### Calculate the minimum pre-tax annual earnings

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1. Washington Corporation plans to buy a new drilling machine for \$60,000, which will save the company \$13,000 annually. Washington will depreciate the machine on the ACRS with three-year life, the annual depreciation being 31%, 49%, and 20%. The machine will run for 5 years, and then Washington will sell it for \$3,000. The company will use 12% as discount rate and its tax rate is 32%. Should Washington buy the machine?

2. Adams Incorporated wants to buy a new machine, which costs \$27,000. Adams will depreciate it over its life of 6 years, using straight-line basis. Adams has income tax rate of 31% and its discount rate is 11%. Calculate the minimum pre-tax annual earnings generated by this machine to justify its purchase.

3. Jefferson Corporation has to decide between the following two air conditioning units for an office building. Both units are adequate in their performance.

 Carrier Worthington Initial cost \$140,000 \$110,000 Annual maintenance cost \$11,000 \$13,000 Annual Electricity cost \$22,000 \$24,000 Expected life 7 years 5 years

The company will use straight line depreciation, with no resale value. The tax rate of Jefferson is 30%, and the proper discount rate is 11%. Which one of these units will prove to be less costly in the long run?

4. Madison Company plans to buy a machine for \$15,000, depreciate it over its life of 5 years and then sell it for 10% of its purchase price. While the machine is running it will generate a pretax annual income with expected value \$5000, with standard deviation \$2000. The income tax rate of Madison is 28% and it uses a discount rate of 12%. Find the probability that this machine will be profitable.

5. Monroe Airlines is planning to acquire a Boeing 757 at a cost of \$30 million. The plane has an uncertain life span: it may last for 6 years (probability 20%), 7 years (probability 30%), or 8 years (probability 50%). The airline will depreciate the plane on a straight-line basis with a life of 6 years, with no residual value. While the plane is flying, it will generate a pretax income of \$7 million annually. The tax rate of Monroe is 28% and its discount rate is 11%. Should Monroe buy the new plane?

6. Jackson Corporation wants to buy a machine for \$90,000. It will depreciate the machine over a six-year period with no salvage value. The machine will generate pre-tax income of \$20,000 annually, the tax rate of Jackson is 34%, and the proper discount rate is 15%. The machine has uncertain life: it may run for 5 years (probability 30%), 6 years (probability 30%), or 7 years (probability 40%). Should Jackson buy the machine?

7. Van Buren Corporation is considering the purchase of a new machine that has an expected life of 6 years with a standard deviation of 3 years. The machine will cost \$60,000 and will generate a pre-tax income of \$13,000 annually. The tax rate of Van Buren is 32% and its cost of capital is 12%. Van Buren will depreciate the machine on a straight-line basis over 6 years with no residual value. Calculate the probability that the machine will have a life of between 5 and 8 years. Is the machine acceptable if it runs for only 5 years?

8. Harrison Company is interested in buying a stamping machine with uncertain life. The following table shows its expected life and resale value:

 Expected life Probability Resale value 4 years 20% \$30,000 5 years 40% \$10,000 6 years 40% \$5,000

The machine will save the company \$50,000 annually while it is running. Harrison will depreciate it fully on a straight-line basis in 4 years. The tax rate of Harrison is 32%, and the proper discount rate in this case is 13%. The cost of the machine is \$120,000. Should Harrison buy it?

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