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Chapter6-1
Accounting and theAccounting and theTime Value of MoneyTime Value of Money
ChapterChapter66
Intermediate Accounting12th Edition
Kieso, Weygandt, and Warfield
Prepared by Coby Harmon, University of California, Santa Barbara
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Chapter6-2
1.1. Identify accounting topics where the time value of moneyIdentify accounting topics where the time value of moneyis relevant.is relevant.
2.2. Distinguish between simple and compound interest.Distinguish between simple and compound interest.
3.3. Use appropriate compound interest tables.Use appropriate compound interest tables.
4.4. Identify variables fundamental to solving interestIdentify variables fundamental to solving interestproblems.problems.
5.5. Solve future and present value of 1 problems.Solve future and present value of 1 problems.
6.6. Solve future value of ordinary and annuity due problems.Solve future value of ordinary and annuity due problems.
7.7. Solve present value of ordinary and annuity due problems.Solve present value of ordinary and annuity due problems.8.8. Solve present value problems related to deferredSolve present value problems related to deferred
annuities and bonds.annuities and bonds.
9.9. Apply expected cash flows to present value measurement.Apply expected cash flows to present value measurement.
Learning ObjectivesLearning Objectives
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Chapter6-3
Accounting and the Time Value of MoneyAccounting and the Time Value of Money
Future valueFuture value
of a singleof a single
sumsum
Present valuePresent value
of a singleof a single
sumsum
Solving forSolving for
otherother
unknownsunknowns
Basic TimeBasic Time
ValueValue
ConceptsConcepts
SingleSingle--SumSum
ProblemsProblemsAnnuitiesAnnuities
MoreMore
ComplexComplex
SituationsSituations
Present ValuePresent Value
MeasurementMeasurement
ApplicationsApplications
The nature ofThe nature of
interestinterest
SimpleSimple
interestinterest
CompoundCompoundinterestinterest
FundamentalFundamental
variablesvariables
Future valueFuture value
of ordinaryof ordinaryannuityannuity
Future valueFuture valueof annuity dueof annuity due
Examples ofExamples of
FV of annuityFV of annuityPresent valuePresent value
of ordinaryof ordinary
annuityannuity
Present valuePresent value
of annuity dueof annuity due
Examples ofExamples of
PV of annuityPV of annuity
DeferredDeferred
annuitiesannuities
Valuation ofValuation of
longlong--termterm
bondsbonds
EffectiveEffective--
interestinterest
method ofmethod of
bondbond
discount/discount/
premiumpremium
amortizationamortization
ExpectedExpected
cash flowcash flow
illustrationillustration
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Chapter6-4
In accounting (and finance), the term indicatesthat a dollar received today is worth more than a
dollar promised at some time in the future.
Basic Time Value ConceptsBasic Time Value Concepts
Time Value of Money
LO 1 Identify accounting topics where the time value of money is relevant.LO 1 Identify accounting topics where the time value of money is relevant.
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Chapter6-5
1. Notes
2. Leases
3. Pensions and OtherPostretirementBenefits
4. Long-Term Assets
Applications toAccounting Topics:
Basic Time Value ConceptsBasic Time Value Concepts
5. Sinking Funds
6. Business Combinations
7. Disclosures
8. Installment Contracts
LO 1 Identifyaccounting topics where the time valueof money is relevant.LO 1 Identifyaccounting topics where the time valueof money is relevant.
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Chapter6-6
Payment for the use of money.
Excess cash received or repaid over the amount
borrowed (principal).
Variables involved in financing transaction:
1. Principal- Amount borrowed or invested.
2. Interest Rate - A percentage.
3. Time - The number of years or portion of a yearthat the principal is outstanding.
Natureof Interest
Basic TimeValue ConceptsBasic TimeValue Concepts
LO1 Identifyaccounting topics where the timevalueof money is relevant.LO1 Identifyaccounting topics where the timevalueof money is relevant.
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Chapter6-7
Interest computed on the principal only.
LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.
Simple InterestSimple Interest
ILLUSTRATION:
On January2
,2007
, Tomalczyk borrows $20
,000
for3
years at a rate of 7% per year. Calculate the annualinterest cost.
Principal $20,000
Interest rate x
7%
Annual interest $ 1,400
Federal law requires the disclosure of interest rates on an annual basisin all contracts.
FULL YEARFULL YEAR
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Chapter6-8 LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.
