Sensitivity Analysis of Investment in a Surface-mount Placement Machine We are c
ID: 1114877 • Letter: S
Question
Sensitivity Analysis of Investment in a Surface-mount Placement Machine We are considering investing in a surface-mount placement (SMP) machine: a $480,000 initial investment, annual savings of $92,500 for a 10-year period, and a salvage value of $46,000. Assume a MARR of 10% per year Determine how sensitive the annual worth (AW) for the investment is to errors in estimating the initial investment, the annual savings, the salvage value, and the MARR. Specifically, for an error range of ± 50% for each parameter, what is the impact on Aw?Explanation / Answer
Answer:
It is an investment project of 10 years duration. Initial investment is $480,000. Each year there is cash flow of $92,500. Salvage is $46,000. Based on MARR 10% present worth and annual worth is -
Year
Initial
Savings
Salvage
Cash
Discount
Present
Investment
flows
factors
worth
at 10%
0
-480,000
-480,000
1
-480000
1
0
92,500
0
92,500
0.90909091
84090.91
2
0
92,500
0
92,500
0.82644628
76446.28
3
0
92,500
0
92,500
0.7513148
69496.62
4
0
92,500
0
92,500
0.68301346
63178.74
5
0
92,500
0
92,500
0.62092132
57435.22
6
0
92,500
0
92,500
0.56447393
52213.84
7
0
92,500
0
92,500
0.51315812
47467.13
8
0
92,500
0
92,500
0.46650738
43151.93
9
0
92,500
0
92,500
0.42409762
39229.03
10
0
92,500
46,000
138,500
0.38554329
53397.75
Total
7.14456711
106107.4
Annual worth = 106107.4/7.14456711
14851.49
-----------------------------------------------------------------------------
Now there will be 50% error in the estimated initial investment, cash flows, salavage and MARR. Consider them one by one to draw following sensitivity analysis
Sesitivity analysis when MARR varies from +50% to -50%
Year
Cash flows
Discounting factors
Present worth
MARR=5%
MARR=10%
MARR=15%
at 5%
at 10%
at 15%
0
-480,000
1
1
1
-480000
-480000
-480000
1
92,500
0.95238
0.9090909
0.8695652
88095.24
84090.9
80434.8
2
92,500
0.90703
0.8264463
0.7561437
83900.23
76446.3
69943.3
3
92,500
0.86384
0.7513148
0.6575162
79904.98
69496.6
60820.3
4
92,500
0.8227
0.6830135
0.5717532
76099.98
63178.7
52887.2
5
92,500
0.78353
0.6209213
0.4971767
72476.17
57435.2
45988.8
6
92,500
0.74622
0.5644739
0.4323276
69024.92
52213.8
39990.3
7
92,500
0.71068
0.5131581
0.375937
65738.02
47467.1
34774.2
8
92,500
0.67684
0.4665074
0.3269018
62607.64
43151.9
30238.4
9
92,500
0.64461
0.4240976
0.2842624
59626.32
39229
26294.3
10
138,500
0.61391
0.3855433
0.2471847
85026.99
53397.7
34235.1
Total
8.72173
7.1445671
6.0187686
262500.5
106107
-4393.4
Change with base MARR of 10%
147.3912
0
-104.14
Annual worth
30097.28
14851.5
-729.95
Change with base MARR of 10%
102.655
0
-104.92
------------------------------------------------------------------------------------------------
Next consider the impact of 50% change in initial cash outflows on either sides
Sesitivity analysis when initial investment varies within 50% on both side
Year
Cash inflows
Discount
Present
Present
Present
with +50%
Base
with -50%
factor at
worth
worth
worth
errors
figure
error
10%
.+50%
Base
-50%
0
-720000
-480,000
-240000
1
-720000
-480000
-240000
1
92,500
92,500
92,500
0.9090909
84090.91
84090.9
84090.9
2
92,500
92,500
92,500
0.8264463
76446.28
76446.3
76446.3
3
92,500
92,500
92,500
0.7513148
69496.62
69496.6
69496.6
4
92,500
92,500
92,500
0.6830135
63178.74
63178.7
63178.7
5
92,500
92,500
92,500
0.6209213
57435.22
57435.2
57435.2
6
92,500
92,500
92,500
0.5644739
52213.84
52213.8
52213.8
7
92,500
92,500
92,500
0.5131581
47467.13
47467.1
47467.1
8
92,500
92,500
92,500
0.4665074
43151.93
43151.9
43151.9
9
92,500
92,500
92,500
0.4240976
39229.03
