New-Project AnalysisMadison Manufacturing is considering a new machine that costs $350,000 and would reduce pre-tax manufacturing costs by $110,000 annually. Madison would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $33,000 at the end of its 5-year operating life. The applicable depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%. Working capital would increase by $35,000 initially, but it would be recovered at the end of the project's 5-year life. Madison's marginal tax rate is 40%, and a 10% cost of capital is appropriate for the project.    1. Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine's salvage value, and the working capital (WC) requirement. She asks you to use the following probabilities and values in the scenario analysis:ScenarioProbabilityCostSavingsSalvageValueWCWorst case0.35$  88,000$28,000$40,000Base case0.35110,00033,00035,000Best case0.30132,00038,00030,000Calculate the project's expected NPV. Round your answer to the nearest dollar.$ Calculate the project's standard deviation. Round your answer to the nearest dollar.$ Calculate the project's coefficient of variation. Round your answer to two decimal places.

Question
Asked Oct 6, 2019
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New-Project Analysis

Madison Manufacturing is considering a new machine that costs $350,000 and would reduce pre-tax manufacturing costs by $110,000 annually. Madison would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $33,000 at the end of its 5-year operating life. The applicable depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%. Working capital would increase by $35,000 initially, but it would be recovered at the end of the project's 5-year life. Madison's marginal tax rate is 40%, and a 10% cost of capital is appropriate for the project.

    

1. Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine's salvage value, and the working capital (WC) requirement. She asks you to use the following probabilities and values in the scenario analysis:


Scenario

Probability
Cost
Savings
Salvage
Value

WC
Worst case 0.35 $  88,000 $28,000 $40,000
Base case 0.35 110,000 33,000 35,000
Best case 0.30 132,000 38,000 30,000


Calculate the project's expected NPV. Round your answer to the nearest dollar.

Calculate the project's standard deviation. Round your answer to the nearest dollar.

Calculate the project's coefficient of variation. Round your answer to two decimal places.

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Expert Answer

Step 1

Calculate the net present value under worst case as follows:

D
G
Particulars
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
(350,000.00)
(40,000.00)
2 Initial cost
3 Net working capital
4
88,000.00
S8,000.00
5 Pre-tax machine costs
88,000.00
116,655.00
(28,655.00)
(11,462.00)
(17,193.00)
88.000.00
88,000.00
6 Less: Depreciation
7 Eamings before tax
8 Less: Tax @ 40%
155,575.00
51,835.00
36,165.00
25,935.00
(67,575.00)
(27,030.00)
(40,545.00)
155,575.00
62,065.00
৪৪,000.00
14,466.00
24,826.00
35,200.00
37,239.00
9 Net income
21,699.00
51,835.00
52,800.00
10 Add: Depreciation
11 Add: After-tax salvage value
12 Add: Recovery of net working capital
13 Operating cash flow
14 PV factors @ 10%
15 Present value
116.655.00
25,935.00
16,800.00
40,000.00
73,534.00
0.909090909090909 0.826446280991735 0.751314800901578 0.683013455365071 0.620921323059155
(390,000.00)
115,030.00
63,174.00
99,462.00
109,600.00
1
(390,000.00)
95,066.12
55,247.18
43,148.69
90,420.00
Net Present Value
68,052.98
(38,065)
16
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Image Transcriptionclose

D G Particulars Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 (350,000.00) (40,000.00) 2 Initial cost 3 Net working capital 4 88,000.00 S8,000.00 5 Pre-tax machine costs 88,000.00 116,655.00 (28,655.00) (11,462.00) (17,193.00) 88.000.00 88,000.00 6 Less: Depreciation 7 Eamings before tax 8 Less: Tax @ 40% 155,575.00 51,835.00 36,165.00 25,935.00 (67,575.00) (27,030.00) (40,545.00) 155,575.00 62,065.00 ৪৪,000.00 14,466.00 24,826.00 35,200.00 37,239.00 9 Net income 21,699.00 51,835.00 52,800.00 10 Add: Depreciation 11 Add: After-tax salvage value 12 Add: Recovery of net working capital 13 Operating cash flow 14 PV factors @ 10% 15 Present value 116.655.00 25,935.00 16,800.00 40,000.00 73,534.00 0.909090909090909 0.826446280991735 0.751314800901578 0.683013455365071 0.620921323059155 (390,000.00) 115,030.00 63,174.00 99,462.00 109,600.00 1 (390,000.00) 95,066.12 55,247.18 43,148.69 90,420.00 Net Present Value 68,052.98 (38,065) 16

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Step 2

Workings:

C
G
Particulars
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
2 Initial cost
-350000
3 Net working capital
40000
88000
-350000*33.33% -350000*44.45%|- 350000*14.81%-350000*7.41%
-C5-C6
-C7 40%
C7-CS
- C6
88000
5 Pre-tax machine costs
6 Less: Depreciation
7 Earnings before tax
8 Less: Tax @ 40%
9 Net income
88000
88000
88000
D5-D6
-D7 *40%
|-D7 - D8
-D6
E5-E6
-E7 40%
E7-ES
- E6
- G5-G6
-G7*40%
- G7 - GS
-G6
-28000 (1-40%)
40000
- SUM(F9F12 )SUM(G9:G12)
- 1 ( ( 1 + 10 % ) 4 )1/ ( ( 1 +10 % ) ^ 5 )
|-G13*G14
-SUM(B15:G15)
=F5-F6
-F7 *40%
- F7- F8
- F6
10 Add: Depreciation
11 Add After-tax salvage value
12 Add Recovery of net working capital
13 Operating cash flow
14 PV factors @ 10%
15 Present value
-SUM(B2B12) -SUM(C9 : C12) SUM(D9D12)
- 1/( 1 + 10% ) 0)1/( ( 1 +10% ) 1 ) -1/((1+10 % ) 2)
-C13 C14
Net Present Value
|-SUM(E9E12)
- 1 / ( ( 1+ 10% ) ^ 3 )
-E13 E14
- F13 F14
B13 B14
-D13 D14
16
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C G Particulars Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 2 Initial cost -350000 3 Net working capital 40000 88000 -350000*33.33% -350000*44.45%|- 350000*14.81%-350000*7.41% -C5-C6 -C7 40% C7-CS - C6 88000 5 Pre-tax machine costs 6 Less: Depreciation 7 Earnings before tax 8 Less: Tax @ 40% 9 Net income 88000 88000 88000 D5-D6 -D7 *40% |-D7 - D8 -D6 E5-E6 -E7 40% E7-ES - E6 - G5-G6 -G7*40% - G7 - GS -G6 -28000 (1-40%) 40000 - SUM(F9F12 )SUM(G9:G12) - 1 ( ( 1 + 10 % ) 4 )1/ ( ( 1 +10 % ) ^ 5 ) |-G13*G14 -SUM(B15:G15) =F5-F6 -F7 *40% - F7- F8 - F6 10 Add: Depreciation 11 Add After-tax salvage value 12 Add Recovery of net working capital 13 Operating cash flow 14 PV factors @ 10% 15 Present value -SUM(B2B12) -SUM(C9 : C12) SUM(D9D12) - 1/( 1 + 10% ) 0)1/( ( 1 +10% ) 1 ) -1/((1+10 % ) 2) -C13 C14 Net Present Value |-SUM(E9E12) - 1 / ( ( 1+ 10% ) ^ 3 ) -E13 E14 - F13 F14 B13 B14 -D13 D14 16

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Step 3

Calculate the net present value u...

D
Year 0
Year 3
Particulars
Year 1
Year 2
Year 4
Year 5
19 Initial cost
(350,000.00)
(35,000.00)
20 Net working capital
21
22 Pre-tax machine costs
110,000.00
110,000.00
110,000.00
110,000.00
110,000.00
23 Less: Depreciation
24 Earmings before tax
25 Less: Tax @ 40%
26 Net income
27 Add: Depreciation
28 Add: After-tax salvage value
29 Add: Recovery of net working capital
25.935.00
116,655.00
155,575.00
51,835.00
(6,655.00)
(2,662.00)
(3,993.00)
116,655.00
(45,575.00)
(18,230.00)
58,165.00
84,065.00
110,000.00
23,266.00
34,899.00
51,835.00
33,626.00
44,000.00
66,000.00
(27,345.00)
50,439.00
25,935.00
155,575.00
19,800.00
35,000.00
86,734.00
0.909090909090909 0.826446280991735 0.751314800901578 0.683013455365071 0.620921323059155
(385,000.00)
30 Operating cash flow
31 PV factors @ 10 %
32 Present value
112,662.00
128,230.00
76,374.00
120.800.00
(385,000.00)
105,975.2
102,420.00
65,164.54
52,164.47
75,007.30
Net Present Value
15,732
33
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Image Transcriptionclose

D Year 0 Year 3 Particulars Year 1 Year 2 Year 4 Year 5 19 Initial cost (350,000.00) (35,000.00) 20 Net working capital 21 22 Pre-tax machine costs 110,000.00 110,000.00 110,000.00 110,000.00 110,000.00 23 Less: Depreciation 24 Earmings before tax 25 Less: Tax @ 40% 26 Net income 27 Add: Depreciation 28 Add: After-tax salvage value 29 Add: Recovery of net working capital 25.935.00 116,655.00 155,575.00 51,835.00 (6,655.00) (2,662.00) (3,993.00) 116,655.00 (45,575.00) (18,230.00) 58,165.00 84,065.00 110,000.00 23,266.00 34,899.00 51,835.00 33,626.00 44,000.00 66,000.00 (27,345.00) 50,439.00 25,935.00 155,575.00 19,800.00 35,000.00 86,734.00 0.909090909090909 0.826446280991735 0.751314800901578 0.683013455365071 0.620921323059155 (385,000.00) 30 Operating cash flow 31 PV factors @ 10 % 32 Present value 112,662.00 128,230.00 76,374.00 120.800.00 (385,000.00) 105,975.2 102,420.00 65,164.54 52,164.47 75,007.30 Net Present Value 15,732 33

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