Simple InterestSimple Interest
ILLUSTRATION continued:
On March 31, 2007, Tomalczyk borrows $20,000 for 3years at a rate of 7% per year. Calculate the interestcost for the year ending December 31, 2007.
Principal $20,000Interest rate x 7%Annual interest $ 1,400
Partial year x 9/12
Interest for 9 months $ 1,050
PARTIALPARTIAL
YEARYEAR
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Chapter6-9
Computes interest on
the principal and
on interest earned to date (assuming interest
is left on deposit).
Compound interest is the typical interestcomputation applied in business situations.
LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.
Compound InterestCompound Interest
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Chapter6-10 LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.
ILLUSTRATION:
On January 2, 2007, Tomalczyk borrows $20,000 for 3years at a rate of 7% per year. Calculate the totalinterest cost for all three years, assuming interest iscompounded annually.
Compound InterestCompound Interest
Compound Interest Accumulated
Date Calculation Interest alance
Jan. 2007 20,000$
2007 $20,000 x 7% 1,400$ 21,400
2008 $21,400 x 7% 1,498 22,898
2009 $22,898 x 7% 1,603 24,501
4,501$
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Chapter6-11 LO 3 Use appropriate compound interest tables.LO 3 Use appropriate compound interest tables.
Compound Interest TablesCompound Interest Tables
Table1 - Future Value of 1
Table 2 - Present Value of 1
Table3 - Future Value of an Ordinary Annuity of 1Table 4 - Present Value of an Ordinary Annuity of 1
Table 5 - Present Value of an Annuity Due of 1
Five Tables in Chapter 6
Number of Periods = number of years x the number ofcompounding periods per year.
Compounding Period Interest Rate = annual rate divided bythe number of compounding periods per year.
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Chapter6-12 LO 3 Use appropriate compound interest tables.LO 3 Use appropriate compound interest tables.
Compound InterestCompound Interest
Compounding can substantially affect the rate ofreturn. A9% annual interest compounded dailyprovides a 9.42% yield.
How compounding affects Effective Yield for a $10,000 investment.
Illustration 6Illustration 6--55
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Chapter6-13 LO 4 Identify variables fundamental to solving interest problems.LO 4 Identify variables fundamental to solving interest problems.
Compound InterestCompound Interest
Rate of Interest
Number of Time Periods
Present Value
Future Value
Variables Fundamental to Compound Interest
Illustration 6Illustration 6--66
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Chapter6-14 LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.
SingleSingle--Sum ProblemsSum Problems
Unknown FutureValue
Generally Classified into Two Categories
Unknown PresentValue
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Chapter6-15 LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.
SingleSingle--Sum ProblemsSum Problems
FutureValue of a Single Sum
Multiply the future value factor by its presentvalue (principal).
Illustration:
BE6-1 Steve Allen invested $10,000 today in afund that earns 8% compounded annually. To what
amount will the investment grow in 3 years?
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Chapter6-16
BE6-1 Steve Allen invested $10,000 today in a fundthat earns 8% compounded annually. To what amount
will the investment grow in3
years?
0 1 2 3 4 5 6
Present Value$10,000
What tabledo we use?
SingleSingle--Sum ProblemsSum Problems
Future Value?
LO 5 Solve futureand present valueof 1 problems.LO 5 Solve futureand present valueof 1 problems.
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Chapter6-19
SingleSingle--Sum ProblemsSum Problems
LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.
Be rev Year-E
Year Ba a e ate I tere t Ba a e Ba a e
1 1 ,$ = + 1 , = 1 ,$
1 , = 6 + 1 , = 11,66
11,66 = 9 + 11,66 = 1 , 9
PROOF - FutureValue of a Single Sum
BE6-1 Steve Allen invested $10,000 today in a fundthat earns 8% compounded annually. To what amountwill the investment grow in 3 years?
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Chapter6-20
BE6-1 Steve Allen invested $10,000 today in a fundthat earns 8% compounded semiannually. To what
amount will the investment grow in3
years?
0 1 2 3 4 5 6
Present Value$10,000
What tabledo we use?
SingleSingle--Sum ProblemsSum Problems
Future Value?
LO 5 Solve futureand present valueof 1 problems.LO 5 Solve futureand present valueof 1 problems.
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Chapter6-23 LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.
