Kế toán tài chính - Chương 5: Balance sheet and statement of cash flows

PREVIEW OF CHAPTER 6Intermediate Accounting16th EditionKieso ● Weygandt ● Warfield Describe the fundamental concepts related to the time value of money.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.LEARNING OBJECTIVESSolve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities, bonds, and expected cash flows.After studying this chapter, you should be able to:Accounting and the Time Value of Money6LO 1A relationship between time and money.A dollar received today is worth more than a dollar promised at some time in the future. Time Value of MoneyBASIC TIME VALUE CONCEPTSWhen deciding among investment or borrowing alternatives, it is essential to be able to compare today’s dollar and tomorrow’s dollar on the same footing—to “compare apples to apples.”LO 1Notes Leases Pensions and Other Postretirement Benefits Long-Term AssetsPresent Value-Based Accounting MeasurementsShared-Based CompensationBusiness CombinationsDisclosuresEnvironmental LiabilitiesApplications of Time Value ConceptsLO 1Payment for the use of money. Excess cash received or repaid over the amount lent or borrowed (principal).The Nature of InterestBASIC TIME VALUE CONCEPTSLO 1Interest computed on the principal only. Simple InterestIllustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year. Compute the total interest to be paid for the 1 year.Federal law requires the disclosure of interest rates on an annual basis.Interest = p x i x n = $10,000 x .08 x 1= $800Annual InterestBASIC TIME VALUE CONCEPTSLO 1Interest computed on the principal only. Simple InterestIllustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year. Compute the total interest to be paid for the 3 years.Interest = p x i x n = $10,000 x .08 x 3= $2,400Total InterestBASIC TIME VALUE CONCEPTSLO 1Simple InterestInterest = p x i x n = $10,000 x .08 x 3/12= $200Interest computed on the principal only. BASIC TIME VALUE CONCEPTSIllustration: If Barstow borrows $10,000 for 3 months at a 8% per year, the interest is computed as follows.Partial YearLO 1Compound InterestComputes interest onprincipal andinterest earned that has not been paid or withdrawn.Typical interest computation applied in business situations.BASIC TIME VALUE CONCEPTSLO 1Illustration: Tomalczyk Company deposits $10,000 in the Last National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$ 10,900.00Year 2 $10,900.00 x 9%$ 981.00$ 11,881.00Year 3 $11,881.00 x 9%$1,069.29$ 12,950.29ILLUSTRATION 6-1 Simple vs. Compound InterestCompound InterestLO 1The continuing debate on Social Security reform provides a great context to illustrate the power of compounding. One proposed idea is for the government to give $1,000 to every citizen at birth. This gift would be deposited in an account that would earn interest tax-free until the citizen retires. Assuming the account earns a modest 5% annual return until retirement at age 65, the $1,000 would grow to $23,839. With monthly compounding, the $1,000 deposited at birth would grow to $25,617.Why start so early? If the government waited until age 18 to deposit the money, it would grow to only $9,906 with annual compounding. That is, reducing the time invested by a third results in more than a 50% reduction in retirement money. This example illustrates the importance of starting early when the power of compounding is involved. WHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? A PRETTY GOOD STARTLO 1Table 6-1 - Future Value of 1Table 6-2 - Present Value of 1Table 6-3 - Future Value of an Ordinary Annuity of 1Table 6-4 - Present Value of an Ordinary Annuity of 1Table 6-5 - 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 1How much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of compound interest.ILLUSTRATION 6-2Excerpt from Table 6-1Compound Interest TablesBASIC TIME VALUE CONCEPTSFUTURE VALUE OF 1 AT COMPOUND INTEREST(Excerpt From Table 6-1, Page 1LO 1Formula to determine the future value factor (FVF) for 1: Where: BASIC TIME VALUE CONCEPTSCompound Interest TablesFVFn,i = future value factor for n periods at i interest n = number of periods i = rate of interest for a single periodLO 1Determine the number of periods by multiplying the number of years involved by the number of compounding periods per year.ILLUSTRATION 6-4Frequency of CompoundingBASIC TIME VALUE CONCEPTSCompound Interest TablesLO 1A 9% annual interest compounded daily provides a 9.42% yield.Effective Yield for a $10,000 investment.ILLUSTRATION 6-5Comparison of Different Compounding PeriodsBASIC TIME VALUE CONCEPTSCompound Interest TablesLO 1Rate of InterestNumber of Time PeriodsFundamental VariablesILLUSTRATION 6-6Basic Time DiagramBASIC TIME VALUE CONCEPTSFuture ValuePresent ValueLO 1Describe the fundamental concepts related to the time value of money.