ch06 Accounting and Time Value of Money.ppt

6-2
C H A P T E R
C H A P T E R 6
6
ACCOUNTING AND THE
ACCOUNTING AND THE
TIME VALUE OF MONEY
TIME VALUE OF MONEY
Intermediate Accounting
IFRS Edition
Kieso, Weygandt, and Warfield

6-3
1. Identify accounting topics where the time value of money is relevant.
2. Distinguish between simple and compound interest.
3. Use appropriate compound interest tables.
4. Identify variables fundamental to solving interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due problems.
7. Solve present value of ordinary and annuity due problems.
8. Solve present value problems related to deferred annuities and
bonds.
9. Apply expected cash flows to present value measurement.
Learning Objectives
Learning Objectives

6-4
Future value
Future value
of a single
of a single
sum
sum
Present value
Present value
of a single
of a single
sum
sum
Solving for
Solving for
other
other
unknowns
unknowns
Basic Time
Basic Time
Value
Value
Concepts
Concepts
Single-Sum
Single-Sum
Problems
Problems
Annuities
Annuities
More
More
Complex
Complex
Situations
Situations
Present Value
Present Value
Measurement
Measurement
Applications
Applications
The nature of
The nature of
interest
interest
Simple interest
Simple interest
Compound
Compound
interest
interest
Fundamental
Fundamental
variables
variables
Future value of
Future value of
ordinary
ordinary
annuity
annuity
Future value of
Future value of
annuity due
annuity due
Examples of
Examples of
FV of annuity
FV of annuity
Present value
Present value
of ordinary
of ordinary
annuity
annuity
Present value
Present value
of annuity due
of annuity due
Examples of
Examples of
PV of annuity
PV of annuity
Deferred
Deferred
annuities
annuities
Valuation of
Valuation of
long-term
long-term
bonds
bonds
Effective-
Effective-
interest
interest
method of
method of
bond discount/
bond discount/
premium
premium
amortization
amortization
Choosing an
Choosing an
appropriate
appropriate
interest rate
interest rate
Example of
Example of
expected cash
expected cash
flow
flow
Accounting and the Time Value of Money
Accounting and the Time Value of Money

6-5
A relationship between time and money.
A dollar received today is worth more than a dollar
promised at some time in the future.
Basic Time Value Concepts
Time Value of Money
LO 1 Identify accounting topics where the time value of money is relevant.

6-6
1. Notes
2. Leases
3. Pensions and Other
Postretirement
Benefits
4. Long-Term Assets
Applications to Accounting Topics:
5. Shared-Based
Compensation
6. Business Combinations
7. Disclosures
8. Environmental Liabilities

6-7
Payment for the use of money.
Excess cash received or repaid over the amount
borrowed (principal).
The Nature of Interest

6-8
Interest computed on the principal only.
LO 2 Distinguish between simple and compound interest.
Simple Interest
Illustration: KC borrows $20,000 for 3 years at a rate of 7%
per year. Compute the total interest to be paid for the 3 years.
Many regulatory frameworks require disclosure of interest rates on an annual basis.
Interest = p x i x n
= $20,000 x .07 x 3
= $4,200
Total
Total
Interest
Interest

6-9
Simple Interest
= $20,000 x .07 x 1
= $1,400
Annual
Annual
Interest
Interest
Illustration: KC borrows $20,000 for 3 years at a rate of 7%
per year. Compute the total interest to be paid for the 1 year.

6-10
Simple Interest
Illustration: On March 31, 2011, KC borrows $20,000 for 3
years at a rate of 7% per year. Compute the total interest to be
paid for the year ended Dec. 31, 2011.
= $20,000 x .07 x 9/12
= $1,050
Partial
Partial
Year
Year

6-11 LO 2 Distinguish between simple and compound interest.
Compound Interest
Computes interest on
 principal and
 interest earned that has not been paid or
withdrawn.
Most business situations use compound interest.

