敏 感 性 性 分 析例：有一个生产城市用小型电动汽车的投资方案，用于确定
现金流量表如下，所采用的数据是根据对未来最可能出
由于对未来影响经济环境的某些因素把握不大，投资额、经营成
收入均有可能在±20%的范围内变化。设基准收益率为11%，不得税，试就以上三个不确定性因素做敏感性分析。
解：设投资为K，年销售收入为B，年经营成本为C，期末资为L。投资的变化率为x，经营成本的变化率为y，年销
则有 NPV=-15000+NPV(10%,0,4600,4600, (6600)
IRR=IRR({-15000,0,4600,4600, (6600)
具体求解如下：
K=15000x=
C=15200y=
B=19800z=
残值2000
销
售 收 入
经 营 成 本
残 值
净现金流量
-150000 累 计净现值-15000.00 -15000.00 NPV=
11396.45 I R R=22%
下面就三个不确定性因素做敏感性分析 单因 素敏感性分析
x NPV IRR
y 0%11396.4522.03%
0%-20%14396.4527.73%
-20%-15%13646.4526.12%
-15%-10%12896.4524.64%
-10%-5%12146.4523.28%
-5%0%11396.4522.03%
0%5%10646.4520.86%
5%10%9896.4519.77%
10%15%9146.4518.76%
15%
两因素 敏感性分析
11396.45
-20%-15%-10%-20%31377.8027132.4622887.12-15%
30627.8026382.4622137.12-10%
29877.8025632.4621387.12-5%29127.8024882.4620637.120%28377.8024132.4619887.125%
27627.8023382.4619137.1210%
26877.8022632.4618387.1215%
26127.8021882.4617637.1220%25377.8021132.4616887.12
11396.45
-20%-15%-10%-20%-7723.99 -2193.88 3336.23-15%-8473.99 -2943.88 2586.23-10%
-9223.99 -3693.88 1836.23-5%
-9973.99 -4443.88 1086.230%-10723.99-5193.88 336.235%
-11473.99-5943.88 -413.77 10%
-12223.99-6693.88 -1163.77 15%-12973.99-7443.88 -1913.77
经营成本的变化(y)投
资的变化x NPV
投
资
的变化x 销售收入的变化(z)NPV
20%-13723.99-8193.88 -2663.77 11396.45-20%-15%-10%-20%6257.362012.02-2233.32 -15%
11787.477542.133296.79-10%
17317.5813072.248826.90-5%
22847.6918602.3514357.010%28377.8024132.4619887.125%33907.9129662.5725417.2410%39438.0235192.6830947.3515%
44968.1340722.7936477.4620%50498.2446252.9042007.57
x=
75.98%y=
13.42%z=-10.30%
x
y z
75.98%13.42%y -20%
-71.49%-12.63%-20%-15%
-34.63%-6.12%-15%-10%
2.24%0.40%-10%-5%
39.11% 6.91%-5%0%
75.98%13.42%0%5%
112.84%19.94%5%10%
149.71%26.45%10%15%186.58%32.96%15%
经营成本的变化(y)销
售收入的变化x NPV
20%223.45%39.47%20% 三因素
敏感性分析13.42%
-20%-15%-10%-20%-9.10%-2.58% 3.93%-15%-9.98%-3.47% 3.05%-10%
-10.86%-4.35% 2.16%-5%
-11.75%-5.23% 1.28%0%-12.63%-6.12%0.40%5%
-13.51%-7.00%-0.49%10%
-14.40%-7.88%-1.37%15%
-15.28%-8.77%-2.25%20%-16.16%-9.65%-3.14%
-100.00%-50.00%
0.00%50.00%
100.00%150.00%
200.00%
250.00%
-30%-20%-10%0%10%20%30%x ,y z 两因素敏感性分析图
x_z
y_z -30%-20%
x ,z 两因素x_y z_y 投
资
的变化x 销售收入的变化(z)
y=40.00%50.00%
三因素敏感分析图
z=-20%z=-15%
-20.00%-10.00%0.00%
10.00%20.00%30.00%40.00%-30%-20%-10%0%10%20%30%y x
z=-15%
z=-10%
z=-5%
z=0
z=5%
z=10%
z=15%
z=20%
分 析
投资方案，用于确定性分析的
可能出现的情况估算的。
大，投资额、经营成本和销售
准收益率为11%，不考虑所得
经营成本为C，期末资产的残值L
，年销售收入的变化率为z, 4600, (6600)
6600})
0%i0=10%
0%NPV=11396.45
0%IRR=22.03%
1980019800198001980015200
1520015200152004600
460046004600-11198.35 -7742.30 -4600.44 -1744.20 NPV
IRR z NPV 11396.45
22.03%0%11396.4528377.80
35.90%-20%-10723.99 24132.46
