Kế toán, kiểm toán - Chương 06: Accounting and the time value of money

C H A P T E R 6ACCOUNTING AND THE TIME VALUE OF MONEYIntermediate Accounting13th EditionKieso, Weygandt, and Warfield Identify accounting topics where the time value of money is relevant.Distinguish between simple and compound interest.Use appropriate compound interest tables.Identify variables fundamental to solving interest problems.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.Solve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities and bonds.Apply expected cash flows to present value measurement.Learning ObjectivesFuture value of a single sumPresent value of a single sumSolving for other unknownsBasic Time Value ConceptsSingle-Sum ProblemsAnnuitiesMore Complex SituationsPresent Value MeasurementApplicationsThe nature of interestSimple interestCompound interestFundamental variablesFuture value of ordinary annuityFuture value of annuity dueExamples of FV of annuityPresent value of ordinary annuityPresent value of annuity dueExamples of PV of annuityDeferred annuitiesValuation of long-term bondsEffective-interest method of bond discount/ premium amortizationChoosing an appropriate interest rateExpected cash flow illustrationAccounting and the Time Value of MoneyIn accounting (and finance), the phrase time value of money indicates a relationship between time and money—that a dollar received today is worth more than a dollar promised at some time in the future. Why?Basic Time Value ConceptsTime Value of MoneyLO 1 Identify accounting topics where the time value of money is relevant.Notes Leases Pensions and Other Postretirement Benefits Long-Term AssetsApplications to Accounting Topics:Basic Time Value ConceptsSinking FundsBusiness CombinationsDisclosuresInstallment ContractsLO 1 Identify accounting topics where the time value of money is relevant.Payment for the use of money. Excess cash received or repaid over the amount borrowed (principal).Variables involved in financing transaction:Principal - Amount borrowed or invested.Interest Rate - A percentage. Time - The number of years or portion of a year that the principal is outstanding.Nature of InterestBasic Time Value ConceptsLO 1 Identify accounting topics where the time value of money is relevant.Interest computed on the principal only. LO 2 Distinguish between simple and compound interest.Basic Time Value ConceptsSimple InterestIllustration: 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.Federal law requires the disclosure of interest rates on an annual basis in all contracts.Interest = p x i x n = $20,000 x .07 x 3= $4,200Total InterestInterest computed on the principal only. LO 2 Distinguish between simple and compound interest.Basic Time Value ConceptsSimple InterestIllustration: 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.Interest = p x i x n = $20,000 x .07 x 1= $1,400Annual InterestInterest computed on the principal only. LO 2 Distinguish between simple and compound interest.Basic Time Value ConceptsSimple InterestIllustration: 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.Interest = p x i x n = $20,000 x .07 x 9/12= $1,050Partial YearLO 2 Distinguish between simple and compound interest.Basic Time Value ConceptsCompound InterestComputes interest onthe principal andany interest earned that has not been paid or withdrawn.Most business situations use compound interest.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, Vasquez will not withdraw any interest until 3 years from the date of deposit.Year 1 $10,000.00 x 9%$ 900.00$ 10,900.00Year 2 $10,900.00 x 9%$ 981.00$ 11,881.00Year 3 $11,881.00 x 9%$1,069.29$ 12,950.29Illustration 6-1Simple versus compound interestLO 2 Distinguish between simple and compound interest.Basic Time Value ConceptsLO 3 Use appropriate compound interest tables.Table 1 - Future Value of 1Table 2 - Present Value of 1Table 3 - Future Value of an Ordinary Annuity of 1Table 4 - Present Value of an Ordinary Annuity of 1Table 5 - Present Value of an Annuity Due of 1Compound Interest TablesNumber 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.Basic Time Value ConceptsLO 3 Use appropriate compound interest tables.How much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of compound interest.Compound InterestBasic Time Value ConceptsIllustration 6-2LO 3 Use appropriate compound interest tables.Compound InterestBasic Time Value ConceptsFormula 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 