SingleSingle--SumProblemsSumProblems
PresentValue of a Single Sum
Multiply the present value factor by the futurevalue.
Illustration:
BE6-2 Itzak Perlman needs $20,000 in 4 years.What amount must he invest today if his investment
earns 12% compounded annually?
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Chapter6-24
BE6-2 Itzak Perlman needs $20,000 in 4 years. Whatamount must he invest today if his investment earns12%
compounded annually?
0 1 2 3 4 5 6
Present Value?
What tabledo we use?
SingleSingle--SumProblemsSumProblems
Future Value$20,000
LO 5 Solve futureand present valueof 1 problems.LO 5 Solve futureand present valueof 1 problems.
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Chapter6-25
er
t ate
er 6 2
2 2 56 5 26 5
5 2 5 6 6 552
6 6 6 56 5 66
6 62 5 2 665
Ta le 6Ta le 6--22
Whatfactor do we use?
SingleSingle--SumProblemsSumProblems
LO 5 Solvefutureand present valueof 1 problems.LO 5 Solvefutureand present valueof 1 problems.
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Chapter6-26
er
t ate
er 6 2
2 2 6 26
2 6 6 2
6 6 6 6 66
6 62 2 66
Ta le 6Ta le 6--22
SingleSingle--SumProblemsSumProblems
LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.
$20,000 x .63552 = $12,710
FutureValue Fa ctor PresentValue
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Chapter6-27
BE6-2 Itzak Perlman needs $20,000 in 4 years. Whatamount must he invest today if his investment earns12%
compounded quarterly?
0 1 2 3 4 5 6
Present Value?
What tabledo we use?
SingleSingle--SumProblemsSumProblems
Future Value$20,000
LO5 Solve futureand present valueof 1 problems.LO5 Solve futureand present valueof 1 problems.
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Chapter6-28
er
t ate
er 6 2
888 8 8 2 8 6 2
8 8 6 62 8 88
2 8 62 6 6 2 668
6 62 6 2 8 6 2
Ta le 6Ta le 6--22
Whatfactor do we use?
SingleSingle--SumProblemsSumProblems
LO5 Solvefutureand present valueof 1 problems.LO5 Solvefutureand present valueof 1 problems.
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Chapter6-29
er
t ate
er 6 9 2
9 92 9 6 2
9 69 62
2 62 6 969 2 66
6 62 9 9 6 2 6 2
Ta le 6Ta le 6--22
SingleSingle--SumProblemsSumProblems
LO5 Solve future and present value of 1 problems.LO5 Solve future and present value of 1 problems.
$20,000 x .62317 = $12,463
FutureValue Fa ctor PresentValue
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Chapter
6-30
AnnuitiesAnnuities
(1) Periodic payments or receipts (calledrents) of the same amount,
(2) The same-length interval between suchrents, and
(3) Compounding of interest once eachinterval.
Annuity requires thefollowing:
LO 6 Solvefuture valueofordinary and annuity due problems.LO 6 Solvefuture valueofordinary 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
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Chapter
6-31 LO 6 Solve future value of ordinary and annuity dueproblems.LO 6 Solve future value of ordinary and annuity dueproblems.
FutureValue of an OrdinaryAnnuity
Rents occur at the end of each period.
No interest during 1st period.
AnnuitiesAnnuities
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
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Chapter
6-32
BE6-13 Bayou Inc. will deposit $20,000 in a 12% fundat the end of each year for 8 years beginningDecember 31, Year 1. What amount will be in the fundimmediately after the last deposit?
0 1
Present Value
What tabledowe use?
Future Valueofan Ordinary AnnuityFuture Valueofan Ordinary Annuity
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
LO 6 Solve future value of ordinary and annuity dueproblems.LO 6 Solve future value of ordinary and annuity dueproblems.
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Chapter
6-35 LO 6 Solve future value of ordinary and annuity dueproblems.LO 6 Solve future value of ordinary and annuity dueproblems.
FutureValue of anAnnuity DueRents occur at the beginning of each period.
Interest will accumulate during 1st period.
Annuity Due has one more interest period thanOrdinary Annuity.
Factor = multiply future value of an ordinaryannuity factor by 1 plus the interest rate.
AnnuitiesAnnuities
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
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Chapter
6-36
Bayou Inc. will deposit $20,000 in a 12% fund at thebeginning 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
What tabledowe use?
