貨幣時(shí)間價(jià)值英語ppt課件(編輯修改稿)
2025-05-30 18:22 本頁面
【文章內(nèi)容簡介】 ? ? ? ?1001 101001 101001 101001 101001 10379 081 2 3 4 5. . . . ..0 1 2 3 4 5 100 100 100 100 100 Present Value of an Annuity (cont.) ? Actually, there is no need to take the present value of each cash flow separately ? We can use a closedform of the PVA equation instead: ? ?? ?PVPmtiPmtiiAtttN N?????????????????11 111Present Value of an Annuity (cont.) ? We can use this equation to find the present value of our example annuity as follows: ? ?PV PmtA ?????????????1 11 100 10379 085...? This equation works for all regular annuities, regardless of the number of payments The Future Value of an Annuity ? We can also use the principle of value additivity to find the future value of an annuity, by simply summing the future values of each of the ponents: ? ? ? ? ? ?FV Pmt i Pmt i Pmt i PmtA t N ttNN NN? ? ? ? ? ? ? ? ? ? ???? ?? 1 1 111122The Future Value of an Annuity (cont.) ? Using the example, and assuming a discount rate of 10% per year, we find that the future value is: ? ? ? ? ? ? ? ?FV A ? ? ? ? ? ?100 1 10 100 1 10 100 1 10 100 1 10 100 610 514 3 2 1. . . . .100 100 100 100 100 0 1 2 3 4 5 } = at year 5 The Future Value of an Annuity (cont.) ? Just as we did for the PVA equation, we could instead use a closedform of the FVA equation: ? ? ? ?FV Pmt i PmtiiA tN ttN N? ? ?? ???????????? 1 1 11? This equation works for all regular annuities, regardless of the number of payments The Future Value of an Annuity (cont.) ? We can use this equation to find the future value of the example annuity: ? ?FV A ???????????1001 10 10 10610 515...Annuities Due 預(yù)付年金 ? Thus far, the annuities that we have looked at begin their payments at the end of period 1。 these are referred to as regular annuities ? A annuity due is the same as a regular annuity, except that its cash flows occur at the beginning of the period rather than at the end 0 1 2 3 4 5 100 100 100 100 100 100 100 100 100 100 5period Annuity Due 5period Regular Annuity Present Value of an Annuity Due ? We can find the present value of an annuity due in the same way as we did for a regular annuity, with one exception ? Note from the timeline that, if we ignore the first cash flow, the annuity due looks just like a fourperiod regular annuity ? Therefore, we can value an annuity due with: ? ? ? ?PV PmtiiPmtADN?????????????????11
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