Intermediate Power Point (6)

8/7/2019 Intermediate Power Point (6)

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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 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.


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.


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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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?


Future Value?

LO 5 Solve futureand present valueof 1 problems.LO 5 Solve futureand present valueof 1 problems.


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Chapter6-19


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



Future Value?



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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?



Future Value$20,000



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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?


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


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?



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?


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


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


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.


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

Copyright 2006 John Wiley & Sons, Inc.All rights reserved.Reproduction or translation of this work beyond that permittedin Section 117 of the 1976 United States Copyright Act withoutthe express written permission of the copyright owner isunlawful. Request for further information should be addressed

to the Permissions Department, John Wiley & Sons, Inc. Thepurchaser may make back-up copies for his/her own use onlyand not for distribution or resale. The Publisher assumes noresponsibility for errors, omissions, or damages, caused by theuse of these programs or from the use of the informationcontained herein.

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