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.LEARNING OBJECTIVESSolve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities, bonds, and expected cash flows.After studying this chapter, you should be able to:Accounting and the Time Value of Money6LO 2SINGLE-SUM PROBLEMSTwo CategoriesILLUSTRATION 6-6Basic Time DiagramUnknown Future ValueUnknown Present ValueLO 2Value at a future date of a given amount invested, assuming compound interest.FV = future valuePV = present value (principal or single sum) = future value factor for n periods at i interestFVFn,iWhere:Future Value of a Single SumSINGLE-SUM PROBLEMSLO 2Illustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 6%.= $66,912ILLUSTRATION 6-7Future Value Time Diagram (n = 5, i = 6%)Future Value of a Single SumLO 2What table do we use?Future Value of a Single SumAlternate CalculationIllustration: Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at an interest rate of 6%.ILLUSTRATION 6-7Future Value Time Diagram (n = 5, i = 6%)LO 2What factor do we use?$50,000Present ValueFactorFuture Valuex 1.33823= $66,912i=6%n=5Future Value of a Single SumAlternate CalculationLO 2LO 2Illustration: Assume that Commonwealth Edison Company deposited $250 million in an escrow account with Northern Trust Company at the beginning of 2017 as a commitment toward a power plant to be completed December 31, 2020. How much will the company have on deposit at the end of 4 years if interest is 10%, compounded semiannually? 0123456Present Value $250,000,000 What table do we use?Future Value?Future Value of a Single SumPresent ValueFactorFuture Value$250,000,000x 1.147746 = $369,395,000Future Value of a Single Sumi=5%n=8LO 2Value now of a given amount to be paid or received in the future, assuming compound interest. SINGLE-SUM PROBLEMSPresent Value of a Single SumWhere:FV = future valuePV = present value (principal or single sum) = present value factor for n periods at i interestPVFn,iLO 2Illustration: What is the present value of $73,466 to be received or paid in 5 years discounted at 8% compounded annually? = $50,000(rounded by $.51)ILLUSTRATION 6-11Present Value Time Diagram (n = 5, i = 8%)Present Value of a Single SumLO 2What table do we use?Present Value of a Single SumAlternate CalculationIllustration: What is the present value of $73,466 to be received or paid in 5 years discounted at 8% compounded annually?ILLUSTRATION 6-11Present Value Time Diagram (n = 5, i = 8%)LO 2$74,466Future ValueFactorPresent Valuex .68058= $50,000What factor?i=8%n=5Present Value of a Single SumLO 2LO 2Illustration: Assume that your rich uncle decides to give you $2,000 for a trip to Europe when you graduate from college 3 years from now. He proposes to finance the trip by investing a sum of money now at 8% compound interest that will provide you with $2,000 upon your graduation. The only conditions are that you graduate and that you tell him how much to invest now.0123456Present Value?What table do we use?Future Value $2,000Present Value of a Single Sum$2,000Future ValueFactorPresent Valuex .79383= $1,587.66What factor?i=8%n=3Present Value of a Single SumLO 2SINGLE-SUM PROBLEMSSolving for Other UnknownsExample—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 6-13 Time Diagram to Solve for Unknown Number of Periods LO 2Example—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 2SINGLE-SUM PROBLEMSExample—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.LO 2ILLUSTRATION 6-15 Time Diagram to Solve for Unknown Interest RateAdvanced Design, Inc. needs $1,070,584 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 $1,070,584, 5 years from now?Solving for Other UnknownsExample—Computation of the Interest RateSINGLE-SUM PROBLEMSLO 2ILLUSTRATION 6-16Using the future value factor of 1.33823, refer to Table 6-1 and read across the 5-period row to find the factor.Example—Computation of the Interest RateSINGLE-SUM PROBLEMSLO 2Using the present value factor of .74726, refer to Table 6-2 and read across the 5-period row to find the factor.Example—Computation of the Interest RateILLUSTRATION 6-16SINGLE-SUM PROBLEMSDescribe the fundamental concepts related to the time value of money.