2.2. Aurora Company plans to buy a machine for $160,000 with uncertain life. The

Question

2.2. Aurora Company plans to buy a machine for $160,000 with uncertain life. The resale value of the machine is zero. The following table shows its expected life:

Expected life

Probability

5 years

35%

6 years

35%

7 years

30%

The machine will save the company $60,000 annually while it is running. Aurora will depreciate it fully on a straight-line basis in 6 years. The tax rate of Aurora is 34%, and the proper discount rate in this case is 13%. Should Aurora buy it?   NPV = $33,138.08, yes

Expected life

Probability

5 years

35%

6 years

35%

7 years

30%

Explanation / Answer

Since the NPV is positive, Aurora should buy it.

Expected life 5 Years Initial outlay 160000 Year 1 year 2 year 3 year 3 year 5 Saving 60000.00 60000.00 60000.00 60000.00 60000.00 Depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 Profit 33333.33 33333.33 33333.33 33333.33 33333.33 Tax 11333.33 11333.33 11333.33 11333.33 11333.33 PAT 22000.00 22000.00 22000.00 22000.00 22000.00 Add back depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 Operating cash flow 48666.67 48666.67 48666.67 48666.67 48666.67 Present value 43067.85 38113.14 33728.44 29848.18 26414.32 NPV 11171.92 Expected life 6 Years Initial outlay 160000 Year 1 year 2 year 3 year 3 year 5 year 6 Saving 60000.00 60000.00 60000.00 60000.00 60000.00 60000.00 Depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 26666.67 Profit 33333.33 33333.33 33333.33 33333.33 33333.33 33333.33 Tax 11333.33 11333.33 11333.33 11333.33 11333.33 11333.33 PAT 22000.00 22000.00 22000.00 22000.00 22000.00 22000.00 Add back depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 26666.67 Operating cash flow 48666.67 48666.67 48666.67 48666.67 48666.67 48666.67 Present value 43067.85 38113.14 33728.44 29848.18 26414.32 23375.50 NPV 34547.42 Expected life 7 Years Initial outlay 160000 160000 Year 1 year 2 year 3 year 3 year 5 year 6 Year 7 Saving 60000.00 60000.00 60000.00 60000.00 60000.00 60000.00 60000.00 Depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 26666.67 0 Profit 33333.33 33333.33 33333.33 33333.33 33333.33 33333.33 60000.00 Tax 11333.33 11333.33 11333.33 11333.33 11333.33 11333.33 20400.00 PAT 22000.00 22000.00 22000.00 22000.00 22000.00 22000.00 39600.00 Add back depreciation 26666.67 26666.67 26666.67 26666.67 26666.67 26666.67 0.00 Operating cash flow 48666.67 48666.67 48666.67 48666.67 48666.67 48666.67 39600.00 Present value 43067.85 38113.14 33728.44 29848.18 26414.32 23375.50 16832.40 NPV 51379.82 NPV 0.35*11171.92+0.35*34547.42+0.3*51379.82 31415.71793

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