6-12
Illustration: Tomalczyk Company deposits $10,000 in the Last National
Bank, where it will earn simple interest of 9% per year. It deposits another
$10,000 in the First State Bank, where it will earn compound interest of 9%
per year compounded annually. In both cases, Tomalczyk will not
withdraw any interest until 3 years from the date of deposit.
Year 1 $10,000.00 x 9% $ 900.00 $ 10,900.00
Year 2 $10,900.00 x 9% $ 981.00 $ 11,881.00
Year 3 $11,881.00 x 9% $1,069.29 $ 12,950.29
Illustration 6-1
Simple vs. Compound Interest

6-13 LO 3 Use appropriate compound interest tables.
LO 3 Use appropriate compound interest tables.
Table 1 - Future Value of 1
Table 2 - Present Value of 1
Table 3 - Future Value of an Ordinary Annuity of 1
Table 4 - Present Value of an Ordinary Annuity of 1
Table 5 - Present Value of an Annuity Due of 1
Compound Interest Tables
Number of Periods = number of years x the number of
compounding periods per year.
Compounding Period Interest Rate = annual rate divided by the
number of compounding periods per year.

How much principal plus interest a dollar accumulates to at the end of
each of five periods, at three different rates of compound interest.
Illustration 6-2
Excerpt from Table 6-1
Compound Interest

Formula to determine the future value factor (FVF) for 1:
Where:
= future value factor for n periods at i interest
n = number of periods
i = rate of interest for a single period
FVFn,i
Compound Interest

Determine the number of periods by multiplying the number
of years involved by the number of compounding periods
per year.
Illustration 6-4
Frequency of Compounding
Compound Interest

9% annual interest compounded daily provides a 9.42%
yield.
Effective Yield for a $10,000 investment.
Illustration 6-5
Comparison of Different
Compounding Periods
Compound Interest

6-18 LO 4 Identify variables fundamental to solving interest problems.
LO 4 Identify variables fundamental to solving interest problems.
Rate of Interest
Number of Time Periods
Future Value
Present Value
Fundamental Variables
Illustration 6-6

6-19 LO 5 Solve future and present value of 1 problems.
LO 5 Solve future and present value of 1 problems.
Single-Sum Problems
Single-Sum Problems
Unknown Future Value
Two Categories
Unknown Present Value
Illustration 6-6

6-20
Value at a future date of a given amount invested, assuming
compound interest.
Single-Sum Problems
Single-Sum Problems
FV = future value
PV = present value (principal or single sum)
= future value factor for n periods at i interest
FVF n,i
Where:
Future Value of a Single Sum

Illustration: Bruegger Co. wants to determine the future
value of $50,000 invested for 5 years compounded annually at
an interest rate of 11%.
= $84,253
Illustration 6-7

What table
do we use?
Alternate
Calculation
Illustration: Bruegger Co. wants to determine the future
value of $50,000 invested for 5 years compounded annually at
an interest rate of 11%.
Illustration 6-7

6-23
What factor do we use?
$50,000
Present Value Factor Future Value
x 1.68506 = $84,253
Future Value of a Single Sum Alternate
Calculation
i=11%
n=5

6-24
BE6-1: Bob Anderson invested $15,000 today in a fund that
earns 8% compounded annually. To what amount will the
investment grow in 3 years?
0 1 2 3 4 5 6
Present Value
$15,000
What table do we use?
Future Value?

$15,000 x 1.25971 = $18,896
i=8%
n=3

Beginning Previous Year-End
Year Balance Rate Interest Balance Balance
1 15,000
$ x 8% = 1,200 + 15,000 = 16,200
$
2 16,200 x 8% = 1,296 + 16,200 = 17,496
3 17,496 x 8% = 1,400 + 17,496 = 18,896
PROOF
earns 8% compounded annually. To what amount will the

6-27
earns 8% compounded semiannually. To what amount will the
0 1 2 3 4 5 6
Present Value $15,000
Future Value?

