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Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,6-,82,C H A P T E R,6,ACCOUNTING AND THE TIME VALUE OF MONEY,Intermediate Accounting,IFRS Edition,Kieso, Weygandt, and Warfield,Future value of a single sum,Present value of a single sum,Solving for other unknowns,Basic Time Value Concepts,Single-Sum Problems,Annuities,More Complex Situations,Present Value Measurement,Applications,The nature of interest,Simple interest,Compound interest,Fundamental variables,Future value of ordinary annuity,Future value of annuity due,Examples of FV of annuity,Present value of ordinary annuity,Present value of annuity due,Examples of PV of annuity,Deferred annuities,Valuation of long-term bonds,Effective-interest method of bond discount/ premium amortization,Choosing an appropriate interest rate,Example of expected cash flow,Accounting and the Time Value of Money,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.,Notes,Leases,Pensions and Other Postretirement Benefits,Long-Term Assets,Applications to Accounting Topics:,Basic Time Value Concepts,Shared-Based Compensation,Business Combinations,Disclosures,Environmental Liabilities,LO 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).,The Nature of Interest,Basic Time Value Concepts,LO 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 Concepts,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 Interest,Interest computed on the principal only.,LO 2 Distinguish between simple and compound interest.,Basic Time Value Concepts,Simple Interest,Interest =,p,x,i,x,n,= $20,000 x .07 x 1,=,$1,400,Annual 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,.,Interest computed on the principal only.,LO 2 Distinguish between simple and compound interest.,Basic Time Value Concepts,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.,Interest =,p,x,i,x,n,= $20,000 x .07 x 9/12,=,$1,050,Partial Year,LO 2 Distinguish between simple and compound interest.,Basic Time Value Concepts,Compound Interest,Computes interest on,principal,and,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, Tomalczyk will not withdraw any interest until 3 years from the date of deposit.,Year 1 $10,000.00 x 9%,Year 2 $10,900.00 x 9%,Year 3 $11,881.00 x 9%,Illustration 6-1,Simple vs. Compound Interest,LO 2 Distinguish between simple and compound interest.,Basic Time Value Concepts,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.,Basic Time Value Concepts,LO 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.,Basic Time Value Concepts,Illustration 6-2,Excerpt from Table 6-1,Compound Interest,LO 3 Use appropriate compound interest tables.,Basic Time Value Concepts,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,FVF,n,i,Compound Interest,LO 3 Use appropriate compound interest tables.,Basic Time Value Concepts,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,LO 3 Use appropriate compound interest tables.,9% annual interest compounded daily provides a 9.42% yield.,Effective Yield for a $10,000 investment.,Basic Time Value Concepts,Illustration 6-5,Comparison of Different Compounding Periods,Compound Interest,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,Basic Time Value Concepts,LO 5 Solve future and present value of 1 problems.,Single-Sum Problems,Unknown,Future Value,Two Categories,Unknown,Present Value,Illustration 6-6,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 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,LO 5 Solve future and present value of 1 problems.,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,LO 5 Solve future and present value of 1 problems.,Future Value of a Single Sum,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,What factor do we use?,$50,000,Present Value,Factor,Future Value,=,$84,253,Future Value of a Single Sum,Alternate Calculation,i=11%,n=5,LO 5 Solve future and present value of 1 problems.,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?,LO 5 Solve future and present value of 1 problems.,Future Value of a Single Sum,LO 5 Solve future and present value of 1 problems.,Present Value,Factor,Future Value,$15,000,x 1.25971,=,$18,896,Future Value of a Single Sum,i=8%,n=3,LO 5 Solve future and present value of 1 problems.,PROOF,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?,Future Value of a Single Sum,BE6-1:,Bob Anderson invested $15,000 today in a fund that earns 8% compounded,semiannually,. 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?,LO 5 Solve future and present value of 1 problems.,Future Value of a Single Sum,LO 5 Solve future and present value of 1 problems.,Present Value,Factor,Future Value,$15,000,x 1.26532,=,$18,980,Future Value of a Single Sum,What factor?,i=4%,n=6,Value now of a given amount to be paid or received in the future, assuming compound interest.,Single-Sum Problems,Present Value of a Single Sum,LO 5 Solve future and present value of 1 problems.,Where:,FV,=future value,PV,=present value (principal or single sum),=present value factor for,n,periods at,i,interest,PVF,n,i,LO 5 Solve future and present value of 1 problems.,Present Value of a Single Sum,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,Present Value of a Single Sum,LO 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,Illustration 6-11,$84,253,Future Value,Factor,Present Value,x .59345,=,$50,000,Present Value of a Single Sum,What factor?,i=11%,n=5,LO 5 Solve future and present value of 1 problems.,BE6-2:,Caroline and Clifford need $25,000 in 4 years. What amount must they invest today if their investment earns 12% compounded,annually,?,LO 5 Solve future and present value of 1 problems.,Present Value of a Single Sum,0,1,2,3,4,5,6,Present Value?,What table do we use?,Future Value $25,000,$25,000,Future Value,Factor,Present Value,x .63552,=,$15,888,Present Value of a Single Sum,What factor?,i=12%,n=4,LO 5 Solve future and present value of 1 problems.,0,1,2,3,4,5,6,Present Value?,Present Value of a Single Sum,Future Value $25,000,LO 5 Solve future and present value