32.72%-15%-5193.88 19887.12
29.37%-10%336.2315641.79
25.82%-5%5866.3411396.45
22.03%0%11396.457151.11
17.92%5%16926.562905.78
13.41%10%22456.67-1339.56
8.32%15%27986.782.34%20%
33516.89
资变化的影
营成本变化
影响
售收入的变
的影响
-5%0%5%10%18641.7914396.4510151.115905.7817891.79
13646.459401.115155.7817141.79
12896.458651.114405.7816391.79
12146.457901.113655.7815641.79
11396.457151.112905.7814891.79
10646.456401.112155.7814141.79
9896.45
5651.111405.7813391.79
9146.454901.11655.7812641.798396.454151.11-94.22
-5%
0%5%10%8866.34
14396.4519926.5625456.678116.34
13646.4519176.5624706.677366.34
12896.4518426.5623956.676616.34
12146.4517676.5623206.675866.34
11396.4516926.5622456.675116.34
10646.4516176.5621706.674366.34
9896.4515426.5620956.673616.349146.4514676.5620206.67
的影响
2866.348396.4513926.5619456.67
-5%0%5%10% -6478.65 -10723.99 -14969.33 -19214.67 -948.54 -5193.88 -9439.22 -13684.56 4581.57336.23-3909.11 -8154.45 10111.685866.341621.00-2624.33 15641.7911396.457151.112905.78 21171.9016926.5612681.228435.89 26702.0122456.6718211.3313966.00 32232.1227986.7823741.4419496.11 37762.2333516.8929271.5525026.22
x z z
75.98%-10.30%x-10.30% 189.19%-25.66%-20%-13.02% 160.88%-21.82%-15%-12.34% 132.58%-17.98%-10%-11.66% 104.28%-14.14%-5%-10.98%
75.98%-10.30%0%-10.30%
47.67%-6.47%5%-9.63%
19.37%-2.63%10%-8.95%
-8.93% 1.21%15%-8.27%
-37.23% 5.05%20%-7.59%-5%
0%5%10%10.44%
16.96%23.47%29.98%9.56%
16.07%22.59%29.10%8.68%
15.19%21.70%28.22%7.79%
14.31%20.82%27.33%6.91%
13.42%19.94%26.45%6.03%
12.54%19.05%25.57%
5.14%
11.66%18.17%24.68%4.26%
10.77%17.29%23.80%3.38%9.89%16.40%22.92%
-50.00%0.00%
50.00%
100.00%150.00%
200.00%
250.00%
0%-10%0%10%20%30%y 两因素敏感性分析图
-15.00%
-10.00%-5.00%0.00%5.00%
10.00%15.00%20.00%-30%-20%-10%0%10%y ,z x
两因素敏感性分析图z_x
y_x
1980019800198001980019800 1520015200152001520015200
46004600460046004600
852.383212.915358.847309.699083.19
IRR
22.03%
-0.07
0.03
0.10
0.17
0.22
0.27
0.31
0.36
0.40
15%
20%1660.44
-2584.90 910.44
-3334.90 160.44
-4084.90 -589.56
-4834.90 -1339.56
-5584.90 -2089.56
-6334.90 -2839.56
-7084.90 -3589.56
-7834.90 -4339.56 -8584.90
15%
20%30986.78
36516.8930236.78
35766.8929486.78
35016.8928736.78
34266.8927986.78
33516.8927236.78
32766.8926486.78
32016.8925736.7831266.89
24986.7830516.89
15%20% -23460.00 -27705.34 -17929.89 -22175.23 -12399.78 -16645.12 -6869.67 -11115.01 -1339.56 -5584.90 4190.55-54.79 9720.665475.32 15250.7711005.43 20780.8816535.54
y
13.42%
16.96%
16.07%
15.19%
14.31%
13.42%
12.54%
11.66%
10.77%
9.89%15%
20%36.50%43.01%35.61%42.12%34.73%41.24%33.85%40.36%32.96%39.47%32.08%38.59%31.20%37.71%30.31%
36.82%29.43%
35.94%