2. Accounting Principles, Ninth Edition
Appendix C
Time Value of Money
Accounting Principles, Ninth Edition

3. Study Objectives Distinguish between simple and compound interest.
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. 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 borrowed or invested.
SO 1 Distinguish between simple and compound interest.

6. Nature of Interest Simple Interest FULL YEAR
Interest computed on the principal only.
Illustration:
On January 2, 2010, assume you borrow $5,000 for 2 years at a simple interest of 12% annually. Calculate the annual interest cost.
Illustration C-1
Interest = p x i x n
FULL YEAR
= $5,000 x x 2
= $1,200
SO 1 Distinguish between simple and compound interest.

7. Nature of Interest 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any interest earned that has not been paid or withdrawn.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.

8. Nature of Interest - Compound Interest
Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another $1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any interest until three years from the date of deposit.
Illustration C-2
Simple versus compound interest
Year 1 $1, x 9%
$ 90.00
$ 1,090.00
Year 2 $1, x 9%
$ 98.10
$ 1,188.10
Year 3 $1, x 9%
$106.93
$ 1,295.03
SO 1 Distinguish between simple and compound interest.

9. Present Value Variables
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 2 Identify the variables fundamental to solving present value problems.

10. Present Value of a Single Amount
Illustration C-3
Formula for present value
Present Value = Future Value / (1 + i )n
p = principal (or present value)
i = interest rate for one period
n = number of periods
SO 3 Solve for present value of a single amount.

11. Present Value of a Single Amount
Illustration: If you want a 10% rate of return, you would compute the present value of $1,000 for one year as follows:
Illustration C-4
SO 3 Solve for present value of a single amount.

12. Present Value of a Single Amount
Illustration C-4
Illustration: If you want a 10% rate of return, you can also compute the present value of $1,000 for one year by using a present value table.
What table do we use?
SO 3 Solve for present value of a single amount.

13. Present Value of a Single Amount
What factor do we use?
$1, x = $909.09
Future Value
Factor
Present Value
SO 3 Solve for present value of a single amount.

14. Present Value of a Single Amount
Illustration C-5
Illustration: If you receive the single amount of $1,000 in two years, discounted at 10%
[PV = $1,000 / 1.102], the present value of your $1,000 is $
What table do we use?
SO 3 Solve for present value of a single amount.

15. Present Value of a Single Amount
What factor do we use?
$1, x = $826.45
Future Value
Factor
Present Value
SO 3 Solve for present value of a single amount.

16. Present Value of a Single Amount
Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now?
$10, x = $7,938.30
Future Value
Factor
Present Value
SO 3 Solve for present value of a single amount.

17. Present Value of a Single Amount
Illustration: Determine the amount you must deposit now in a bond investment, paying 9% interest, in order to accumulate $5,000 for a down payment 4 years from now on a new Toyota Prius.
$5, x = $3,542.15
Future Value
Factor
Present Value
SO 3 Solve for present value of a single amount.

18. 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 4 Solve for present value of an annuity.

19. Present Value of an Annuity
Illustration C-8
Illustration: Assume that you will receive $1,000 cash annually for three years at a time when the discount rate is 10%.
What table do we use?
SO 4 Solve for present value of an annuity.

20. Present Value of an Annuity
What factor do we use?
$1, x = $2,484.85
Future Value
Factor
Present Value
SO 4 Solve for present value of an annuity.

21. Present Value of an Annuity
Illustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of $6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the amount used to capitalize the leased equipment?
$6, x = $21,628.68
SO 4 Solve for present value of an annuity.

22. Time Periods and Discounting
Illustration: When the time frame is less than one year, you need to convert the annual interest rate to the applicable time frame. Assume that the investor received $500 semiannually for three years instead of $1,000 annually when the discount rate was 10%.
$ x = $2,537.85
SO 4 Solve for present value of an annuity.

23. Present Value of a Long-term Note or Bond
Two Cash Flows:
Periodic interest payments (annuity).
Principal paid at maturity (single-sum).
100,000
$5,000
5,000
5,000
5,000
5,000
5,000 1 2 3 4 9 10
SO 5 Compute the present value of notes and bonds.

24. Present Value of a Long-term Note or Bond
Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1. Calculate the present value of the principal and interest payments.
100,000
$5,000
5,000
5,000
5,000
5,000
5,000 1 2 3 4 9 10
SO 5 Compute the present value of notes and bonds.

25. Present Value of a Long-term Note or Bond
PV of Principal
$100,000 x = $61,391
Principal
Factor
Present Value
SO 5 Compute the present value of notes and bonds.

26. Present Value of a Long-term Note or Bond
PV of Interest
$5,000 x = $38,609
Principal
Factor
Present Value
SO 5 Compute the present value of notes and bonds.

27. Present Value of a Long-term Note or Bond
Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January 1 and July 1.
Present value of Principal $61,391
Present value of Interest 38,609
Bond current market value $100,000
SO 5 Compute the present value of notes and bonds.

28. Present Value of a Long-term Note or Bond
Illustration: Now assume that the investor’s required rate of return is 12%, not 10%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate
of 6% (12% / 2) must be used. Calculate the present value of the principal and interest payments.
Illustration C-14
SO 5 Compute the present value of notes and bonds.

29. Present Value of a Long-term Note or Bond
Illustration: Now assume that the investor’s required rate of return is 8%. The future amounts are again $100,000 and $5,000, respectively, but now a discount rate
of 4% (8% / 2) must be used. Calculate the present value of the principal and interest payments.
Illustration C-15
SO 5 Compute the present value of notes and bonds.

30. Copyright
“Copyright © 2009 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.”