Question

Your firm is contemplating the purchase of a new $1,110,000 computer-based order entry system. The system will be depreciated straight-line to zero over its 5-year life. It will be worth $108,000 at the end of that time. You will be able to reduce working capital by $150,000 (this is a one-time reduction). The tax rate is 30 percent and your required return on the project is 22 percent and your pretax cost savings are $496,900 per year. Requirement 1: What is the NPV of this project? Requirement 2: What is the NPV if the pretax cost savings are $357,750 per year? Requirement 3: At what level of pretax cost savings would you be indifferent between accepting the project and not accepting it?

Answer 1

I am assuming that the reduction in working capital goes back to normal levels at the end of the life of project, i.e., their is a cash outflow in year 5 as nothing is mentioned regarding that. In case you get incorrect answers, try removing the working capital in year 5.

Requirement 1

Requirement 2

Requirement 3

Let the indifferent pretax cost savings be "P".

Year	1	2	3	4	5
Pretax cost of savings	P	P	P	P	P
Less: Depreciation	$222,000	$222,000	$222,000	$222,000	$222,000
Earnings before tax	P - $222,000	P - $222,000	P - $222,000	P - $222,000	P - $222,000
Less: Tax@30%	0.30P - $66,600	0.30P - $66,600	0.30P - $66,600	0.30P - $66,600	0.30P - $66,600
Net Income	0.70P - $155,400	0.70P - $155,400	0.70P - $155,400	0.70P - $155,400	0.70P - $155,400
Add: Depreciation	$222,000.00	$222,000.00	$222,000.00	$222,000.00	$222,000.00
Cash flow from operations	0.70P + $66,600	0.70P + $66,600	0.70P + $66,600	0.70P + $66,600	0.70P + $66,600
Add: Salvage value of equipment net of tax [Salvage value x (1 - tax rate)]					$75,600
Less: Working capital back to normal levels					$150,000
Total Cash Flows	0.70P + $66,600	0.70P + $66,600	0.70P + $66,600	0.70P + $66,600	0.70P - 7800
Present value interest factor (PVIF) @22%	0.819672	0.671862	0.550707	0.451399	0.369999
Present Value of Cash Inflows	0.5737704 P + $54590.1552	0.4703034 P + $44,746.0092	0.3854949 P + $36,677.0862	0.3159793 P + $30,063.1734	0.2589993 P - $2,885.9922

Now, for the pretax savings to be indifferent, the total present value of cash inflows should be equal to the initial investment, i.e., NPV should be zero.

Total Present value of Cash Inflows = Initial Investment

or, 2.0045473 P + $163,190.4318 = $960,000

or, 2.0045473 P = $796,809.5682

or, P = $397,501.005937 or $397,501.01