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.LEARNING OBJECTIVESSolve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities, bonds, and expected cash flows.After studying this chapter, you should be able to:Accounting and the Time Value of Money6LO 3Periodic payments or receipts (called rents) of the same amount, Same-length interval between such rents, and Compounding of interest once each interval.Annuity requires:Ordinary Annuity - rents occur at the end of each period. Annuity Due - rents occur at the beginning of each period.Two TypesANNUITIESLO 3Future Value of an Ordinary AnnuityRents occur at the end of each period.No interest during 1st period.01Present Value2345678$20,00020,00020,00020,00020,00020,00020,00020,000Future ValueANNUITIESLO 3LO 3Illustration: Assume that $1 is deposited at the end of each of 5 years (an ordinary annuity) and earns 5% 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 Solving for the Future Value of an Ordinary AnnuityFuture Value of an Ordinary Annuity R = periodic rent FVF-OA = future value factor of an ordinary annuity i = rate of interest per period n = number of compounding periodsA formula provides a more efficient way of expressing the future value of an ordinary annuity of 1. Where:n,iFuture Value of an Ordinary AnnuityLO 3Illustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 6%? = $28,185.45ILLUSTRATION 6-19 Time Diagram for Future Value of Ordinary Annuity (n = 5, i = 6%)Future Value of an Ordinary AnnuityLO 3What table do we use?Future Value of an Ordinary AnnuityAlternate CalculationIllustration: What is the future value of five $5,000 deposits made at the end of each of the next 5 years, earning interest of 6%?ILLUSTRATION 6-19 Time Diagram for Future Value of Ordinary Annuity (n = 5, i = 6%)LO 3$5,000DepositsFactorFuture Valuex 5.63709= $28,185.45What factor?Future Value of an Ordinary Annuityi=6%n=5LO 3Illustration: Hightown Electronics deposits $75,000 at the end of each 6-month period for the next 3 years, to accumulate enough money to meet debts that mature in 3 years. What is the future value that the company will have on deposit at the end of 3 years if the annual interest rate is 10%?01Present ValueWhat table do we use?2345678$74,00075,00075,00075,00075,00075,000Future ValuesFuture Value of an Ordinary AnnuityLO 3DepositFactorFuture Value$75,000x 6.80191= $510,143.25Future Value of an Ordinary Annuityi=5%n=6LO 3Future 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.01234567820,00020,00020,00020,00020,00020,00020,000$20,000Future ValuesANNUITIESLO 3ILLUSTRATION 6-21Comparison of the Future Value of an Ordinary Annuity with an Annuity DueFuture Value of an Annuity DueLO 3Illustration: To illustrate the use of the ordinary annuity tables in converting to an annuity due, assume that Sue Lotadough plans to deposit $800 a year on each birthday of her son Howard. She makes the first deposit on his tenth birthday, at 6% interest compounded annually. Sue wants to know the amount she will have accumulated for college expenses by her son’s eighteenth birthday. Future Value of an Annuity DueILLUSTRATION 6-22 Annuity Due Time DiagramLO 3Referring to the “future value of an ordinary annuity of 1” table for 8 periods at 6%, Sue finds a factor of 9.89747. She then multiplies this factor by (1 + .06) to arrive at the future value of an annuity due factor. As a result, the accumulated value on Howard’s eighteenth birthday is $8,393.06, as calculated in Illustration 6-23.Future Value of an Annuity DueILLUSTRATION 6-22 Annuity Due Time DiagramILLUSTRATION 6-23 Computation of Accumulated Value of Annuity DueLO 3There is great power in compounding of interest, and there is no better illustration of this maxim than the case of retirement