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April 17th, 2011, 03:03 AM   #1
 
Joined: May 2009

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Incremental NPV

Company has an old machine, purchased for $200,000 five years ago. It provides annual income of $70,000 and depreciation allowances of $20,000 as its life is 10 years. The market value of the machine currently is $90,000 and it will be worthless in 5 years.

Company is considering replacing this with a new machine for the last 5 years of its life. The new machine costs $400,000 with a life of 5 years and will provide annual income of $180,000 and depreciation charges of $80,000. It is assumed the salvage value of the machine is zero.

The companyís tax rate is 30% and the projectís required rate of return in 12%.

Is it worth boying the new machine. what is the incremental NPV?

This is what i did:

Keep old machine
Year 1 2 3 4 5
Income 70 70 70 70 70
Depn -20 -20 -20 -20 -20
taxable income 50 50 50 50 50

Tax payable -15 -15 -15 -15 -15
income 70 70 70 70 70
cash flow after tax 55 55 55 55 55

NPV = $198.26 (dont take into account the $200,000 purchase as it is a sunk cost)


Buy new machine
Year 0 1 2 3 4 5
Income 180 180 180 180 180
Depn -80 -80 -80 -80 -80
taxable income 100 100 100 100 100

Loss on disposal -10

Tax payable +3 -30 -30 -30 -30 -30
income 180 180 180 180 180

Salavge 0
Initial outlay -400

cash flow after tax 150 150 150 150 150

NPV = 540.72 - 397 = 143.7

Incremental NPV = 143.7 -198.26 =??????????

The answer is: "Replace existing machine as the NPV of replacing is $35,456 higher"

How did they get this answer?
thekiterunner is offline  
 
April 30th, 2011, 04:15 AM   #2
 
Joined: Apr 2011
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Re: Incremental NPV

Quote:
Originally Posted by thekiterunner

Keep old machine
Year 1 2 3 4 5
Income 70 70 70 70 70
Depn -20 -20 -20 -20 -20
taxable income 50 50 50 50 50

Tax payable -15 -15 -15 -15 -15
income 70 70 70 70 70
cash flow after tax 55 55 55 55 55

NPV = $198.26 (dont take into account the $200,000 purchase as it is a sunk cost)
Everything was fine through here except that you didn't account for the 90,000 market price. There's a built-in assumption that you're going to sell it for this amount and have a 90,000 positive inflow of cash. And see below.


Quote:
Buy new machine
Year 0 1 2 3 4 5
Income 180 180 180 180 180
Depn -80 -80 -80 -80 -80
taxable income 100 100 100 100 100

Loss on disposal -10

Tax payable +3 -30 -30 -30 -30 -30
income 180 180 180 180 180

Salavge 0
Initial outlay -400

cash flow after tax 150 150 150 150 150

NPV = 540.72 - 397 = 143.7
The 397 isn't right.

It took me a bit to figure out what the 3 thousand was. I think it threw me because the loss on disposal would go with the old machine because that's part of the selling of it. I see now you're accounting for the tax benefit from that loss. But that would go up at the top section and affect the 90,000, not down here. So the investment should remain at 400.

So looks like the 90,000 is the only missing number.
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