$15,000 x 1.26532 = $18,980
What factor?
i=4%
n=6

6-29
Value now of a given amount to be paid or received in
the future, assuming compound interest.
Single-Sum Problems
Single-Sum Problems
Present Value of a Single Sum
Where:
FV = future value
PV = present value (principal or single sum)
= present value factor for n periods at i interest
PVF n,i

Illustration: What is the present value of $84,253 to be
received or paid in 5 years discounted at 11% compounded
annually?
= $50,000
Illustration 6-11

6-31
What table
do we use?
Illustration: What is the present value of $84,253 to be
received or paid in 5 years discounted at 11% compounded
annually?
Alternate
Calculation
Illustration 6-11

6-32
$84,253
Future Value Factor Present Value
x .59345 = $50,000
What factor?
i=11%
n=5

6-33
BE6-2: Caroline and Clifford need $25,000 in 4 years.
What amount must they invest today if their investment
earns 12% compounded annually?
0 1 2 3 4 5 6
Present Value?
Future Value
$25,000

6-34
$25,000
x .63552 = $15,888
What factor?
i=12%
n=4

6-35
0 1 2 3 4 5 6
Present Value?
Future Value
$25,000
BE6-2: Caroline and Clifford need $25,000 in 4 years.
What amount must they invest today if their investment
earns 12% compounded quarterly?

6-36
$25,000
x .62317 = $15,579
i=3%
n=16

6-37
Single-Sum Problems
Single-Sum Problems
Solving for Other Unknowns
Example—Computation of the Number of Periods
The Village of Somonauk wants to accumulate $70,000 for the
construction of a veterans monument in the town square. At the
beginning of the current year, the Village deposited $47,811 in a
memorial fund that earns 10% interest compounded annually.
How many years will it take to accumulate $70,000 in the
memorial fund?
Illustration 6-13

6-38
Single-Sum Problems
Single-Sum Problems
Illustration 6-14
Using the future value factor of
1.46410, refer to Table 6-1 and read
down the 10% column to find that
factor in the 4-period row.

6-39
Single-Sum Problems
Single-Sum Problems
Using the present value factor
of .68301, refer to Table 6-2 and
read down the 10% column to find
that factor in the 4-period row.
Illustration 6-14

6-40
Single-Sum Problems
Single-Sum Problems
The Village of Somonauk wants to accumulate $70,000 for the
construction of a veterans monument in the town square. At the
beginning of the current year, the Village deposited $47,811 in a
memorial fund that earns 10% interest compounded annually.
How many years will it take to accumulate $70,000 in the
memorial fund?
Illustration 6-13

6-41
Single-Sum Problems
Single-Sum Problems
Example—Computation of the Interest Rate
Illustration 6-15
Advanced Design, Inc. needs €1,409,870 for basic research 5
years from now. The company currently has €800,000 to invest
for that purpose. At what rate of interest must it invest the
€800,000 to fund basic research projects of €1,409,870, 5 years
from now?

6-42
Single-Sum Problems
Single-Sum Problems
Illustration 6-16
Using the future value factor of
1.76234, refer to Table 6-1 and
read across the 5-period row to
find the factor.

6-43
Single-Sum Problems
Single-Sum Problems
Illustration 6-16
Using the present value factor
of .56743, refer to Table 6-2 and
read across the 5-period row to
find the factor.

6-44
Annuities
Annuities
(1) Periodic payments or receipts (called rents) of the
same amount,
(2) Same-length interval between such rents, and
(3) Compounding of interest once each interval.
Annuity requires:
LO 6 Solve future value of ordinary and annuity due problems.
Ordinary Annuity - rents occur at the end of each period.
Annuity Due - rents occur at the beginning of each period.
Two
Types

6-45 LO 6 Solve future value of ordinary and annuity due problems.
Future Value of an Ordinary Annuity
Rents occur at the end of each period.
No interest during 1st
period.
Annuities
Annuities
0 1
Present Value
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,000 20,000
Future Value

Illustration: Assume that $1 is deposited at the end of
each of 5 years (an ordinary annuity) and earns 12%
interest compounded annually. Following is the
computation of the future value, using the “future value of 1”
table (Table 6-1) for each of the five $1 rents.
Illustration 6-17

6-47
R = periodic rent
FVF-OA = future value factor of an ordinary annuity
i = rate of interest per period
n = number of compounding periods
A formula provides a more efficient way of expressing the
future value of an ordinary annuity of 1.
Where:
n,i

6-48
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next 5 years, earning interest
of 12%?
= $31,764.25
Illustration 6-19

6-49
Illustration: What is the future value of five $5,000 deposits
made at the end of each of the next 5 years, earning interest
of 12%?
What table
do we use?
Alternate
Calculation
Illustration 6-19

6-50
$5,000
Deposits Factor Present Value
x 6.35285 = $31,764
What factor?
i=12%
n=5