savings, especially for young adults. Under current tax rules for individual retirement accounts (IRAs), you can contribute up to $5,500 in an investment fund, which will grow tax-free until you reach retirement age. What’s more, you get a tax deduction for the amount contributed in the current year. Financial planners encourage young adults to take advantage of the tax benefits of IRAs. Indeed, one type of IRA—a Roth—is tax-free when you receive payments in retirement. By starting early, you can use the power of compounding to grow a pretty good nest egg. As shown in the adjacent chart, starting earlier can have a big impact on the value of your WHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? DON’T WAIT TO MAKE THAT CONTRIBUTION!continuedretirement fund. As shown, by setting aside $1,000 each year, beginning when you are 25 and assuming a rate of return of 6%, your retirement account at age 65 will have a tidy balance of $154,762 [$1,000 × 154.76197 (FVF-OA40,6%)]. That’s the power of compounding. Not too bad you say, but hey, there are a lot of things you might want to spend that $1,000 on (clothes, a trip to Vegas or Europe, new golf clubs). However, if you delay starting those contributions until age 30, your retirement fund will grow only to a value of $111,435 ($1,000 × 111.43478 (FVF-OA35,6%)). That is quite a haircut—about 28%. That is, by delaying or missing contributions, you miss out on the power of compounding and put a dent in your projected nest egg.Source: Adapted from T. Rowe Price, “A Roadmap to Financial Security for Young Adults,” Invest with Confidence (troweprice.com).WHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? DON’T WAIT TO MAKE THAT CONTRIBUTION!LO 3Illustration: 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 = $1,166.07ILLUSTRATION 6-24 Future Value of Ordinary Annuity Time Diagram (n = 10, i = 4%)Computation of RentFuture Value of Ordinary AnnuityLO 3Computation of RentILLUSTRATION 6-24$14,000= $1,166.0712.00611Future Value of Ordinary AnnuityAlternate CalculationLO 3Illustration: 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 Future Value of Ordinary Annuity Time Diagram, to Solve for Unknown Number of PeriodsComputation of Number of Periodic Rents5.86660LO 3Future Value of Ordinary AnnuityIllustration: 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 Accumulated Value of an Annuity DueComputation of Future ValueFuture Value of an Annuity DueLO 3Illustration: Bayou Inc. will deposit $20,000 in a 5% fund at the beginning of each year for 7 years beginning January 1, Year 1. What amount will be in the fund at the end of Year 7?01Present ValueUse future value of ordinary annuity table.2345678$20,00020,00020,00020,00020,00020,00020,00020,000Future ValuesFuture Value of an Annuity DueLO 3DepositFactorFuture Value8.14201 x 1.05 = 8.5491105 $20,000x 8.5491105= $170,982.21Future Value of an Annuity Duei=5%n=7LO 3Describe the fundamental concepts related to the time value of money.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.LEARNING OBJECTIVESSolve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities, bonds, and expected cash flows.After studying this chapter, you should be able to:Accounting and the Time Value of Money6LO 4Present 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.01Present Value2341920$100,000100,000100,000100,000100,000. . . . .100,000ANNUITIESLO 4Illustration: Assume that $1 is to be received at the end of each of 5 periods, as separate amounts, and earns 5% interest compounded annually. ILLUSTRATION 6-28Solving for the Present Value of an Ordinary AnnuityPresent Value of an Ordinary AnnuityLO 4A formula provides a more efficient way of expressing the present value of an ordinary annuity of 1. Where:Present Value of an Ordinary AnnuityLO 4Illustration: 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 6%?ILLUSTRATION 6-30Present Value of an Ordinary AnnuityLO 4Illustration: 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$100,000100,000100,000100,000100,000. . . . .100,000Present Value of an Ordinary AnnuityLO 4$100,000ReceiptsFactorPresent Valuex 9.81815= $981,815i=8%n=20Present Value of an Ordinary AnnuityLO 4Time value of money concepts also can be relevant to public