periodFVFn,iLO 3 Use appropriate compound interest tables.Compound InterestBasic Time Value ConceptsDetermine the number of periods by multiplying the number of years involved by the number of compounding periods per year.Illustration 6-4LO 3 Use appropriate compound interest tables.A 9% annual interest compounded daily provides a 9.42% yield.Effective Yield for a $10,000 investment.Illustration 6-5Compound InterestBasic Time Value ConceptsLO 4 Identify variables fundamental to solving interest problems.Rate of InterestNumber of Time PeriodsPresent ValueFuture ValueFundamental Variables to Compound InterestIllustration 6-6Basic Time Value ConceptsLO 5 Solve future and present value of 1 problems.Single-Sum ProblemsUnknown Future ValueTwo CategoriesUnknown Present ValueThe value at a future date of a given amount invested, assuming compound interest.LO 5 Solve future and present value of 1 problems.Single-Sum ProblemsFV = future valuePV = present value (principal or single sum) = future value factor for n periods at i interestFVFn,iWhere:Future Value of a Single SumLO 5 Solve future and present value of 1 problems.Future Value of a Single SumIllustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 11%.= $84,253LO 5 Solve future and present value of 1 problems.Future Value of a Single SumIllustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 11%.What table do we use?Alternate CalculationWhat factor do we use?$50,000Present ValueFactorFuture Valuex 1.68506= $84,253Future Value of a Single SumAlternate Calculationi=11%n=5LO 5 Solve future and present value of 1 problems.BE6-1: Chris Spear invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?0123456Present Value $15,000 What table do we use?Future Value?LO 5 Solve future and present value of 1 problems.Future Value of a Single SumLO 5 Solve future and present value of 1 problems.Present ValueFactorFuture Value$15,000x 1.25971 = $18,896Future Value of a Single Sumi=8%n=3LO 5 Solve future and present value of 1 problems.PROOFBE6-1: Chris Spear invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?Future Value of a Single SumBE6-1: Chris Spear invested $15,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years?0123456Present Value $15,000 What table do we use?Future Value?LO 5 Solve future and present value of 1 problems.Future Value of a Single SumLO 5 Solve future and present value of 1 problems.Present ValueFactorFuture Value$15,000x 1.26532 = $18,980Future Value of a Single SumWhat factor?i=4%n=6The value now of a given amount to be paid or received in the future, assuming compound interest. Single-Sum ProblemsPresent Value of a Single SumLO 5 Solve future and present value of 1 problems.Where:FV = future valuePV = present value (principal or single sum) = present value factor for n periods at i interestPVFn,iLO 5 Solve future and present value of 1 problems.Present Value of a Single SumIllustration: What is the present value of $84,253 to be received or paid in 5 years discounted at 11% compounded annually? = $50,000Present Value of a Single SumLO 5 Solve future and present value of 1 problems.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$84,253Future ValueFactorPresent Valuex .59345= $50,000Present Value of a Single SumWhat factor?i=11%n=5LO 5 Solve future and present value of 1 problems.BE6-2: Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded annually?LO 5 Solve future and present value of 1 problems.Present Value of a Single Sum0123456Present Value?What table do we use?Future Value $25,000$25,000Future ValueFactorPresent Valuex .63552= $15,888Present Value of a Single SumWhat factor?i=12%n=4LO 5 Solve future and present value of 1 problems.0123456Present Value?Present Value of a Single SumFuture Value $25,000LO 5 Solve future and present value of 1 problems.BE6-2: Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns 12% compounded quarterly?What table do we use?