payback period and ae analysis

静态回收期=累计净现金流量开始出现正值的年份数 - 1 + [上年累计净现金流量的绝对值/当年净现金流量]

Does not consider the time value of money.

动态回收期=累计净现金流量折现值开始出现正值的年份数 - 1 + [上年累计净现金流量折现值的绝对值/当年净现金流量折现值]

Cash flows occurring after discounted payback period(DPP) are ignored.

Method1:

Method2:

A special case of the PW criterion is useful when the life of a proposed project is perpetual or the service life is extremely long.
The capitalized cost represents the amount of money that must be invested today in order to yield a certain return A at the end of each and every period forever.
一次性投入以在以后的每个阶段(例如每年、每月等)产生一个确定的回报A。

$C E ( i ) = P W ( i ) = A ( P / A , i , N ) = A / i (nrightarrow infty)$

在评估项目时，如果使用现值分析(PW)应当保证两个项目的分析期(项目存活周期)相同。如果不同，可以采用最小公倍数法统一分析期，但这种方法很麻烦。这种情况下，可以使用年金等值分析，计算每一年的平均花费，然后进行比较。二者的关系是$mathrm { AE } ( mathrm { i } ) = mathrm { PW } ( mathrm { i } ) ( mathrm { A } / mathrm { P } , mathrm { i } , mathrm { N } )$。

$begin{aligned} mathrm { CR } ( i ) & = I ( A / P , i , N ) - S ( A / F , i , N ) \ & = ( I - S ) ( A / P , i , N ) + i S end{aligned}$
$I$为一开始购进设备的花费，$S$为设备的残值。