL YEAR
Annual interest $ 1,400
SO 1 Distinguish between simple and compound interest.

7. Simple Interest PARTIAL YEAR ILLUSTRATION continued:
On March 31, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the interest cost for the year ending December 31, 2007.
Principal $20,000
Interest rate x %
PARTIAL YEAR
Annual interest $ 1,400
Partial year x /12
Interest for 9 months $ 1,050
SO 1 Distinguish between simple and compound interest.

8. Compound Interest Computes interest on the principal and
any interest earned that has not been paid or withdrawn.
Most business situations use compound interest.
SO 1 Distinguish between simple and compound interest.

9. Compound Interest ILLUSTRATION:
On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the total interest cost for all three years, assuming interest is compounded annually.
SO 1 Distinguish between simple and compound interest.

10. Future Value Concepts Future Value of a Single Amount
The value at a future date of a given amount invested assuming compound interest.
FV = p x (1 + i )n
Illustration C-3
Formula for future value
FV = future value of a single amount
p = principal (or present value)
i = interest rate for one period
n = number of periods
SO 2 Solve future value of a single amount.

11. Future Value Concepts Future Value of a Single Amount
The value at a future date of a given amount invested assuming compound interest.
Illustration:
Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?
SO 2 Solve future value of a single amount.

12. Future Value Concepts What table do we use? Present Value $10,0001 2 3 4 5 6
Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?
What table do we use?
SO 2 Solve future value of a single amount.

13. Future Value Concepts What factor do we use? Table 1
SO 2 Solve future value of a single amount.

14. Future Value Concepts Table 1 $10,000 x 1.25971 = $12,597
Present Value
Factor
Future Value
SO 2 Solve future value of a single amount.

15. Future Value Concepts PROOF - Future Value of a Single Sum
Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?
SO 2 Solve future value of a single amount.

16. Future Value Concepts What table do we use? Present Value $10,0001 2 3 4 5 6
Exercise: Steve Allen invested $10,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years?
What table do we use?
SO 2 Solve future value of a single amount.

17. Future Value Concepts What factor do we use? Table 1
6 compounding periods
4% interest per period
SO 2 Solve future value of a single amount.

18. Future Value Concepts Table 1 $10,000 x 1.26532 = $12,653
Present Value
Factor
Future Value
SO 2 Solve future value of a single amount.

19. Future Value Concepts Annuity requires the following:
Periodic payments or receipts of the same amount,
Same-length interval between payments or receipts,
Compounding of interest each interval.
The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound
interest on them.
SO 3 Solve for future value of an annuity.

20. Future Value Concepts Future Value of an Annuity
Rents occur at the end of each period.
No interest during 1st period.
Present Value
Future Value
$20,000
20,000
20,000
20,000
20,000
20,000
20,000
20,000 1 2 3 4 5 6 7 8
SO 3 Solve for future value of an annuity.

21. Future Value Concepts What table do we use? Present Value Future Value
$20,000
20,000
20,000
20,000
20,000
20,000
20,000
20,000 1 2 3 4 5 6 7 8
Exercise: Bayou Inc. will deposit $20,000 in a 12% fund at the end of each year for 8 years beginning December 31, Year 1. What amount will be in the fund immediately after the last deposit?
What table do we use?
SO 3 Solve for future value of an annuity.

22. Future Value Concepts What factor do we use? Table 2
SO 3 Solve for future value of an annuity.

23. Future Value Concepts Table 2 $20,000 x 12.29969 = $245,994 Deposit
Factor
Future Value
SO 3 Solve for future value of an annuity.

24. Present Value Concepts
The present value is the value now of a given amount to be paid or received in the future, assuming compound interest.
Present value variables:
Dollar amount to be received in the future,
Length of time until amount is received, and
Interest rate (the discount rate).
SO 4 Identify the variables fundamental to solving present value problems.

25. Present Value Concepts
Present Value of a Single Amount
PV = FV / (1 + i )n
Illustration C-9
Formula for present value
PV = present value of a single amount FV = future value of a single amount
p = principal (or present value)
i = interest rate for one period
n = number of periods
SO 5 Solve for present value of a single amount.

26. Present Value Concepts
Present Value of a Single Amount
Multiply the present value factor by the future value.
Illustration:
Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually?
SO 5 Solve for present value of a single amount.

