Question

A firm is considering an investment in a new machine with a price of $18.02 million to replace its existing machine. The current machine has a book value of $6.02 million and a market value of $4.52 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 $6.72 million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of $252,000 in net working capital. The required return on the investment is 10 percent and the tax rate is 35 percent. What is the NPV of the decision to purchase a new machine?

Answer 1

Calculation of NPV of the decision to purchase a new machine
Year	0	1	2	3	4
Investment in a new machine	-$18,020,000.00
After tax Market value of current Machine	$5,045,000.00
Investment in net working capital	-$252,000.00
Savings in operating cost		$6,720,000.00	$6,720,000.00	$6,720,000.00	$6,720,000.00
Tax @ 35% on savings		-$2,352,000.00	-$2,352,000.00	-$2,352,000.00	-$2,352,000.00
Depreciation Tax shield		$1,050,000.00	$1,050,000.00	$1,050,000.00	$1,050,000.00
Net Cash flow	-$13,227,000.00	$5,418,000.00	$5,418,000.00	$5,418,000.00	$5,418,000.00
x Discount factor @ 10%	1.00000	0.90909	0.82645	0.75131	0.68301
Present Value	-$13,227,000.00	$4,925,454.55	$4,477,685.95	$4,070,623.59	$3,700,566.90
NPV of the decision to purchase a new machine	$3,947,330.99
Working
Calculation of depreciation tax shield on additional depreciation
Depreciation per year on New machine = $18.02 million / 4 years =			$4,505,000.00
Less : Depreciation per year on Current machine = $6.02 million / 4 years =			$1,505,000.00
Additional Depreciation per year			$3,000,000.00
x Tax rate @ 35%			35%
Depreciation Tax shield per year			$1,050,000.00
Calculation of after tax market value of current machine
Sale value	$4,520,000.00
Less : Book value of current machine	$6,020,000.00
Loss on sale of current machine	-$1,500,000.00
Tax benefit @ 35% of loss on sale	$525,000.00
After tax market value of current machine [Sale value + Tax benefit]	$5,045,000.00