Time Value of Money

Chapter 6-1Accounting and the Time Value of MoneyAccounting and the Accounting and the Time Value of MoneyTime Value of MoneyChapter Chapter 66Prepared by Coby Harmon, University of California, Santa BarbaraChapter 6-2In accounting (and finance), the term indicates that a dollar received today is worth more than a dollar promised at some time in the future.Basic Time Value ConceptsBasic Time Value ConceptsBasic Time Value ConceptsTime Value of MoneyLO 1 Identify accounting topics where the time value of money isLO 1 Identify accounting topics where the time value of money isrelevant.relevant.Chapter 6-31. Notes 2. Leases 3. Pensions and Other Postretirement Benefits 4. Long-Term AssetsApplications to Accounting Topics:Basic Time Value ConceptsBasic Time Value ConceptsBasic Time Value Concepts5. Sinking Funds6. Business Combinations7. Disclosures8. Installment ContractsLO 1 Identify accounting topics where the time value of money isLO 1 Identify accounting topics where the time value of money isrelevant.relevant.Chapter 6-4Payment 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 year that the principal is outstanding.Nature of InterestBasic Time Value ConceptsBasic Time Value ConceptsBasic Time Value ConceptsLO 1 Identify accounting topics where the time value of money isLO 1 Identify accounting topics where the time value of money isrelevant.relevant.Chapter 6-5Interest computed on the principal only. LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.Simple InterestSimple InterestSimple InterestILLUSTRATION:On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the annual interest cost.Federal law requires the disclosure of interest rates on an annual basis in all contracts.FULL YEARFULL YEARChapter 6-6LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.Simple InterestSimple InterestSimple InterestILLUSTRATION continued:On March 31, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the interest cost for the year ending December 31, 2007.Principal $20,000Interest rate x 7%Annual interest $ 1,400PARTIAL PARTIAL YEARYEARChapter 6-7Computes interest on¾ the principal and¾ on interest earned to date (assuming interest is left on deposit).Compound interest is the typical interest computation applied in business situations.LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.Compound InterestCompound InterestCompound InterestChapter 6-8LO 2 Distinguish between simple and compound interest.LO 2 Distinguish between simple and compound interest.ILLUSTRATION:On January 2, 2007, Tomalczyk borrows $20,000 for 3 years at a rate of 7% per year. Calculate the total interest cost for all three years, assuming interest is compounded annually.Compound InterestCompound InterestCompound InterestCompound Interest AccumulatedDate Calculation Interest BalanceJan. 2007 20,000$ 2007 $20,000 x 7% 1,400$ 21,400 2008 $21,400 x 7% 1,498 22,898 2009 $22,898 x 7% 1,603 24,501 4,501$ Chapter 6-9LO 3 Use appropriate compound interest tables.LO 3 Use appropriate compound interest tables.Compound Interest TablesCompound Interest TablesCompound Interest TablesTable 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 1Five Tables in Chapter 6Number 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.Chapter 6-10LO 3 Use appropriate compound interest tables.LO 3 Use appropriate compound interest tables.Compound InterestCompound InterestCompound InterestCompounding can substantially affect the rate of return. A 9% annual interest compounded daily provides a 9.42% yield.How compounding affects Effective Yield for a $10,000 investment.Illustration 6Illustration 6--55Chapter 6-11LO 4 Identify variables fundamental to solving interest problemsLO 4 Identify variables fundamental to solving interest problems..Compound InterestCompound InterestCompound InterestRate of InterestNumber of Time PeriodsPresent ValueFuture ValueVariables Fundamental to Compound InterestIllustration 6Illustration 6--66Chapter 6-12LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.Single-Sum ProblemsSingleSingle--Sum ProblemsSum ProblemsUnknown Future ValueGenerally Classified into Two CategoriesUnknown Present ValueChapter 6-13LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.Single-Sum ProblemsSingleSingle--Sum ProblemsSum ProblemsFuture Value of a Single SumMultiply the future value factor by its present value (principal).Illustration:BE6-1 Roger Wong invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?Chapter 6-14BE6-1 Roger Wong invested $10,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years?0123456Present Value $10,000 What table do we use?Single-Sum ProblemsSingleSingle--Sum ProblemsSum ProblemsFuture Value?LO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.Chapter 6-15Numberof Discount RatePeriods 2% 4% 6% 8% 10%1 1.02000 1.04000 1.06000 1.08000 1.10000 2 1.04040 1.08160 1.12360 1.16640 1.21000 3 1.06121 1.12486 1.19102 1.25971 1.33100 4 1.08243 1.16986 1.26248 1.36049 1.46410 5 1.10408 1.21665 1.33823 1.46933 1.61051 Table 6Table 6--11What factor do we use?Single-Sum ProblemsSingleSingle--Sum ProblemsSum ProblemsLO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.Chapter 6-17Single-Sum ProblemsSingleSingle--Sum ProblemsSum ProblemsLO 5 Solve future and present value of 1 problems.LO 5 Solve future and present value of 1 problems.Beginning PreviousYear-EndYear Balance Rate Interest Balance Balance1 10,000$ x 8% = 800 + 10,000 = 10,800$ 2 10,800 x 8% = 864 + 10,800 =