6-51
BE6-13: Gomez Inc. will deposit $30,000 in a 12% fund at the
end of each year for 8 years beginning December 31, 2010.
What amount will be in the fund immediately after the last
deposit?
0 1
Present Value
2 3 4 5 6 7 8
$30,000 30,000 30,000 30,000 30,000 30,000 30,000 30,000
Future Value

6-52
Deposit Factor Future Value
$30,000 x 12.29969 = $368,991
i=12%
n=8

Future Value of an Annuity Due
Rents occur at the beginning of each period.
Interest will accumulate during 1st
period.
Annuity Due has one more interest period than Ordinary
Annuity.
Factor = multiply future value of an ordinary annuity factor
by 1 plus the interest rate.
Annuities
Annuities
0 1 2 3 4 5 6 7 8
20,000 20,000 20,000 20,000 20,000 20,000 20,000
$20,000
Future Value

Illustration 6-21
Comparison of Ordinary Annuity with an Annuity Due

6-55
Illustration: Assume that you plan to accumulate $14,000 for a
down payment on a condominium apartment 5 years from now. For
the next 5 years, you earn an annual return of 8% compounded
semiannually. How much should you deposit at the end of each 6-
month period?
R = $1,166.07
Illustration 6-24
Computation of Rent

6-56
Computation of Rent
Illustration 6-24
$14,000
= $1,166.07
12.00611
Alternate
Calculation

6-57
Illustration: Suppose that a company’s goal is to accumulate
$117,332 by making periodic deposits of $20,000 at the end of each
year, which will earn 8% compounded annually while accumulating.
How many deposits must it make?
Illustration 6-25
Computation of Number of Periodic Rents
5.86660

6-58
Illustration: Mr. Goodwrench deposits $2,500 today in a savings
account that earns 9% interest. He plans to deposit $2,500 every
year for a total of 30 years. How much cash will Mr. Goodwrench
accumulate in his retirement savings account, when he retires in 30
years?
Illustration 6-27
Computation of Future Value

6-59
Illustration: Bayou Inc. will deposit $20,000 in a 12% fund at
the beginning of each year for 8 years beginning January 1,
Year 1. What amount will be in the fund at the end of Year 8?
0 1
Present Value
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,000
20,000
Future Value

6-60
Deposit Factor Future Value
12.29969 x 1.12 = 13.775652
i=12%
n=8
$20,000 x 13.775652 = $275,513

6-61 LO 7 Solve present value of ordinary and annuity due problems.
LO 7 Solve present value of ordinary and annuity due problems.
Present Value of an Ordinary Annuity
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the end of the period.
Annuities
Annuities
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . .
100,000

Illustration: Assume that $1 is to be received at the end of
each of 5 periods, as separate amounts, and earns 12%
interest compounded annually.
Illustration 6-28

6-63
A formula provides a more efficient way of expressing the
present value of an ordinary annuity of 1.
Where:

6-64
Illustration: What is the present value of rental receipts of
$6,000 each, to be received at the end of each of the next 5
years when discounted at 12%?
Illustration 6-30

6-65
Illustration: 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. How much has she actually won? Assume an
appropriate interest rate of 8%.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
. . . . .
100,000

$100,000
Receipts Factor Present Value
x 9.81815 = $981,815
i=5%
n=20

Present Value of an Annuity Due
Present value of a series of equal amounts to be
withdrawn or received at equal intervals.
Periodic rents occur at the beginning of the period.
Annuities
Annuities
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000
100,000
. . . . .
100,000

6-68
Illustration 6-31
Comparison of Ordinary Annuity with an Annuity Due

6-69
Illustration: Space Odyssey, Inc., rents a communications
satellite for 4 years with annual rental payments of $4.8 million
to be made at the beginning of each year. If the relevant
annual interest rate is 11%, what is the present value of the
rental obligations?
Illustration 6-33

6-70
Illustration: Jaime Yuen wins $2,000,000 in the state lottery.
She will be paid $100,000 at the beginning of each year for the
next 20 years. How much has she actually won? Assume an
appropriate interest rate of 8%.
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000
100,000
. . . . .
100,000

