2.1. Aries Incorporated wants to buy a new machine, which costs $24,000. Aries will depreciate it fully over its useful life of 6 years, on a straight-line basis. Aries has income tax rate of 35% and it uses a discount rate of 7%. Calculate the minimum pre-tax annual earnings generated by this machine to justify its purchase.$5592.46 ?2.2. National Cancer Institute is planning to acquire an NMR machine at a cost of $24 million. The machine has an uncertain life span: it may last for 6 years (probability 50%), 7 years (probability 30%), or 8 years (probability 20%).2.1. Aries Incorporated wants to buy a new machine, which costs $24,000. Aries will depreciate it fully over its useful life of 6 years, on a straight-line basis. Aries has income tax rate of 35% and it uses a discount rate of 7%. Calculate the minimum pre-tax annual earnings generated by this machine to justify its purchase.

$5592.46 ♥

2.2. National Cancer Institute is planning to acquire an NMR machine at a cost of $24 million. The machine has an uncertain life span: it may last for 6 years (probability 50%), 7 years (probability 30%), or 8 years (probability 20%). The Institute will depreciate the machine on a straight-line basis with a life of 6 years, with no residual value. While the machine is in operation, it will generate a pretax income of $6 million annually. The tax rate of Institute is 40% and it uses a discount rate of 9%. Should the Institute buy the new machine?

Yes, NPV = $672,782 ♥

2.3. Capricorn Company is interested in buying a computer with uncertain life. The following table shows its expected life and resale value:

 

Expected life Probability Resale value   

3 years 20% $20,000   

4 years 30% $10,000   

5 years 50% $5,000  

The computer will save the company $40,000 annually while it is running. Capricorn will depreciate it fully on a straight-line basis in 3 years. The tax rate of Capricorn is 30%, and the proper discount rate in this case is 12%. The cost of the computer is $90,000. Should Capricorn buy it?

Yes, NPV = $25,367.91 ♥

2.4. Gemini Corporation wants to buy a machine and depreciate it over a five-year period with no salvage value. The machine will generate pre-tax revenue of $20,000 annually, the tax rate of Gemini is 32%, and the proper discount rate is 11%. The machine has uncertain life: it may run for 5 years (probability 50%), 6 years (probability 30%), or 7 years (probability 20%). What is the maximum price that Gemini should pay for the machine?

$72,315 ♥

 

2.5. Virgo Corporation is considering the purchase of a new machine that has an expected life of 5 years with a standard deviation of 2 years. The machine will cost $40,000 and will generate a pre-tax income of $10,000 annually. The tax rate of Virgo is 40% and its cost of capital is 7%. Virgo will depreciate the machine on a straight-line basis over 5 years with no residual value. Calculate the probability that the machine will have a life of between 4 and 7 years. Is the machine acceptable if it runs for only 4 years?

53.28%; no, NPV = −$6396.39 ♥

2.6. Aquarius Water Company plans to buy a new water pump for $50,000 that is expected to save the company $12,000 annually. Aquarius will depreciate the pump on the ACRS with three-year life, the annual depreciation being 29%, 47%, and 24%. The company will use the equipment for 5 years, and then sell it for $5,000. The tax rate of the company is 40% and it will use 8% as the discount rate. Should Aquarius buy the pump? 

No, NPV = –$1,970.99, no ♥

2.7. Libra Corporation plans to buy a truck for $40,000 and depreciate it fully over 5 years using straight-line method of depreciation. However, it plans to use it for 8 years and then sell it for an unknown amount. The truck will save $8000 annually, before taxes. The discount rate in this case is 12% and the income tax rate 33%. Find the resale value of the truck after 8 years just to break even.

$14,252.83 ♥

2.8. Leo Hospital, a non-profit entity, wants to buy a machine for $30,000, which will run for 7 years. The savings from the machine is uncertain, with expected value $5000 per year, and standard deviation $1000. The hospital uses 11% as the discount rate and it does not pay any income taxes. Find the probability that the machine will be profitable, that is, its NPV > 0.

8.59% ♥