$25,000Future ValueFactorPresent Valuex .62317= $15,579Present Value of a Single Sumi=3%n=16LO 5 Solve future and present value of 1 problems.Single-Sum ProblemsSolving for Other UnknownsLO 5 Solve future and present value of 1 problems.Example—Computation of the Number of PeriodsThe 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 6-13Single-Sum ProblemsLO 5 Solve future and present value of 1 problems.Example—Computation of the Number of PeriodsIllustration 6-14Using 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.Single-Sum ProblemsLO 5 Solve future and present value of 1 problems.Example—Computation of the Number of PeriodsIllustration 6-14Using 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.Single-Sum ProblemsSolving for Other UnknownsLO 5 Solve future and present value of 1 problems.Example—Computation of the Interest RateIllustration 6-15Single-Sum ProblemsLO 5 Solve future and present value of 1 problems.Illustration 6-16Using the future value factor of 1.76234, refer to Table 6-1 and read across the 5-period row to find the factor.Example—Computation of the Interest RateSingle-Sum ProblemsLO 5 Solve future and present value of 1 problems.Illustration 6-16Using the present value factor of .56743, refer to Table 6-2 and read across the 5-period row to find the factor.Example—Computation of the Interest RateAnnuitiesPeriodic payments or receipts (called rents) of the same amount, Same-length interval between such rents, and 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 TypesLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Ordinary AnnuityRents occur at the end of each period.No interest during 1st period.Annuities01Present Value2345678$20,00020,00020,00020,00020,00020,00020,00020,000Future ValueLO 6 Solve future value of ordinary and annuity due problems.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.Future Value of an Ordinary AnnuityIllustration 6-17A formula provides a more efficient way of expressing the future value of an ordinary annuity of 1. Where: R = periodic rentFVF-OA = future value factor of an ordinary annuity i = rate of interest per period n = number of compounding periodsn,iLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Ordinary AnnuityFuture Value of an Ordinary AnnuityIllustration: 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%? = $31,764.25LO 6 Solve future value of ordinary and annuity due problems.Illustration 6-19Future Value of an Ordinary AnnuityIllustration: 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%?LO 6 Solve future value of ordinary and annuity due problems.Illustration 6-19What table do we use?Alternate Calculation$5,000DepositsFactorPresent Valuex 6.35285= $31,764What factor?Future Value of an Ordinary Annuityi=12%n=5LO 6 Solve future value of ordinary and annuity due problems.BE6-13: Bayou 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?01Present ValueWhat table do we use?Future Value of an Ordinary Annuity2345678$30,00030,00030,00030,00030,00030,00030,00030,000Future ValueLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Ordinary AnnuityDepositFactorFuture ValueLO 6 Solve future value of ordinary and annuity due problems.$30,000x 12.29969= $368,991i=12%n=8LO 6 Solve future value of ordinary and annuity due problems.Future Value of an Annuity DueRents 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.Annuities01234567820,00020,00020,00020,00020,00020,00020,000$20,000Future ValueLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Annuity DueIllustration 6-21Comparison of Ordinary Annuity with an Annuity DueFuture Value of an Annuity DueIllustration: 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 = $1,166.07LO 6 Solve future value of ordinary and annuity due problems.Illustration 6-24Computation of RentFuture Value of an Annuity DueComputation of RentIllustration 6-24$14,000= $ $1,166.0712.00611Alternate CalculationLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Annuity DueIllustration: 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?LO 6 Solve future value of ordinary and annuity due problems.Illustration 6-25Computation of Number of Periodic Rents5.86660Future Value of an Annuity DueIllustration: 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?LO 6 Solve future value of ordinary and annuity due problems.Illustration 6-27Computation of Future ValueIllustration: 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?01Present ValueWhat table do we use?Future Value of an Annuity Due2345678$20,00020,00020,00020,00020,00020,00020,00020,000Future ValueLO 6 Solve future value of ordinary and annuity due problems.DepositFactorFuture ValueLO 6 Solve future value of ordinary and annuity due problems.Future Value of an Annuity Due12.29969 x 1.12 = 13.775652i=12%n=8$20,000x 13.775652= $275,513LO 7 Solve present value of ordinary and annuity due problems.Present Value of an Ordinary AnnuityPresent value of a series of equal amounts to be withdrawn or received at equal intervals.Periodic rents occur at the end of the period.Annuities01Present Value2341920$100,000100,000100,000100,000100,000. . . . .100,000LO 7 Solve present value of ordinary and annuity due problems.