39229
39229
10
138,500
138,500
138,500
0.3855433
53397.75
53397.7
53397.7
Total
7.1445671
-133892.6
106107
346107
Chage with base initial investment
-226.1858
0
226.186
Annual worth
-18740.47
14851.5
48443.4
Change with base initial investment
-226.1858
0
226.186
------------------------------------------------------------------------
Next is the effect of variation in cash inflows:
Sesitivity analysis when cash flows varies within 50% on both side
Year
Cash inflows
Discount
Present
Present
Present
with +50%
Base
with -50%
factor at
worth
worth
worth
errors
figure
error
10%
.+50%
Base
-50%
0
-480,000
-480,000
-480,000
1
-480000
-480000
-480000
1
138,750
92,500
46,250
0.9090909
126136.4
84090.9
42045.5
2
138,750
92,500
46,250
0.8264463
114669.4
76446.3
38223.1
3
138,750
92,500
46,250
0.7513148
104244.9
69496.6
34748.3
4
138,750
92,500
46,250
0.6830135
94768.12
63178.7
31589.4
5
138,750
92,500
46,250
0.6209213
86152.83
57435.2
28717.6
6
138,750
92,500
46,250
0.5644739
78320.76
52213.8
26106.9
7
138,750
92,500
46,250
0.5131581
71200.69
47467.1
23733.6
8
138,750
92,500
46,250
0.4665074
64727.9
43151.9
21576
9
138,750
92,500
46,250
0.4240976
58843.54
39229
19614.5
10
138,500
138,500
138,500
0.3855433
53397.75
53397.7
53397.7
Total
7.1445671
372462.3
106107
-160247
Chage with base initial investment
251.0237
0
-251.02
Annual worth
52132.24
14851.5
-22429
Change with base initial investment
251.0237
0
-251.02
------------------------------------------------------------------------------
Finally consider the impact of salvage value estimation error
Sesitivity analysis when saklvage value varies within 50% on both side
Year
Cash inflows
Discount
Present
Present
Present
with +50%
Base
with -50%
factor at
worth
worth
worth
errors
figure
error
10%
.+50%
Base
-50%
0
-480,000
-480,000
-480,000
1
-480000
-480000
-480000
1
92,500
92,500
92,500
0.9090909
84090.91
84090.9
84090.9
2
92,500
92,500
92,500
0.8264463
76446.28
76446.3
76446.3
3
92,500
92,500
92,500
0.7513148
69496.62
69496.6
69496.6
4
92,500
92,500
92,500
0.6830135
63178.74
63178.7
63178.7
5
92,500
92,500
92,500
0.6209213
57435.22
57435.2
57435.2
6
92,500
92,500
92,500
0.5644739
52213.84
52213.8
52213.8
7
92,500
92,500
92,500
0.5131581
47467.13
47467.1
47467.1
8
92,500
92,500
92,500
0.4665074
43151.93
43151.9
43151.9
9
92,500
92,500
92,500
0.4240976
39229.03
39229
39229
10
161,500
138,500
115,500
0.3855433
62265.24
53397.7
44530.2
Total
7.1445671
114974.9
106107
97240
Chage with base initial investment
8.357091
0
-8.3571
Annual worth
16092.64
14851.5
13610.3
Change with base initial investment
8.357091
0
-8.3571
Result: Errors in cash flow error is very crucial. It can change annual worth by 252% approximately on either directrion. Least sensitive is salavage value estimation error. It will affect 8% of annual worth. It will not cause negative annul worh. Impact of MARR error is less serious than cash flow errors. But annual worth can be negative, in worst case here. So maximum care is required in cash flow estimation,
Year
Initial
Savings
Salvage
Cash
Discount
Present
Investment
flows
factors
worth
at 10%
0
-480,000
-480,000
1
-480000
1
0
92,500
0
92,500
0.90909091
84090.91
2
0
92,500
0
92,500
0.82644628
76446.28
3
0
92,500
0
92,500
0.7513148
69496.62
4
0
92,500
0
92,500
0.68301346
63178.74
5
0
92,500
0
92,500
0.62092132
57435.22
6
0
92,500
0
92,500
0.56447393
52213.84
7
0
92,500
0
92,500
0.51315812
47467.13
8
0
92,500
0
92,500
0.46650738
43151.93
9
0
92,500
0
92,500
0.42409762
39229.03
10
0
92,500
46,000
138,500
0.38554329
53397.75
Total
7.14456711
106107.4
Annual worth = 106107.4/7.14456711
14851.49
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