policy debates. For example, several states had to determine how to receive the payments from tobacco companies as settlement for a national lawsuit against the companies for the healthcare costs of smoking. The State of Wisconsin was due to collect 25 years of payments totaling $5.6 billion. The state could wait to collect the payments, or it could sell the payments to an investment bank (a process called securitization). If it were to sell the payments, it would receive a lump-sum payment today of $1.26 billion. Is this a good deal for the state? Assuming a discount rate of 8% and that the payments will be received in equal amounts (e.g., an annuity), the present value of the tobacco payment is: $ 5.6 billion ÷ 25 = $224 million $224 million × 10.67478* = $2.39 billion *PV-OA (i = 8%, n = 25)Why would some in the state be willing to take just $1.26 billion today for an annuity whose present value is almost twice that amount? One reason is thatWHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? UP IN SMOKEcontinuedLO 4Wisconsin was facing a hole in its budget that could be plugged in part by the lump-sum payment. Also, some believed that the risk of not getting paid by the tobacco companies in the future makes it prudent to get the money earlier. If this latter reason has merit, then the present value computation above should have been based on a higher interest rate. Assuming a discount rate of 15%, the present value of the annuity is $1.448 billion ($5.6 billion ÷ 25 = $224 million; $224 million × 6.46415), which is much closer to the lump-sum payment offered to the State of Wisconsin. WHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? UP IN SMOKELO 4Present 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.01Present Value2341920$100,000100,000100,000100,000100,000. . . . .100,000ANNUITIESLO 4ILLUSTRATION 6-31Comparison of Present Value of an Ordinary Annuity with an Annuity DuePresent Value of an Annuity DueLO 4Illustration: 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 5%, what is the present value of the rental obligations?ILLUSTRATION 6-33Computation of Present Value of an Annuity DuePresent Value of an Annuity DueLO 401Present ValueWhat table do we use?2341920$200,000200,000200,000200,000200,000. . . . .200,000Present Value of Annuity ProblemsIllustration: Jaime Yuen wins $4,000,000 in the state lottery. She will be paid $200,000 at the beginning of each year for the next 20 years. How much has she actually won? Assume an appropriate interest rate of 8%. LO 4$200,000ReceiptsFactorPresent Valuex 10.60360= $2,120,720i=8%n=20Present Value of Annuity ProblemsLO 4Illustration: 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 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) - 1]. 12 Present Value of Annuity ProblemsLO 4Illustration: Norm and Jackie Remmers have saved $36,000 to finance their daughter Dawna’s college education. They deposited the money in the Bloomington Savings and Loan Association, where it earns 4% interest compounded semiannually. What equal amounts can their daughter withdraw at the end of every 6 months during her 4 college years, without exhausting the fund?Computation of a Periodic Rent 12 Present Value of Annuity ProblemsLO 4Describe the fundamental concepts related to the time value of money.Solve future and present value of 1 problems.Solve future value of ordinary and annuity due problems.LEARNING OBJECTIVESSolve present value of ordinary and annuity due problems.Solve present value problems related to deferred annuities, bonds, and expected cash flows.After studying this chapter, you should be able to:Accounting and the Time Value of Money6LO 5Rents begin after a specified number of periods.Future Value of a Deferred Annuity - Calculation same as the future value of an annuity not deferred.Present Value of a Deferred Annuity - Must recognize the interest that accrues during the deferral period.012341920100,000100,000100,000. . . . .Future ValuePresent ValueDeferred AnnuitiesOTHER TIME VALUE OF MONEY ISSUESLO 5Two 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 BondsOTHER TIME VALUE OF MONEY ISSUESLO 501Present Value234565,0005,000105,000$5,0005,000Valuation of Long-Term BondsIllustration: Alltech Corporation on