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. Present Value of an Ordinary AnnuityIllustration 6-28A formula provides a more efficient way of expressing the present value of an ordinary annuity of 1. Where:Present Value of an Ordinary AnnuityLO 7 Solve present value of ordinary and annuity due problems.Present Value of an Ordinary AnnuityIllustration: 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 6-30LO 7 Solve present value of ordinary and annuity due problems.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%. 01Present ValueWhat table do we use?2341920$100,000100,000100,000100,000100,000Present Value of an Ordinary Annuity. . . . .LO 7 Solve present value of ordinary and annuity due problems.100,000LO 7 Solve present value of ordinary and annuity due problems.Present Value of an Ordinary Annuity$100,000ReceiptsFactorPresent Valuex 9.81815= $981,815i=5%n=20LO 7 Solve present value of ordinary and annuity due problems.Present Value of an Annuity DuePresent value of a series of equal amounts to be withdrawn or received at equal intervals.Periodic rents occur at the beginning of the period.Annuities01Present Value2341920$100,000100,000100,000100,000100,000. . . . .100,000Present Value of an Annuity DueIllustration 6-31Comparison of Ordinary Annuity with an Annuity DueLO 7 Solve present value of ordinary and annuity due problems.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 therelevant annual interest rate is 11%, what is the present value of the rental obligations?Illustration 6-33LO 7 Solve present value of ordinary and annuity due problems.Present Value of an Annuity DueIllustration: 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%. 01Present ValueWhat table do we use?2341920$100,000100,000100,000100,000100,000. . . . .LO 7 Solve present value of ordinary and annuity due problems.100,000Present Value of an Annuity DueLO 7 Solve present value of ordinary and annuity due problems.$100,000ReceiptsFactorPresent Valuex 10.60360= $1,060,360Present Value of an Annuity Duei=8%n=20Illustration: 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?LO 7 Solve present value of ordinary and annuity due problems.Present Value of an Annuity DueComputation of Interest RateReferring 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)12 - 1]. 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 Situations012341920100,000100,000100,000. . . . .Future ValuePresent ValueDeferred AnnuitiesLO 8 Solve present value problems related to deferred annuities and bonds.Two Cash Flows: Periodic interest payments (annuity). Principal paid at maturity (single-sum).01234910140,000140,000140,000$140,000. . . . .140,000140,0002,000,000Valuation of Long-Term BondsMore Complex SituationsBE6-15: Clancey Inc. issues $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 Clancey receive when it issues the bonds?01Present Value234910140,000140,000140,000$140,000. . . . .140,000Valuation of Long-Term Bonds2,140,000LO 8 Solve present value problems related to deferred annuities and bonds.LO 8 Solve present value problems related to deferred annuities and bonds.$140,000 x 6.71008 = $939,411Interest PaymentFactorPresent ValueValuation of Long-Term BondsPV of Interesti=8%n=10LO 8 Solve present value problems related to deferred annuities and bonds.$2,000,000 x .46319 = $926,380PrincipalFactorPresent ValueValuation of Long-Term BondsPV of Principali=8%n=10BE6-15: Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. Valuation of Long-Term BondsLO 8 Solve present value problems related to deferred annuities and bonds.Present value of Interest $939,411Present value of Principal 926,380 Bond current market value $1,865,791 Valuation of Long-Term BondsLO 8 Solve present value problems related to deferred annuities and bonds.BE6-15:Concepts Statement No. 7 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 RateThree Components of Interest:Pure RateExpected Inflation RateCredit Risk RateLO 9 Apply expected cash flows to present value measurement.Present Value MeasurementRisk-free rate of return. FASB states a company should discount expected cash flows by the risk-free rate of return.Copyright © 2009 John Wiley & Sons, Inc. All rights reserved. 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