Kế toán, kiểm toán - Appendix A: The time value of money

2Appendix A:The Time Value of Money3Learning Objective 1Describe the concept of the time value of money and be able to compute the future value of a single sum. 4Time Value of MoneyFuture inflows and outflows associated with an asset or liability are predicted and adjusted in a way that reflects the time value of these inflows and outflowsThe economic value of an asset or liability is its present value – that is the value of those inflows and outflows adjusted for when they will be received or paidYou would rather have a dollar now rather than a dollar a year from now because you can invest it to make it grow5Interest: The Price of MoneyMoney, like other scarce resources, has a price.InterestInterest is expressed as a percent over a period of time (usually a year)Interest = Principal X Rate X Time6Future ValueThe future value is the amount that money will grow to at a certain interest rate after a certain amount of time. Simple InterestCompound Interest – Interest earns interest7Future Value (cont.)Tables have been developed to expedite the calculation process as periods become much further out. The tables are the extension of the formulas.8Future Value (cont.)Figure A-1 Future Value9Learning Objective 2Define an ordinary annuity and an annuity due and be able to compute their future values.10Future Value of Ordinary AnnuitiesIt often happens that cash payments of equal amounts are made periodically throughout a period of time. A flow of cash payments of equal amounts paid at periodic intervals is called an annuity. If these payments are made at the end of each period it is called an ordinary annuity or annuity in arrears.11Figure A-2 Future Value of ordinary annuities12Future Value of an Annuity DueAnnuities paid at the beginning of a period rather than the end are referred to as an annuity dueThe future value follows the same concept as an ordinary annuity, except that one more period of interest is calculated because the each payment is made at the beginning of the period. 13Figure A-3 Future Value of an annuity due14Concept Practice 2 15Learning Objective 3Be able to compute the present value of the following cash flows: single sum, ordinary annuity, and annuity due.16Present ValueWhat is the present value of a future payment?The computation of the present value is exactly the reciprocal of the future value computation.If present value involves more than one period.17Present Value (cont.)As with future values, tables exist to expedite calculations.Present values for ordinary annuities and annuities due are also computed.18Figure A-4 Present Value of an ordinary annuity (cont. on next slide)19Figure A-4 Present Value of an ordinary annuity (cont.)20Figure A-5 Present Value of an annuity due (cont. on next slide)21Figure A-5 Present Value of an annuity due (cont.)22Equivalent ValueThere are different ways to look at problems; however, present and future value answers are the same regardless of the methodology used. The concept of equivalent value means that an investor is indifferent as to the receipt of various amounts once the time value of money is applied. In the example of the $500 annuity payments in the book, the investor would be indifferent as to an ordinary annuity of $500 for five years, $1,804 now or $3,176 five years from now.23Equivalent ValueFigure A-7 Equivalent values24Concept Practice 3 25Learning Objective 4Be able to compute an implicit (internal) rate of return.26Computing Implicit Rates of Return and Interest RatesIn many business situations it can be useful, or necessary to compute the expected or actual rate of return (or interest) generated by an investment (or note).In these cases we want to compute the interest rate by either knowing or estimating the present value, the future cash flows, and the time period.See next slide for examples27Computing Implicit Rates of Return and Interest Rates (cont.)Figure A-8 Computing an implicit rate of returnThe investment amount is $1,000 and is the present value in a project expected to produce cash receipts of $300 per year for five years.28Computing Implicit Rates of Return and Interest Rates (cont.)Figure A-9 Computing an implicit rate of return A purchase of property is made with a fair market value of $100,000 paying by signing a note payable requiring cash payments of $20,000 at the beginning of each year for six years.29Learning Objective 5Explain the role of present value in the preparation of the financial statements.30Present value information is extremely useful to present the economic reality of a business; however,future cash flows and future interest rates must be predicted.This is highly subjective (perhaps impossible) and not verifiable.Because present value is a goal but is often not attainable, substitute measures are used.Historical cost, fair market value, replacement cost and net realizable value are all surrogate measures.Present Value and Financial Accounting31Wiley © 2018