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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×s_Abbs.3c3t.com#J-í%>¥Ý

年×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý 末×s_Abbs.3c3t.com#J-í%>¥Ý	折现系数×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý (P/F,10%,n）×s_Abbs.3c3t.com#J-í%>¥Ý	方案A×s_Abbs.3c3t.com#J-í%>¥Ý			方案B×s_Abbs.3c3t.com#J-í%>¥Ý
		投资与×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý 利益×s_Abbs.3c3t.com#J-í%>¥Ý	净现值×s_Abbs.3c3t.com#J-í%>¥Ý	累计净现×s_Abbs.3c3t.com#J-í%>¥Ý 值×s_Abbs.3c3t.com#J-í%>¥Ý	投资与利×s_Abbs.3c3t.com#J-í%>¥Ý 益×s_Abbs.3c3t.com#J-í%>¥Ý	净现值×s_Abbs.3c3t.com#J-í%>¥Ý	累计净现×s_Abbs.3c3t.com#J-í%>¥Ý 值×s_Abbs.3c3t.com#J-í%>¥Ý
1×s_Abbs.3c3t.com#J-í%>¥Ý	0.9091×s_Abbs.3c3t.com#J-í%>¥Ý	-1 200×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	-2 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
2×s_Abbs.3c3t.com#J-í%>¥Ý	0.8264×s_Abbs.3c3t.com#J-í%>¥Ý	-1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	-2 300×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
3×s_Abbs.3c3t.com#J-í%>¥Ý	0.7513×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
4×s_Abbs.3c3t.com#J-í%>¥Ý	0.6830×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
5×s_Abbs.3c3t.com#J-í%>¥Ý	0.6209×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
6×s_Abbs.3c3t.com#J-í%>¥Ý	0.5645×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
7×s_Abbs.3c3t.com#J-í%>¥Ý	0.5132×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
8×s_Abbs.3c3t.com#J-í%>¥Ý	0.4665×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý
9×s_Abbs.3c3t.com#J-í%>¥Ý	0.4241×s_Abbs.3c3t.com#J-í%>¥Ý	850×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	1 500×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý	×s_Abbs.3c3t.com#J-í%>¥Ý ×s_Abbs.3c3t.com#J-í%>¥Ý

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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