You are presented with the two machine alternatives below. The annual expenses a

Question

You are presented with the two machine alternatives below. The annual expenses and revenue are end-of-period amounts. Based solely on the information here, which should you choose? (10 pts)
Machine A Machine B
First Cost $ 15,000 $ 25,000

Annual operating expense $ 4,000 $ 6,000

Annual revenue from machine operation
$ 10,000, increase by 1000/yr $ 15,000, increase by 7.5%/yr

Salvage $ 2000 $ 4000

Life span 6 years 9 years

Effective annual interest rate 10% 10%


Hint: When compare two machines with different life span, you will have to create a scenario in which they are compared for the same time scale. For instance, if machine A has a life span of 4 years, and machine B has a life span of 6 years, to compare them, you will need to look at a 12 year time span, during which 3 As and 2 Bs will be used in sequence, respectively. Only by looking at the same time scale, will you be able to have a fair comparison. It is not correct to calculate for A with 4 years and B with 6 years. The example (6/9 years) in the note was put in there as it was purposefully to show the wrong approach, as I said so in thursday's class.

Explanation / Answer

You are presented with the two machine alternatives below. The annual expenses and revenue are end-of-period amounts. Based solely on the information here, which should you choose? (10 pts)

Machine A Machine B

First Cost $ 15,000 $ 25,000
Annual operating expense $ 4,000 $ 6,000
Annual revenue from machine operation

$ 10,000, increase by 1000/yr $ 15,000, increase by 7.5%/yr
Salvage $ 2000 $ 4000
Life span 6 years 9 years
Effective annual interest rate 10% 10% same interest rate, so we disregard this variable in our calculations

Let's compare the machines.

Machine A:

- $15,000 (initial cost) - $4,000(6 years) for operating + $10,000(6 yrs) + $5,000 + $4,000 + $3,000 + $2,000 + $1,000 (for increases) =

9 + 6 - 15 - 24 + 60 = $36,000 net profit for Machine A

Machine B:

-$25,000 (initial cost) - $6,000(9 years of operation) + $15,000(9 years) + $1216.22

= -59 + 135 + 1.216 = $77,216 net profit for Machine B

Since Machine B earns us a greater profit, we choose Machine B.

**Note that we calculated $1216.22 (the earnings from the 7.5% growth) by the following: 15000(0.075^1) + 15000(0.075^2) + 15000(0.075^3) +15000(0.075^4) + 15000(0.075^5) + 15000(0.075^6) +15000(0.075^7) + 15000(0.075^8)

I hope that you found this answer useful towards your studies. It took quite some thought and effort to compose, and and I'd greatly appreciate a lifesaver rating! It would really make my day! :)

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