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 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 Year 5. Madison’s tax rate is 40%, and its WACC is 10%.a) Calculate the project’s NPV, IRR, MIRR, and payback.b) Management is unsure about the $110,000 cost savings—it could be plus or minus 20%. What would be the NPVs under each extreme?c) Suppose the CFO wants you to do a scenario analysis with different values of the cost savings, the machine’s salvage value, and the working capital requirement. She gives you the following table: Scenario          Probability      Cost Savings     Salvage Value     Working CapitalWorst case            0.35              $88,000               $28,000                $40,000Base case             0.35              110,000                 33,000                  35,000Best case              0.30              132,000                 38,000                  30,000       Calculate the project’s expected NPV, its standard deviation, and its coefficient of variation. Would you recommend that the project be accepted?

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Asked Nov 14, 2019
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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 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 Year 5. Madison’s tax rate is 40%, and its WACC is 10%.

a) Calculate the project’s NPV, IRR, MIRR, and payback.

b) Management is unsure about the $110,000 cost savings—it could be plus or minus 20%. What would be the NPVs under each extreme?

c) Suppose the CFO wants you to do a scenario analysis with different values of the cost savings, the machine’s salvage value, and the working capital requirement. She gives you the following table:

 

Scenario          Probability      Cost Savings     Salvage Value     Working Capital

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, its standard deviation, and its coefficient of variation. Would you recommend that the project be accepted?   

 
 
 
 
 
 
 
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Expert Answer

Step 1

a.

Calculate the NPV, IRR, MIRR, and Payback period as follows:

 

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A E G Year 2 Year 4 Particulars Year 0 Year 1 Year 3 Year 5 1 2 Initial cost 3 Net working capital (350,000.00) (35,000.00) 4 5 Pre-tax savings 6 Less: Tax effect on savings 110,000.00 110,000.00 110,000.00 110,000.00 110,000.00 44,000.00 46,662.00 44,000.00 62,230.00 44,000.00 44,000.00 10,374.00 44,000.00 20,734.00 7 Add: Depreciation tax shield 8 Add: Net working capital 9 Add: After-tax salvage value 10 Operating cash flows 11 PV factor@ 11% 35,000.00 19,800.00 120,800.00 (385,000.00 112,662.00 128,230.00 86,734.00 76,374.00 0.9009009009 0.8116224332 0.7311913813 0.6587309741 059345 13281 1 (385,000.00) Present value 101,497.30 104,074.34 63,419.15 50,309.92 71,688.92 12 NPV 5,989.64 13 IRR 11.64% 14 MIRR 11.64% 15 Payback period 3.75 16

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Step 2

Workings:

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A В C D E F G Year 2 Particulars Year 0 Year Year 3 Year 4 Year 5 1 -350000 -35000 2 Initial cost 3 Net working capital 4 5 Pre-tax savings 6 Less: Tax effect on savings 110000 - C5 40 % - 33.33 % 350000 0.4-44.45 % 350000*0.414.81% 350000 0.4-7.41%* 3550000 0.4 110000 -E5 *40 % 110000 -D5 40% 110000 -F5 400 % 110000 - G5 40% 7Add Depreciation tax shield 8 Add Net working capital 9 Add After-tax salvage vahue 10 Operating cash flows 11 PV factor @ 11% - 35000 - 33000 ( 1-40%%) - G5-G6+ G7+G8+G9 - 1 /( (1 + 11 % ) 5 ) -G10 G11 -SUM(B12:G12) -IRR( B10 : G10) -SUM(B2.B9 )-C5-C6+ C7 1((1+11% ) 0 ) -1/ ( (1 + 11 9% ) 1 ) = B10 B11 - E5- E6 + E7 - 1 / ( ( 1+ 11 9% ) 3) ΕΕ10-ΕΙ1 -D5-D6+ D7 - 1 /( (1 + 1 1 9 % ) ^ 2 ) -D10 D11 - F5- F6+ F7 - 1/ ( ( 1 + 11 % ) ) F10 F11 -C10 C11 Present value 12 NPV 13 IRR 14 MIRR MIRR ( B10 : G10,G14,G14) 15 Payback period 3+(385000- (SUM(C10:E10)) F10) 16

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Step 3

b.

Calculate the net present value if the pre-t...

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B E G Year 4 Year 5 Year (350,000.00) (35,000.00) Particulars Year 1 Year 2 Year 3 18 19 Initial cost 20 Net working capital 21 22 Pre-tax machine costs 23 Less: Depreciation 132,000.00 51,835.00 80,165.00 32,066.00 132,000.00 155,575.00 (23,575.00) 132,000.00 25,935.00 132,000.00 116,655.00 132,000 00 24 Earnings before tax 25 Less: Tax@ 40% 15,345.00 106,065.00 132,000.00 6,138.00 9,207.00 116,655.00 (9,430.00) (14,145.00 155,575.00 52,800.00 42,426.00 26 Net income 27 Add Depreciation 63,639 00 79 200 00 48,099.00 51,835.00 25,935.00 28 Add After-tax salvage value 29 Add Recovery of net working capital 30 Operating cash flow 31 PV factors@ 10% 32 Present value 19,800.00 35,000.00 134,000.00 0.909090909090909 0.826446280991735 0.751314800901578 0.683013455365071 0.620921323059155 (385,000.00) 125,862.00 141,430.00 99 934.00 89.574.00 1 114.420 00 Net Present Value (385.000.00) 116.884.30 75,081.89 61,180.25 83,203.46 65,770 33

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