$100,000
Receipts Factor Present Value
x 10.60360 = $1,060,360
i=8%
n=20

6-72
Illustration: Assume you receive a statement from MasterCard with
a balance due of $528.77. You may pay it off in 12 equal monthly
payments of $50 each, with the first payment due one month from
now. What rate of interest would you be paying?
Computation of the Interest Rate
Referring to Table 6-4 and reading across the 12-period row, you find 10.57534 in
the 2% column. Since 2% is a monthly rate, the nominal annual rate of interest is
24% (12 x 2%). The effective annual rate is 26.82413% [(1 + .02) - 1].
12

6-73 LO 8 Solve present value problems related to deferred annuities and bonds.
LO 8 Solve present value problems related to deferred annuities and bonds.
Rents begin after a specified number of periods.
Future Value - Calculation same as the future value of an
annuity not deferred.
Present Value - Must recognize the interest that accrues
during the deferral period.
More Complex Situations
0 1 2 3 4 19 20
100,000 100,000 100,000
. . . . .
Future Value
Present Value
Deferred Annuities

Two Cash Flows:
 Periodic interest payments (annuity).
 Principal paid at maturity (single-sum).
0 1 2 3 4 9 10
140,000 140,000 140,000
$140,000
. . . . .
140,000 140,000
2,000,000
Valuation of Long-Term Bonds

6-75
BE6-15: Wong Inc. issues HK$2,000,000 of 7% bonds due in 10
years with interest payable at year-end. The current market rate
of interest for bonds of similar risk is 8%. What amount will Wong
receive when it issues the bonds?
0 1
Present Value
2 3 4 9 10
140,000 140,000 140,000
$140,000
. . . . .
140,000
2,140,000

$140,000 x 6.71008 = $939,411
Interest Payment Factor Present Value
PV of Interest
i=8%
n=10

$2,000,000 x .46319 = $926,380
Principal Factor Present Value
PV of Principal
i=8%
n=10

6-78
BE6-15: Wong Inc. issues $2,000,000 of 7% bonds due in 10
years with interest payable at year-end.
Present value of Interest $939,411
Present value of Principal 926,380
Bond current market value $1,865,791
Account Title Debit Credit
Cash 1,865,791
Bonds payable 1,865,791
Date

6-79
Cash Bond Carrying
Interest Interest Discount Value
Date Paid Expense Amortization of Bonds
1/1/10 1,865,791
12/31/10 140,000 149,263 9,263 1,875,054
12/31/11 140,000 150,004 10,004 1,885,059
12/31/12 140,000 150,805 10,805 1,895,863
12/31/13 140,000 151,669 11,669 1,907,532
12/31/14 140,000 152,603 12,603 1,920,135
12/31/15 140,000 153,611 13,611 1,933,746
12/31/16 140,000 154,700 14,700 1,948,445
12/31/17 140,000 155,876 15,876 1,964,321
12/31/18 140,000 157,146 17,146 1,981,467
12/31/19 140,000 158,533 * 18,533 2,000,000
* rounding
Schedule of Bond Discount Amortization
10-Year, 7% Bonds Sold to Yield 8%
BE6-15:

6-80
International Accounting Standard No. 36 introduces
an expected cash flow approach that uses a range of cash
flows and incorporates the probabilities of those cash flows.
Choosing an Appropriate Interest Rate
Three Components of Interest:
Pure Rate
Expected Inflation Rate
Credit Risk Rate
LO 9 Apply expected cash flows to present value measurement.
Present Value Measurement
Risk-free rate of
return. IASB states a
company should
discount expected
cash flows by the risk-
free rate of return.

6-81
E6-21: Angela Contreras is trying to determine the amount
to set aside so that she will have enough money on hand in 2 years to
overhaul the engine on her vintage used car. While there is some
uncertainty about the cost of engine overhauls in 2 years, by conducting
some research online, Angela has developed the following estimates.
Instructions: How much should Angela Contreras deposit today in an
account earning 6%, compounded annually, so that she will have enough
money on hand in 2 years to pay for the overhaul?

6-82 LO 9 Apply expected cash flows to present value measurement.
Instructions: How much should Angela Contreras deposit today in an
account earning 6%, compounded annually, so that she will have enough
money on hand in 2 years to pay for the overhaul?

6-83
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ch06 Accounting and Time Value of Money.ppt

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