货币时间价值英语.pptx
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1、The Time Value of MoneyWhat is Time Value?We say that money has a time value because that money can be invested with the expectation of earning a positive rate of returnIn other words,“a dollar received today is worth more than a dollar to be received tomorrow”That is because todays dollar can be in
2、vested so that we have more than one dollar tomorrowThe Terminology of Time ValuePresent Value-An amount of money today,or the current value of a future cash flowFuture Value-An amount of money at some future time periodPeriod-A length of time(often a year,but can be a month,week,day,hour,etc.)Inter
3、est Rate-The compensation paid to a lender(or saver)for the use of funds expressed as a percentage for a period(normally expressed as an annual rate)AbbreviationsPV-Present valueFV-Future valuePmt-Per period payment amountN-Either the total number of cash flows or the number of a specific periodi-Th
4、e interest rate per periodTimelines012345PVFVTodayvA timeline is a graphical device used to clarify the timing of the cash flows for an investmentvEach tick represents one time periodCalculating the Future ValueSuppose that you have an extra$100 today that you wish to invest for one year.If you can
5、earn 10%per year on your investment,how much will you have in one year?012345-100?Calculating the Future Value(cont.)Suppose that at the end of year 1 you decide to extend the investment for a second year.How much will you have accumulated at the end of year 2?012345-110?Generalizing the Future Valu
6、eRecognizing the pattern that is developing,we can generalize the future value calculations as follows:vIf you extended the investment for a third year,you would have:Compound InterestNote from the example that the future value is increasing at an increasing rateIn other words,the amount of interest
7、 earned each year is increasingYear 1:$10Year 2:$11Year 3:$12.10The reason for the increase is that each year you are earning interest on the interest that was earned in previous years in addition to the interest on the original principle amountCompound Interest GraphicallyThe Magic of CompoundingOn
8、 Nov.25,1626 Peter Minuit,a Dutchman,reportedly purchased Manhattan from the Indians for$24 worth of beads and other trinkets(珠子和其他饰品).Was this a good deal for the Indians?This happened about 371 years ago,so if they could earn 5%per year they would now(in 1997)have:vIf they could have earned 10%per
9、 year,they would now have:Thats about 54,563 Trillion(万亿)dollars!The Magic of Compounding(cont.)The Wall Street Journal(17 Jan.92)says that all of New York city real estate is worth about$324 billion.Of this amount,Manhattan is about 30%,which is$97.2 billionAt 10%,this is$54,562 trillion!Our U.S.GN
10、P is only around$6 trillion per year.So this amount represents about 9,094 years worth of the total economic output of the USA!.Calculating the Present ValueSo far,we have seen how to calculate the future value of an investmentBut we can turn this around to find the amount that needs to be invested
11、to achieve some desired future value:Present Value:An ExampleSuppose that your five-year old daughter has just announced her desire to attend college.After some research,you determine that you will need about$100,000 on her 18th birthday to pay for four years of college.If you can earn 8%per year on
12、 your investments,how much do you need to invest today to achieve your goal?AnnuitiesAn annuity is a series of nominally equal payments equally spaced in time(等时间间隔)Annuities are very common:RentMortgage paymentsCar paymentPension incomeThe timeline shows an example of a 5-year,$100 annuity012345100
13、100100100100The Principle of Value AdditivityHow do we find the value(PV or FV)of an annuity?First,you must understand the principle of value additivity:The value of any stream of cash flows is equal to the sum of the values of the componentsIn other words,if we can move the cash flows to the same t
14、ime period we can simply add them all together to get the total value价值相加Present Value of an AnnuityWe can use the principle of value additivity to find the present value of an annuity,by simply summing the present values of each of the components:Present Value of an Annuity(cont.)Using the example,
15、and assuming a discount rate of 10%per year,we find that the present value is:01234510010010010010062.0968.3075.1382.6490.91379.08Present Value of an Annuity(cont.)Actually,there is no need to take the present value of each cash flow separatelyWe can use a closed-form of the PVA equation instead:Pre
16、sent Value of an Annuity(cont.)We can use this equation to find the present value of our example annuity as follows:vThis equation works for all regular annuities,regardless of the number of paymentsThe Future Value of an AnnuityWe can also use the principle of value additivity to find the future va
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- 货币 时间 价值 英语
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