Question

A firm is considering an investment in a new machine with a price of $18 million to replace its existing machine. The current machine has book value of $6 million and a salvage value today of $4.5 million. The new machine is expected to have a four-year life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save $6.7 million in operating costs each year over the next four years. Both machines are depreciated using straight-line method and will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $250,000 in net working capital. The required return on the investment is 10 percent, and the tax rate is 39 percent. What is the net present value (NPV) of the decision to replace the old machine?

Answer 1

Following information is given in the question for the firm:

1. Cost of new proposed machine is $18,000,000
2. Book value of current machine is $6,000,000
3. Salvage value of current machine today at 0 period is $4,500,000
4. Expected useful life of new proposed machine is 4 years
5. Expected remaining useful life of current machine is also 4 years
6. Operating cost saving from replacement of current machine with new proposed machine is $6,700,000 over next 4 years
7. Depreciation method is straight-line method for both machines and no salvage value after 4 years
8. Net working capital investment of $250,000 is required if new proposed machine is purchased
9. Required rate of return or cost of capital is 10% (used for calculating discounting factor)
10. Tax rate is 39%

Now, let us assess the relevant savings and expenses from the decision to replace the old machine with the new machine.

Following are the relevant savings from the replacement:

Particulars	Working	Amount ($)
Operating cost saving for 4 years	given	6,700,000
Depreciation saving on current machine for 4 years	[$6,000,000/4] (using straight line depreciation method)	1,500,000

Following are the relevant expenses from the replacement:

Particulars	Working	Amount ($)
Loss from sale of current machine at 0 year	[$6,000,000 - $4,500,000] (Book value of current machine – Salvage value of current machine)	1,500,000
Depreciation on new machine for 4 years	[$18,000,000/4] (using straight line depreciation method)	4,500,000

Statement showing Cash Flows

Particulars	Year 0	Year 1 to 4
Operating Cost Saving		$     6,700,000
Depreciation Saving on current machine		$     1,500,000
Loss from sale of current machine	$   (1,500,000)
Depreciation on new machine		$   (4,500,000)
Earnings before tax (A)	$   (1,500,000)	$     3,700,000
Tax @ 39% on (A)	$         585,000	$   (1,443,000)
Earnings after tax	$       (915,000)	$     2,257,000
Depreciation on new machine		$     4,500,000
Depreciation on current machine		$   (1,500,000)
Cash Flows	$       (915,000)	$     5,257,000

Statement showing Net Present Value of the decision to replace the old machine

Year	Particulars	Amount (A)	Discounted Factor @ 10% (B)	Present Value (A * B)
0	Cost of new machine	$ (18,000,000)	1	$ (18,000,000)
0	Sale proceeds of current machine	$      4,500,000	1	$      4,500,000
0	Working capital investment	$       (250,000)	1	$       (250,000)
0	Cash Flows	$       (915,000)	1	$       (915,000)
1 to 4	Cash Flows	$      5,257,000	3.17	$    16,664,690
4	Working capital salvage	$          250,000	0.683	$          170,750
	Net Present value			$      2,170,440