Future Valueofan Annuity DueFuture Valueofan Annuity Due
2 3 4 5 6 7 8
$20,000 20,000 20,000 20,000 20,000 20,000 20,00020,000
Future Value
LO 6 Solve future value of ordinary and annuity dueproblems.LO 6 Solve future value of ordinary and annuity dueproblems.
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Chapter
6-39 LO 7 Solvepresent value of ordinary and annuity dueproblems.LO 7 Solvepresent value of ordinary and annuity dueproblems.
PresentValue of an OrdinaryAnnuity
Present value of a series of equal amounts to bewithdrawn or received at equal intervals.
Periodic rents occur at the end of the period.
Present Value of an OrdinaryAnnuityPresent Value of an OrdinaryAnnuity
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000. . . . .
100,000
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Chapter
6-40
Jaime Yuen wins $2,000,000 in the state lottery. Shewill be paid $100,000 at the end of each year for thenext 20 years. How much has she actually won?
Assume an appropriate interest rate of 8%.
0 1
Present Value
What tabledowe use?
2 3 4 19 20
$100,000 100,000 100,000 100,000 100,000
Present Valueofan Ordinary AnnuityPresent Valueofan Ordinary Annuity
. . . . .
LO 7 Solvepresent value of ordinary and annuity dueproblems.LO 7 Solvepresent value of ordinary and annuity dueproblems.
100,000
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Chapter
6-43 LO 7 Solvepresent value of ordinary and annuity dueproblems.LO 7 Solvepresent value of ordinary and annuity dueproblems.
PresentValue of anAnnuityDue
Present value of a series of equal amounts to bewithdrawn or received at equal intervals.
Periodic rents occur at the beginning of the period.
Present Value of anAnnuity DuePresent Value of anAnnuity Due
0 1
Present Value
2 3 4 19 20
$100,000 100,000 100,000 100,000100,000
. . . . .
100,000
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Chapter
6-44
Jaime Yuen wins $2,000,000 in the state lottery. Shewill be paid $100,000 at the beginning of each year forthe next 20 years. How much has she actually won?
Assume an appropriate interest rate of 8%.
0 1
Present Value
What tabledowe use?
2 3 4 19 20
$100,000 100,000 100,000 100,000100,000
. . . . .
LO 7 Solvepresent value of ordinary and annuity dueproblems.LO 7 Solvepresent value of ordinary and annuity dueproblems.
100,000
Present Value of an Annuity DuePresent Value of an Annuity Due
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Chapter
6-47 LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.
Rents begin after a specified number of periods.
FutureValue - Calculation same as the futurevalue of an annuity not deferred.
PresentValue - Must recognize the interest thataccrues during the deferral period.
DeferredAnnuitiesDeferredAnnuities
0 1 2 3 4 19 20
100,000 100,000 100,000
. . . . .
Future ValuePresent Value
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Chapter
6-48 LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.
Two Cash Flows:
Periodic interest payments (annuity).
Principal paid at maturity (single-sum).
Bonds current market value is the combined presentvalues of the both cash flows.
Valuation ofLongValuation ofLong--TermBondsTermBonds
0 1 2 3 4 9 10
70,000 70,000 70,000$70,000
. . . . .
70,000 70,000
1,000,000
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Chapter
6-49
BE6-15 Arcadian Inc. issues $1,000,000 of 7% bondsdue in 10 years with interest payable at year-end. The
current market rate of interest for bonds is 8%. Whatamount will Arcadian receive when it issues the bonds?
0 1
Present Value
2 3 4 9 10
70,000 70,000 70,000$70,000
. . . . .
70,000
Valuation ofLongValuation ofLong--TermBondsTermBonds
1,070,000
LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.LO 8 Solvepresent valueproblemsrelated to deferred annuities and bonds.
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Chapter
6-52
BE6-15 Arcadian Inc. issues $1,000,000 of 7% bondsdue in 10 years with interest payable at year-end.
Valuation ofLongValuation ofLong--TermBondsTermBonds
LO8 Solvepresent valueproblemsrelated to deferred annuities and bonds.LO8 Solvepresent valueproblemsrelated to deferred annuities and bonds.
Present value of Interest $469,706
Present value of Principal 463,190Bond current market value $932,896
ount Title ebit reditCash 932,896
Discount on Bonds 67,104
Bonds payable 1,000,000
ate
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Chapter
6 54
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