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In: Finance

One year ago, your company purchased a machine used in manufacturing for $120,000. You have learned...

One year ago, your company purchased a machine used in manufacturing for $120,000. You have learned that a new machine is available that offers many advantages; you can purchase it for $160,000 today. It will be depreciated on a straight-line basis over ten years, after which it has no salvage value. You expect that the new machine will contribute EBITDA (earnings before interest, taxes, depreciation, and amortization) of $40,000 per year for the next ten years. The current machine is expected to produce EBITDA of $22,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, after which it will have no salvage value, so depreciation expense for the current machine is $10,909 per year. All other expenses of the two machines are identical. The market value today of the current machine is $50,000. Your company's tax rate is 38%, and the opportunity cost of capital for this type of equipment is 11%. The NPV of the replacement is? Is it profitable to replace the year-old machine?

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Expert Solution

Old Machine Cost                  120,000
Useful Life in years                           11
Annual depreciation                    10,909
Current book value (after 1 year)=120000-10909=                  109,091
Current Market Value                    50,000
Capital Loss on sale                    59,091
Tax Rate 38%
Tax Savings from Capital Loss =59091*38%=                    22,455
New Machine cost                  160,000
Useful Life in years                           10
Annual SL depreciation                    16,000
Annual Incremental Depreciation over old m/c                      5,091
Annual Tax shield on incremental depreciation@38%=                      1,935
EBITDA difference
Annual EBITDA from New Machine                    40,000
Annual EBITDA from Old Machine                    22,000
Annual Incremental EBITDA from New Machine                    18,000
Tax on Annual Incremental EBITDA @38%                      6,840
After Tax Annual Incremental Income from New Machine                    11,160
NPV of Repalcement Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10
New Machine cost                (160,000)
Sale Proceeds of Old machine                    50,000
Tax Savings from Capital Loss on old machine sale=                    22,455
a Net Initial Investment                  (87,545)
Cash flow from Operations
After Tax incremental Operating income                  11,160                     11,160                11,160                  11,160                 11,160              11,160               11,160                 11,160              11,160           11,160
Incremental Depreciation Tax shield                     1,935                       1,935                  1,935                    1,935                   1,935                1,935                 1,935                   1,935                 1,935              1,935
b Operating cash flow                  13,095                     13,095                13,095                  13,095                 13,095              13,095               13,095                 13,095              13,095           13,095
c Free Cash flow from Project =a+b=                  (87,545)                  13,095                     13,095                13,095                  13,095                 13,095              13,095               13,095                 13,095              13,095           13,095
d PV Factor @11% =1/1.11^n=                              1                  0.9009                    0.8116                0.7312                  0.6587                 0.5935             0.5346               0.4817                 0.4339              0.3909           0.3522
e PV of Free Cash flows=c*d=                  (87,545)                  11,797                     10,628                  9,575                    8,625                   7,772                7,000                 6,308                   5,682                 5,119              4,612
f NPV of Replacement=Sum of PV of free cash flows=                  (10,429)
As the NPV of the replacement is negative, the year-old machine should not be replaced.

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