January 1, 2017, issues $100,000 of 5% bonds due in 5 years with interest payable annually at year-end. The current market rate of interest for bonds of similar risk is 6%. What will the buyers pay for this bond issue?LO 5 $5,000 x 4.21236 = $21,061.80Interest PaymentFactorPresent ValuePV of Interesti=6%n=5Valuation of Long-Term BondsLO 5 $100,000 x .74726 = $74,726.00PrincipalFactorPresent ValuePV of PrincipalValuation of Long-Term Bondsi=6%n=5LO 5Illustration: Alltech Corporation issues $100,000 of 5% bonds due in 5 years with interest payable at year-end. Present value of Interest $21,061.80Present value of Principal 74,726.00 Bond current market value $95,787.80 Valuation of Long-Term BondsLO 5Valuation of Long-Term BondsILLUSTRATION 6-45 Effective-Interest Amortization ScheduleLO 5Concept 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 RateRisk-free rate of return. FASB states a company should discount expected cash flows by the risk-free rate of return.Present Value MeasurementLO 5Illustration: Al’s Appliance Outlet offers a 2-year warranty on all products sold. In 2017, Al’s Appliance sold $250,000 of a particular type of clothes dryer. Al’s Appliance entered into an agreement with Ralph’s Repair to provide all warranty service on the dryers sold in 2017. Since there is not a ready market for these warranty contracts, Al’s Appliance uses expected cash flow techniques to value the warranty obligation. Based on prior warranty experience, Al’s Appliance estimates the expected cash outflows associated with the dryers sold in 2017, as shown.Present Value MeasurementILLUSTRATION 6-46 Expected Cash Outflows—WarrantiesIllustration 6-47 shows the present value of these cash flows, assuming a risk-free rate of 5% and cash flows occurring at the end of the year.Present Value MeasurementILLUSTRATION 6-47Present Value of Cash FlowsLO 5Management of the level of interest rates is an important policy tool of the Federal Reserve Bank and its chair, Janet Yellen. Through a number of policy options, the Fed has the ability to move interest rates up or down, and these rate changes can affect the wealth of all market participants. For example, if the Fed wants to raise rates (because the overall economy is getting overheated), it can raise the discount rate, which is the rate banks pay to borrow money from the Fed. This rate increase will factor into the rates banks and other creditors use to lend money. As a result, companies will think twice about borrowing money to expand their businesses. The result will be a slowing economy. A rate cut does just the opposite. It makes borrowing cheaper, and it can help the economy expand as more companies borrow to expand their operations. Keeping rates low had been the Fed’s policy in the early 2000s. The low rates did help keep the economy humming. But these same low rates may have also resulted in too much real estate lending and the growth of a real estate bubble, as the price of housing was fueled by cheaper low-interest mortgage loans. But, as the old saying goes, “What goes up, mustWHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? HOW LOW CAN THEY GO?continuedLO 5come down.” That is what real estate prices did, triggering massive loan write-offs, a seizing up of credit markets, and a slowing economy. So just when a rate cut might have helped the economy, the Fed’s rate-cutting toolbox was empty. In response, the Fed began repurchasing long-term government bonds—referred to as “quantitative easing.” These repurchases put money into the market and reduce long-term Interest rates. After three rounds of quantitative easing, it now appears that the Fed was able to spur the economy out of its persistent funk. More recently, Fed watchers are trying to predict when the Fed will allow rates to rise, with many concerned that a rate increase could disrupt the economy’s fragile recovery. Sources: Adam Shell, “Five Investments to Consider if the Fed Uncorks QE3,” USA TODAY (September 1, 2012); and M. Crutsinger, “Yellen Reiterates Fed’s Patience in Raising Rates,” Associated Press (February 24, 2015).WHAT’S YOUR PRINCIPLEWHAT DO THE NUMBERS MEAN? HOW LOW CAN THEY GO?LO 5“Copyright © 2016 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.”COPYRIGHT