Dog Up! Franks is looking at a new sausage system with an installed cost of $460,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $66,000. The sausage system will save the firm $230,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $25,000. If the tax rate is 30 percent and the discount rate is 8 percent, what is the NPV of this project?

Dog Up! Franks is looking at a new sausage system with an installed cost of $460,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for $66,000. The sausage system will save the firm $230,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $25,000. If the tax rate is 30 percent and the discount rate is 8 percent, what is the NPV of this project? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

NPV

$

Explanation:

First we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation = $460,000/5

Annual depreciation = $92,000

Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:

Aftertax salvage value = MV + (BV − MV)T

Very often the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:

   

Aftertax salvage value = MV + (0 − MV)T

Aftertax salvage value = MV(1 − T)

We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is:

Aftertax salvage value = $66,000(1 − 0.30)

Aftertax salvage value = $46,200

Using the tax shield approach, we find the OCF for the project is:

OCF = $230,000(1 − 0.30) + 0.30($92,000)

OCF = $188,600

Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.

NPV = −$460,000 − 25,000 + $188,600(PVIFA8%,5) + [($46,200 + 25,000) / 1.085]

NPV = $316,482.64

Consider an asset that costs $712,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $184,000. If the relevant tax rate is 35 percent, what is the aftertax cash flow from the sale of this asset?

Consider an asset that costs $712,000 and is depreciated straight-line to zero over its eight-year tax life. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for $184,000. If the relevant tax rate is 35 percent, what is the aftertax cash flow from the sale of this asset?

Aftertax salvage value

$

Explanation:

The asset has an eight-year useful life and we want to find the BV of the asset after five years. With straight-line depreciation, the depreciation each year will be:

Annual depreciation = $712,000/8

Annual depreciation = $89,000

So, after five years, the accumulated depreciation will be:

Accumulated depreciation = 5($89,000)

Accumulated depreciation = $445,000

The book value at the end of Year 5 is thus:

BV5 = $712,000 − 445,000

BV5 = $267,000

The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured.

Aftertax salvage value = $184,000 + ($267,000 − 184,000)(0.35)

Aftertax salvage value = $213,050

To find the taxes on salvage value, remember to use the equation:

Taxes on salvage value = (BV − MV)T

This equation will always give the correct sign for a tax inflow (refund) or outflow (payment).

Compute the payback period for each of these two separate investments: a. A new operating system for an existing machine is expected to cost $270,000 and have a useful life of six years. The system yields an incremental after-tax income of $77,884 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000. b. A machine costs $190,000, has a $14,000 salvage value, is expected to last eleven years, and will generate an after-tax income of $43,000 per year after straight-line depreciation.

Compute the payback period for each of these two separate investments:

a.	A new operating system for an existing machine is expected to cost $270,000 and have a useful life of six years. The system yields an incremental after-tax income of $77,884 each year after deducting its straight-line depreciation. The predicted salvage value of the system is $10,000.
b.	A machine costs $190,000, has a $14,000 salvage value, is expected to last eleven years, and will generate an after-tax income of $43,000 per year after straight-line depreciation.

a.

		Cost of investment		$270,000
Payback period	=		=		=	2.23 years
		Annual net cash flow		$121,217

  Where

Annual after-tax income	$	77,884
Plus depreciation*		43,333
Annual net cash flow	$	121,217

		$270,000 – $10,000
*Annual depreciation	=		=	$43,333
		6

b.

		Cost of investment		$190,000
Payback period	=		=		=	3.22 years
		Annual net cash flow		$59,000

  Where

Annual after-tax income	$	43,000
Plus depreciation*		16,000
Annual net cash flow	$	59,000

		$190,000 – $14,000
*Annual depreciation	=		=	$16,000
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