1. Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)
Weygandt
, and
Warfield
Chapter 6: The Time Value of Money
Prepared by
Krishnan
Ranganathan
, Angelo State University,
San Angelo, Texas
11/8/2018
Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

2. Basic Time Value Concepts
The time value of money is the relationship between time and money.
According to the present value of money concept, a dollar earned today is worth more than a dollar earned in the future.
This concept is used to choose among alternative investment proposals.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

3. Accounting Applications
The following are some of the applications of time value of money concept:
Valuing non-current receivables and payables
Valuing assets and obligations to be capitalized under long term leases
Measuring post retirement obligations and pension expense
Measuring the value of future cash flows from oil and gas reserves
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

4. Choosing an Interest Rate in Time Value Measurements
The relevance and reliability of accounting information depend on the selection of appropriate interest rates.
The interest rate in turn depends on:
the pure rate of interest (2% - 4%)
credit risk rate of interest (0% - 5%)
expected inflation rate of interest (0% - ?)
The higher the credit risk, the higher the interest rate.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

5. Simple and Compound Interests
Simple interest is determined on the principal only.
principal * interest rate (%) * time
Compound interest is determined on:
the principal, and
any interest earned (and not withdrawn)
Compound interest is the typical computation applied in most time value applications.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

6. Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)
Compound Interest Tables (5) in Time Value of Money Measurements (1 of 2)
Future value of $1: $1 deposited today and left to accumulate for a specified number of periods till a future date
Present value of $1: Amount to be deposited today to yield $1 at some specified future date
Future value of an ordinary annuity of $1: $1 deposited end of each period and left to accumulate until a specified future date.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

7. Compound Interest Tables in Time Value Measurements (2 of 2)
Present value of an ordinary annuity of $1: Amount to be deposited today to permit withdrawals of $1 at the end of each period for a specified number of periods
Present value of an annuity due of $1: Amount to be deposited today to permit withdrawals of $1 at the beginning of each period for a specified number of periods
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

8. Interest Rates and Frequency of Compounding
Interest rate per year: 12%
Frequency of
Compounding
Interest rate per
compounding
Number of compounding
periods
Annual
12%
One (1)
Semi-annual 6%
Two (2)
Quarterly 3%
Four (4)
Monthly 1%
Twelve (12)
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

9. Single Sum Problems - Future Value of a Single Sum
Given:
Amount of deposit today: $50,000
Interest rate 11%
Frequency of compounding: Annual
Number of periods (5 years): 5 periods
Determine the future value of this single sum.
$50,000 * ( ) = $84,253
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

10. Single Sum Problems - Present Value of a Single Sum
Given:
Amount of deposit end of 5 years: $84,253
Interest rate (discount) rate 11%
Frequency of compounding: Annual
Number of periods (5 years): 5 periods
Determine the present value of this single sum.
$84,253 * ( ) = $50,000
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

11. Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)
Annuity Computations
An annuity requires that:
the periodic payments or receipts always be of the same amount,
the interval between such payments or receipts be the same, and
the interest be compounded once each interval
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

12. Annuities - Future Value of an Ordinary Annuity
Given:
Deposit made at the end of each period: $5,000
Compounding: Annual
Number of periods: Five
Interest rate %
Determine the future value of these deposits.
$5,000 * ( ) = $ 31,764.25
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

13. Annuities - Present Value of an Ordinary Annuity
Given:
Rental receipts at the end of each period: $6,000
Compounding: Annual
Number of periods (years): 5
Interest rate %
Determine the present value of these receipts.
$6,000 * ( ) = $ 21,268.68
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

14. Annuities - Future Value of an Annuity Due
Given:
Deposit made at the beginning of each period: $ 800
Compounding: Annual
Number of periods: Eight
Interest rate %
Determine the future value of these deposits.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

15. Annuities - Future Value of an Annuity Due1 2 3 4 5 6 7 8
R = $ $ $ $800 $800 $ $ $800
End of period,
no receipt.
Interest rate = 12% N=
1. Ordinary annuity factor: 8 periods, 12% :
2. Convert to annuity due factor: * 1.12 :
3. Future value of annuity due: $800 * : $ 11,020.52
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

16. Annuities - Present Value of an Annuity Due
Given:
Payment made at the beginning of each period: $ 4.8M
Compounding: Annual
Number of periods: Four
Interest rate %
Determine the present value of these payments.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

17. Annuities - Present Value of an Annuity Due1
R = $4.8M $4.8M $4.8M $4.8M
Interest rate = 11% N= 4 3 2
1. Ordinary annuity factor: 4 periods, 11% :
2. Convert to annuity due factor: * 1.11 :
3. Present value of annuity due: $4.8M * : $ 16,529,856
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

18. Annuities - Future Value of a Deferred Annuity
Given:
Deposit made at end of fourth, fifth, and sixth period: $80,000 each period
No deposits were made at end of the first, second, or the third periods.
Compounding: Annual
Interest rate: 12%
Number of periods: 6
Determine the future value of the deferred annuity.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

19. Annuities - Future Value of a Deferred Annuity1 6 5 3 4 2
R= $ $ $ $80, $80,000 $80,000
Interest rate = 12%
1. Deferred annuity is calculated like ordinary annuity.
2. $80,000 * ( ) = $269,952
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

20. Annuities - Present Value of a Deferred Annuity
Given:
Payments made at end of fifth through tenth period (6 payments): $5,000 each period
No payments were made at end of the first through the fourth periods (deferred periods = 4).
Compounding: Annual
Interest rate: 8%
Number of periods: 10 total
Determine the present value of the deferred annuity.
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

21. Annuities - Present Value of a Deferred Annuity1 2 3 4 5 6 7 8
R = $5, , , ,000 5, ,000
Interest rate = 8% 9 10
Deferred period
1. Present value of an ordinary annuity (10 periods):
2. Less: P.V. of an ordinary annuity (deferred 4 periods):( )
3. Present value of an annuity (6 periods):
4. Present value of the deferred annuity = $5,000 *
= $16,989.75
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Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

22. Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)
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11/8/2018
Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)