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...

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Answered Same DayDec 21, 2021

Answer To: Aries Incorporated wants to buy a new machine, which costs $24,000. Aries will depreciate it fully...

David answered on Dec 21 2021
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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%. Calcu
late the minimum pre-tax annual earnings generated by this machine to
justify its purchase.
$5592.46 ♥

Solution:

Let the minimum pre-tax annual earnings be X

Tax on depreciation = $24,000/6 x 0.35 = 1,400

Annual earnings after tax = X (1 – 0.35) = 0.65X

NPV = -24,000 + ∑



+ ∑





0 = -24,000 + 0.65X (4.76654) + 1400 (4.76654)

0 = -24,000 + 3.09825X + 6673.155

3.09825X = 17,326.845

X = $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 ♥
Solution:

Tax on depreciation = $24 million/6 x 0.40 = $1.6 million

Annual earnings after tax = $6 million x (1 – 0.40) = $3.6 million

Annual cash flow = $3.6 million + $1.6 million = $5.2 million

(In millions)

NPV = -24 + 0.5 *∑



+ + 0.3 *∑




+ + 0.2 *∑





+

= -24+0.5 (23.326777) +0.3(23.326777+1.969323) +0.2(23.326777+1.969323 + 1.8067186)
= -24 + 24.672782

= $0.672782 million

= $672,782

Institute should buy the new machine because NPV is positive.

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%....
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