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发表于 2014-09-19 22:10 |只看楼主

某建设项目有A、B两个投资方案，基准收益率ic=10%,其现金流量（投资与效益）见下表

现金流量表®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5

年®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 末®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	折现系数®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 (P/F,10%,n）®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	方案A®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5			方案B®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
		投资与®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 利益®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	净现值®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	累计净现®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 值®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	投资与利®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 益®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	净现值®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	累计净现®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 值®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
1®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.9091®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	-1 200®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	-2 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
2®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.8264®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	-1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	-2 300®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
3®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.7513®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
4®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.6830®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
5®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.6209®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
6®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.5645®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
7®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.5132®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
8®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.4665®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5
9®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	0.4241®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	850®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	1 500®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5	®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5 ®.Ü\¨Å?bbs.3c3t.comûhÂwð¨B5

参考系数：
[P/A,20%,2]=1.5278
[P/A,25%,2]=1.4400
[P/A,20%,1]=0.8333
[P/A,30%,2]=1.3609
[P/A,25%,2]=1.2894
[P/A,25%,1]=0.8000
[P/A,20%,7]=3.6046
[P/A,20%,2]=3.1611
[P/A,10%,7]=4.8683
[P/A,30%,7]=2.8021
[P/A,20%,2]=2.5075
[P/A,20%,2]=0.6944
[P/A,20%,2]=0.6400
[P/A,30%,2]=0.5917
[P/A,20%,2]=0.5487
[问题]
试分别应用如下两种方法，对A、B两方案进行评价和优选。
1、净现值法；2、内部收益率法。
[参考答案]
1、净现值法：
NPVA＝-1200[P/F,10%,1]-1500[P/F,10%,2]+850[P/A,10%,7][P/F,10%,2]

＝-1200×0.9091-1500×0.8264＋850×4.8683×0.8264

＝1089.17(万元)

NPVB＝-2500[P/F,10%,1]-2300[P/F,10%,2]+1500[P/A,10%,7][P/F,10%,2]

＝-2500×0.9091-2300×0.8264＋1500×4.8683×0.8264

＝1861.27(万元)

两方案的净现值均大于0，作为单方案在经济上都是可行的。
但A、B方案相比， NPVB > NPVA，表明B方案的经济效果更好，因此应采用B 方案。
2、内部收益率法：
根据内部收益率的定义，令NPV=0，求IRR。
⑴．求A方案的IRR:
NPVA＝-1200[P/F,IRRA,1]-1500[P/F,IRRA,2]+850[P/A,IRRA,7][P/F,IRRA,2]
①用试算法计算
假设IRRA＝20％:
NPVA＝-1200[P/F,20％,1]-1500[P/F,20％,2]+850[P/A,20％,7][P/F,20％,2]

＝86.027（万元）
假设IRRA＝25％:
NPVA＝-1200[P/F,25％,1]-1500[P/F,25％,2]+850[P/A,25％,7][P/F,25％,2]

＝-200.36（万元）

②用插值法求IRRA

IRRA＝20％＋86.02/(86.02+200.36)×（25％-20％）＝21.5％

⑵．求B方案的IRR:
NPVB＝-2500[P/F,IRRB,1]-2300[P/F,IRRB,2]+1500[P/A,IRRB,7][P/F,IRRB,2]
①用试算法计算
假设IRRB＝20％
NPVB＝-2500[P/F,20％,1]-2300[P/F,20％,2]+1500[P/A,20％,7][P/F,20％,2]

＝74.18（万元）
假设IRRB＝25％
NPVB＝-2500[P/F,25％,1]-2300[P/F,25％,2]+1500[P/A,25％,7][P/F,25％,2]

＝-437.34（万元）
②用插值法求IRRB

IRRB＝20％＋74.18/(74.18+437.34)×（25％-20％）＝20.7％
因为A、B两方案内部收益率均大于基准收益率ic=10%，说明两个方案作为单方案在经济上是可行的。但两方案相比IRRA > IRRB ，故采用A方案优。

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