Question

You're evaluating a new electron microscope for the QA (quality assurance) unit. The microscope will cost $19,000 to buy and another $2,000 to install, and will be sold for $1,800 after 3 years. It falls into the 3-year MACRS class, with depreciation rates as follows:

Year	1	2	3	4
Depreciation rate	33%	45%	15%	7%

The microscope will require an inventory of spare parts worth $5,000. The equipment will not increase revenue, but will save the company $10,000 in labor costs each year.

Your company's marginal tax rate (federal plus state) is 34% and its weighted average cost of capital is 8%.

What is the initial (year-0) free cash flow from the project? Choose the right sign.

What is the free cash flow in year 1?

What is the free cash flow in year 2?

What is the after-tax salvage value of the equipment at the end of year 3?
What is the free cash flow in year 3?

What is the NPV of this project?

Answer 1

The initial (year-0) free cash flow from the project
Cost of microscope	-$19,000.00
Installation cost	-$2,000.00
Investment in spare parts	-$5,000.00
Cash flow at Year 0	-$26,000.00
The free cash flow in year 1
Saving in labor cost	$10,000.00
Tax @ 34% on saving	-$3,400.00
Depreciation tax shield	$2,356.20
Cash flow in Year 1	$8,956.20
The free cash flow in year 2
Saving in labor cost	$10,000.00
Tax @ 34% on saving	-$3,400.00
Depreciation tax shield	$3,213.00
Cash flow in Year 2	$9,813.00
Calculation of the after-tax salvage value of the equipment at the end of year 3
Salvage value	$1,800.00
Less : Book value	$1,470.00
Gain on sale	$330.00
Tax on Gain @ 34%	$112.20
After tax salvage value (Sale value - Tax)	$1,687.80
The free cash flow in year 3
Saving in labor cost	$10,000.00
Tax @ 34% on saving	-$3,400.00
Depreciation tax shield	$1,071.00
After Tax salvage value	$1,687.80
Cash flow in Year 3	$9,358.80
Calculation of NPV of project
Year	Cash flow	Discount factor @ 8%	Present Value
0	-$26,000.00	1.00000	-$26,000.00
1	$8,956.20	0.92593	$8,292.78
2	$9,813.00	0.85734	$8,413.07
3	$9,358.80	0.79383	$7,429.32
NPV			-$1,864.84
Working
Calculation of depreciation tax shield
Year	Depreciable Value of microscope	Depreciation rate	Depreciation	Depreciation Tax shield @ 34%
1	$21,000.00	33%	$6,930.00	$2,356.20
2	$21,000.00	45%	$9,450.00	$3,213.00
3	$21,000.00	15%	$3,150.00	$1,071.00
4	$21,000.00	7%	$1,470.00	$499.80
Book value of microscope at the end of 3rd year = Cost - accumulated depreciation
Book value of microscope at the end of 3rd year = $21000 - $19530 = $1470