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Q: calculate the NPV of replacing existing equipment ( Answered 5 out of 5 stars,   1 Comment )
Subject: calculate the NPV of replacing existing equipment
Category: Business and Money > Finance
Asked by: dj555-ga
List Price: $20.00
Posted: 19 Aug 2006 10:04 PDT
Expires: 18 Sep 2006 10:04 PDT
Question ID: 757649
ABC industries is considering a new assembly line costing $6,000,000. 
The assembly line will be fully depreciated by the simplified straight
line method over its 5 year depreciable life.  Operating costs of the
new machine are expected to be 1,100,000 per year.

The existing assembly line has 5 years remaining before it will be
fully depreciated and has a net book value of $3,000,000.  If sold
today the company would receive $2,400,000 for the existing machine. 
Annual operating costs on the existing machine are $2,100,000 per
year.  ABC is in the 46 percent marginal tax bracket and has a
required rate of return of 12 percent.

Calculate the net present value of replacing the existing machine.
Subject: Re: calculate the NPV of replacing existing equipment
Answered By: elmarto-ga on 21 Aug 2006 08:58 PDT
Rated:5 out of 5 stars
In order to find the present value of replacing the machine, we must
calculate the incremental cash flows that result from doing it.

First of all, notice that the new machine will represent a $1,000,000
savings per year in operating costs. Given that the tax rate is 46%,

After-tax Savings in operating costs = (1 - 0.46)*1000000 = $540,000

There will also be some savings due to the fact that the depreciation
tax shield will be greater for the new machine. The depreciation for
the new machine will be $1,200,000 per year for the next 5 years
(since its cost is $6,000,000 and it will be depreciated straight line
during its 5-year life). The depreciation for the old machine would be
$600,000 per year (its current book value is $3,000,000 and it will be
depreciated straight line for the next 5 years until full
depreciation). Clearly, thus,

Incremental Depreciation = 1200000 - 600000 = $600,000

The tax shield generated by this depreciation will be:

Tax Shield = 0.46 * 600000 = $276,000

Therefore, we find that:

Incremental Cash Flows = 540000 + 276000 = $816,000 per year, for 5 years.

Let's now find the initial capital outlay. We know that the old
machine is being sold $2,400,000, while its book value is $3,000,000.
Therefore, the after-tax salvage value is:

After-Tax Salvage Value = 2400000 - 0.46*(2400000 - 3000000) = $2,676,000

Now, since the new machine costs $6,000,000, we get that the initial
capital outlay is: 6000000 - 2676000 = $3,324,000.

So now we have all the incremental cash flows generated by the
replacement of the machine. We know that a net $3,324,000 will have to
be paid today for the replacement, and a net $816,000 will be
"received" each year for the next 5 years. Therefore, at a 12%
required rate of return, the present value of the replacement is:

NPV = -3,324,000 + 816,000/1.12 + 816,000/1.12^2 + ... + 816,000/1.12^5
NPV = -382,503

Since the NPV is negative, the machine should not be replaced.

I've also written this analysis in an Excel file. You can download it from

For another "Replacement Problem" example, look at this pdf document:

I hope this helps! If you have any doubt regarding my answer, please
don't hesitate to request clarification before rating it. Otherwise, I
await your rating and final comments.

Best wishes!
dj555-ga rated this answer:5 out of 5 stars and gave an additional tip of: $10.00
Thank you!  Fully answered, with a clear explanation for each step. 
Your inclusion of the Excel file was above and beyond.  Thank you for
a job well done.

Subject: Re: calculate the NPV of replacing existing equipment
From: ubiquity-ga on 21 Aug 2006 10:57 PDT
Actually, there is not enough information to answer the question.

1. One must know the life of the old and new machine.  I know it will
fully depreciate in 5 years.  That is merely an accounting (tax)
schedule.  the machines may survive and be productive well beyond the
five year.  So, unless you are assuming that the machines life matches
the depreciation schedule, you do not have sufficient information to
answer the question.

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