of 1 problems.,What table do we use?,BE6-2:,Caroline and Clifford need $25,000 in 4 years. What amount must they invest today if their investment earns 12% compounded,quarterly,?,$25,000,Future Value,Factor,Present Value,x .62317,=,$15,579,Present Value of a Single Sum,i=3%,n=16,LO 5 Solve future and present value of 1 problems.,Single-Sum Problems,Solving for Other Unknowns,LO 5 Solve future and present value of 1 problems.,ExampleComputation 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,Single-Sum Problems,LO 5 Solve future and present value of 1 problems.,ExampleComputation of the Number of Periods,Illustration 6-14,Using the future value factor of , refer to Table 6-1 and read down the 10% column to find that factor in the 4-period row.,Single-Sum Problems,LO 5 Solve future and present value of 1 problems.,ExampleComputation of the Number of Periods,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,Single-Sum Problems,Solving for Other Unknowns,LO 5 Solve future and present value of 1 problems.,ExampleComputation 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,Single-Sum Problems,Solving for Other Unknowns,LO 5 Solve future and present value of 1 problems.,ExampleComputation 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?,Single-Sum Problems,LO 5 Solve future and present value of 1 problems.,Illustration 6-16,Using the future value factor of , refer to Table 6-1 and read across the 5-period row to find the factor.,ExampleComputation of the Interest Rate,Single-Sum Problems,LO 5 Solve future and present value of 1 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.,ExampleComputation of the Interest Rate,Annuities,Periodic 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 Types,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 1,st,period.,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,LO 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 Annuity,Illustration 6-17,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,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Ordinary Annuity,Future Value of an Ordinary Annuity,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%?,LO 6 Solve future value of ordinary and annuity due problems.,Illustration 6-19,Future Value of an Ordinary Annuity,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%?,LO 6 Solve future value of ordinary and annuity due problems.,What table do we use?,Alternate Calculation,Illustration 6-19,$5,000,Deposits,Factor,Present Value,=,$31,764,What factor?,Future Value of an Ordinary Annuity,i=12%,n=5,LO 6 Solve future value of ordinary and annuity due problems.,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,What table do we use?,Future Value of an Ordinary Annuity,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,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Ordinary Annuity,Deposit,Factor,Future Value,LO 6 Solve future value of ordinary and annuity due problems.,$30,000,=,$368,991,i=12%,n=8,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Annuity Due,Rents occur at the beginning of each period.,Interest will accumulate during 1,st,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,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,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Annuity Due,Illustration 6-21,Comparison of Ordinary Annuity with an Annuity Due,Future Value of an Annuity Due,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,LO 6 Solve future value of ordinary and annuity due problems.,Illustration 6-24,Computation of Rent,Future Value of an Annuity Due,Computation of Rent,Illustration 6-24,$14,000,=,Alternate Calculation,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Annuity Due,Illustration:,Suppose that a companys 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 6-25,Computation of Number of Periodic Rents,Future Value of an Annuity Due,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?,LO 6 Solve future value of ordinary and annuity due problems.,Illustration 6-27,Computation of Future Value,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,What table do we use?,Future Value of an Annuity Due,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 due problems.,Deposit,Factor,Future Value,LO 6 Solve future value of ordinary and annuity due problems.,Future Value of an Annuity Due,12.29969 x,i=12%,n=8,$20,000,=,$275,513,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,0,1,Present Value,2,3,4,19,20,$100,000,100,000,100,000,100,000,100,000,. . . . .,100,000,LO 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 Annuity,Illustration 6-28,A formula provides a more efficient way of expressing the present value of an ordinary annuity of 1.,Where:,Present Value of an Ordinary Annuity,LO 7 Solve present value of ordinary and annuity due problems.,Present Value of an Ordinary Annuity,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,LO 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%.,0,1,Present Value,What table do we use?,2,3,4,19,20,$100,000,100,000,100,000,100,000,100,000,Present Value of an Ordinary Annuity,. . . . .,LO 7 Solve present value of ordinary and annuity due problems.,100,000,LO 7 Solve present value of ordinary and annuity due problems.,Present Value of an Ordinary Annuity,$100,000,Receipts,Factor,Present Value,=,$981,815,i=5%,n=20,LO 7 Solve present value of ordinary and annuity due problems.,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,0,1,Present Value,2,3,4,19,20,$100,000,100,000,100,000,100,000,100,000,. . . . .,100,000,Present Value of an Annuity Due,Illustration 6-31,Comparison of Ordinary Annuity with an Annuity Due,LO 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 the relevant annual interest rate is 11%, what is the present value of the rental obligations?,Illustration 6-33,LO 7 Solve present value of ordinary and annuity due problems.,Present Value of an Annuity Due,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
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