Class 17 Chapter 9 LiabilitiesPlanTime Value of moneyPresent and Future Value ConceptsSlide 5PowerPoint PresentationSlide 7Time value of MoneySlide 9How to solve PV and FV problems?Time Value TablesFuture Value of a Single AmountSlide 13Slide 14Present Value of a Single AmountSlide 16Slide 17Slide 18Future Value of an AnnuitySlide 20Slide 21Slide 22Present Value of an AnnuitySlide 24Slide 25Slide 26PP1PP2PP3PP4Next Class1Class 17Chapter 9 LiabilitiesAccounting 2610Xiumin Martin3/19/20132Plan Time Value of MoneySingle paymentMultiple payments (annuities)Practice problemsWhat are liabilities?Current LiabilitiesNon-current Liabilities3Time Value of moneyWould you rather have $1,000 today or $1,050 today?Would you rather have $1,000 today or $1,050 a year from today?4Present and Future Value Concepts$1,000 invested today at 10%.Present ValuePresent ValueFuture ValueFuture ValueMoney grows over time because it earns interest.FV1=1,000*(1+0.1)1 = 1,100FV25=1,000*(1+0.1)25 = 10,834.71Compounding*(1 )nnPVFV r= +5Present and Future Value Concepts$1,100 in 1 year$10,834 in 25 yearsWe can manipulate the formula to compute PV’s.Present ValuePresent ValueFuture ValueFuture ValueDiscounting1*(1 )nnPV FVr=+PV=1,100/(1+0.1)1 = 1,000PV=10,834/(1+0.1)25 = 1,00067Present and Future Value ConceptsThe growth is a mathematical function of four variables:1. The value today (PV).2. The interest rate (r).3. The time period (n).4. The frequency of compounding (so far we did it annually)The growth is a mathematical function of four variables:1. The value today (PV).2. The interest rate (r).3. The time period (n).4. The frequency of compounding (so far we did it annually)Time value of Money8Time value of moneyPresent value (P)Future value (F)Periods of Payment (n)Interest/discount rate (I)9Present and Future Value ConceptsTwo types of cash flows can be involved:TodaySingle paymentPeriodic payments called annuities.10How to solve PV and FV problems?Solve the equation with a regular calculator.We can solve for any one variable if we are given the other 3. Use tables (Libby book Appendix A-toward the end of the book)Use a financial calculator or a spreadsheetUse an internet calculator, e.g.: http://www.uic.e du/classes/actg/actg500/pfvatutor.htm*(1 )nnPVFV r= +11Time Value Tables Present and future value tables are available in Appendix A for:Future value, single amount.Present value, single amount.Future value, annuity.Present value, annuity. Present and future value tables are available in Appendix A for:Future value, single amount.Present value, single amount.Future value, annuity.Present value, annuity.12Future Value of a Single AmountHow much will an amount today be worth in the future?TodayPresent ValueFutureValueInterest compoundingAmount Known???13Future Value of a Single AmountIf we invest $1,000 today earning 10% interest, compounded annually, how much will it be worth in three (3) years?14Future Value of a Single AmountIf we invest $1,000 today earning 10% interest, compounded annually, how much will it be worth in three (3) years?Using the tables (FV-SA): The invested amount is $1,000.i = 10% & n = 3 yearsThe factor is 1.331.$1,000 × 1.331 = $1,331Using the tables (FV-SA): The invested amount is $1,000.i = 10% & n = 3 yearsThe factor is 1.331.$1,000 × 1.331 = $1,3311000*(1.1)*(1.1)*(1.1)=1,000*(1.1)3=1,3311000*(1.1)*(1.1)*(1.1)=1,000*(1.1)3=1,331Internet calculatorhttp://www.uic.edu/classes/actg/actg500/pfvatutor.htmInternet calculatorhttp://www.uic.edu/classes/actg/actg500/pfvatutor.htm15Present Value of a Single AmountHow much is a future amount worth today?TodayPresent ValueFutureValueInterest discounting??? Amount Known16Present Value of a Single AmountHow much do we need to invest today at 10% interest, compounded annually, if we need $1,331 in three (3) years?17Present Value of a Single AmountHow much do we need to invest today at 10% interest, compounded annually, if we need $1,331 in three (3) years?Using Tables (PV-SA): The future amount is $1,331.i = 10% & n = 3 yearsthe factor is .7513.$1,331 × .7513 = $1,000.00 (rounded)Using Tables (PV-SA): The future amount is $1,331.i = 10% & n = 3 yearsthe factor is .7513.$1,331 × .7513 = $1,000.00 (rounded)1,331/[(1.1)*(1.1)*(1.1)]=1,331/[(1.1)3]=1,0001,331/[(1.1)*(1.1)*(1.1)]=1,331/[(1.1)3]=1,000Internet calculatorInternet calculator18Plan Time Value of MoneySingle paymentMultiple payments (annuities)Practice problemsWhat are liabilities?Current LiabilitiesNon-current Liabilities19Future Value of an AnnuityEqual payments are made each period.The payments and interest accumulate over time.Present ValueFutureValueInterest compoundingPayment 1 Payment 2Amount Known???Amount KnownAmount KnownPayment 320Future Value of an AnnuityIf we invest $1,000 at the end of each year for the next three years at interest of 10%, compounded annually, how much will we have at the end of three years?21Future Value of an AnnuityWe can do it the long way by using the single amount formula three times. 1,0001,0001,0000 1 2 31,1001,210FV= 3,3101,000*(1 )nnPVFV r= +22Future Value of an AnnuityBut, we can also calculate it using the tables or calculators. The annual investment amount is $1,000.i = 10% & n = 3 yearsUsing the future value of an annuity table (A.3), the factor is 3.3100.$1,000 × 3.3100 = $3,310The annual investment amount is $1,000.i = 10% & n = 3 yearsUsing the future value of an annuity table (A.3), the factor is 3.3100.$1,000 × 3.3100 = $3,310Internet calculatorInternet calculator23Present Value of an Annuity What is the value today of a series of payments to be received or paid out in the future?TodayPresent ValueFutureValueInterest discountingPayment 1 Payment 2 Payment 3Amount Known???Amount KnownAmount Known24Present Value of an AnnuityWhat is the present value of receiving $1,000 at the end of each year for three years at interest of 10%, compounded annually?25Present Value of an AnnuityWe can do it the long way by using the single amount formula three times. 1,0001,0001,0000 1 2 3826.45751.31PV= 2,486.85909.091*(1 )nnPV FVr=+26Present Value of an AnnuityBut, we can also calculate it using the tables or calculators. The annual receipt amount is $1,000.i = 10% & n = 3 yearsUsing the present value of an annuity table (A.4), the factor is 2.4869.$1,000 × 2.4869 = $2,486.90The annual receipt amount is $1,000.i = 10% & n
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