27. Present Value Concepts
Future Value $20,000 1 2 3 4 5 6
Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually?
What table do we use?
SO 5 Solve for present value of a single amount.

28. Present Value Concepts
Table 3
What factor do we use?
SO 5 Solve for present value of a single amount.

29. Present Value Concepts
Table 3
$20, x = $12,710
Future Value
Factor
Present Value
SO 5 Solve for present value of a single amount.

30. Present Value Concepts
Future Value $20,000 1 2 3 4 5 6
Exercise: Itzak Perlman needs $20,000 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly?
What table do we use?
SO 5 Solve for present value of a single amount.

31. Present Value Concepts
Table 3
What factor do we use?
SO 5 Solve for present value of a single amount.

32. Present Value Concepts
Table 3
$20, x = $12,463
Future Value
Factor
Present Value
SO 5 Solve for present value of a single amount.

33. Present Value Concepts
Present Value of an Annuity
The value now of a series of future receipts or payments, discounted assuming compound interest.
Present Value
$100,000
100,000
100,000
100,000
100,000
100,000 1 2 3 4 19 20
SO 6 Solve for present value of an annuity.

34. Present Value Concepts
$100,000
100,000
100,000
100,000
100,000
100,000 1 2 3 4 19 20
Jaime Yuen wins $2,000,000 in the state lottery. She will be paid $100,000 at the end of each year for the next 20 years. What is the present value of her winnings? Assume an appropriate interest rate of 8%.
What table do we use?
SO 6 Solve for present value of an annuity.

35. Present Value Concepts
Table 4
What factor do we use?
SO 6 Solve for present value of an annuity.

36. Present Value Concepts
Table 4
$100, x = $981,815
Receipt
Factor
Present Value
SO 6 Solve for present value of an annuity.

37. Present Value Concepts
Present Value of a Long-term Note or Bond
Two Cash Flows:
Periodic interest payments (annuity).
Principal paid at maturity (single-sum).
1,000,000
$70,000
70,000
70,000
70,000
70,000
70,000 1 2 3 4 9 10
SO 7 Compute the present value of notes and bonds.

38. Present Value Concepts
$70,000
70,000
70,000
70,000
70,000
1,070,000 1 2 3 4 9 10
Exercise: Arcadian Inc. issues $1,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds is 8%. What amount will Arcadian receive when it issues the bonds?
SO 7 Compute the present value of notes and bonds.

39. Present Value Concepts
Table 4
PV of Interest
$70,000 x = $469,706
Interest Payment
Factor
Present Value
SO 7 Compute the present value of notes and bonds.

40. Present Value Concepts
Table 3
PV of Principal
$1,000,000 x = $463,190
Principal Payment
Factor
Present Value
SO 7 Compute the present value of notes and bonds.

41. Present Value Concepts
Exercise: Arcadian Inc. issues $1,000,000 of 7% bonds due in 10 years with interest payable at year-end.
Present value of Interest $469,706
Present value of Principal 463,190
Bond current market value $932,896
SO 7 Compute the present value of notes and bonds.

42. Using Financial Calculators
Illustration C-22
Financial calculator keys
PV = present value of a single amount
N = number of periods
I = interest rate per period
PV = present value
PMT = payment
FV = future value
SO 8 Use a financial calculator to solve time value of money problems.

43. Using Financial Calculators
Present Value of a Single Sum
Assume that you want to know the present value of $84,253 to be received in five years, discounted
at 11% compounded annually.
Illustration C-23
Calculator solution for
present value of a single sum
SO 8 Use a financial calculator to solve time value of money problems.

44. Using Financial Calculators
Present Value of an Annuity
Assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12%.
Illustration C-24
Calculator solution for
present value of an annuity
SO 8 Use a financial calculator to solve time value of money problems.

45. Using Financial Calculators
Useful Applications – Auto Loan
The loan has a 9.5% nominal annual interest rate, compounded monthly. The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase.
Illustration C-25
SO 8 Use a financial calculator to solve time value of money problems.

46. Using Financial Calculators
Useful Applications – Mortgage Loan
You decide that the maximum mortgage payment you can afford is $700 per month. The annual interest rate is 8.4%. If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum purchase price you can afford?
Illustration C-26
SO 8 Use a financial calculator to solve time value of money problems.

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