Question

Capital Budgeting Problems

The company is considering replacing a machine. The old one is currently being depreciated at $70,000 per year (straight-line), and is scheduled to end in five years with no remaining book value. If you don’t replace it, you will be lucky to get it removed for the amount you could salvage it for, so you don’t expect any profit in five years.

If you replace it now, you believe you can salvage it for $400,000 (net) and buy a new machine for $850,000, plus $26,000 shipping fee and another $14,000 for installation. The machine will reduce the operating costs of the company by $143,250 per year. The new machine will be depreciated using the three-year MACRS (for simplicity purposes - same as in the example). The useful life of this machine is five years, and is expected to yield $15,000 in net salvage value at the end of the five years. You may assume a tax rate of 34%.

Using the cost of capital in your firm, should you invest in the new machine? Why?

Answer 1

We can take decision about investment in new machine based on NPV criteria which one of the capital Budgeting technique.
If NPV i.e. net present value of new machine proposal turns out positive , we will replace the old machine with new one otherwise not.
Let us assume the cost of capital in your firm be 10%
Calculation of NPV
Year	0	1	2	3	4	5	NPV
Purchase of new machine	-$890,000.00
After tax salvage value of old machine	$383,000.00
Reduction in operating cost		$143,250.00	$143,250.00	$143,250.00	$143,250.00	$143,250.00
Tax @ 34% on reduction in operating cost		-$48,705.00	-$48,705.00	-$48,705.00	-$48,705.00	-$48,705.00
Tax shield on additional depreciation		$75,356.58	$109,005.70	$19,315.06	-$3,077.34	-$25,500.00
Net salvage value of new machine						$15,000.00
Tax @ 34% on net salvage value of new machine						-$5,100.00
Net Cash flow	-$507,000.00	$169,901.58	$203,550.70	$113,860.06	$91,467.66	$78,945.00
x Discount Factor @ 10%	1.00000	0.90909	0.82645	0.75131	0.68301	0.62092
Present Value	-$507,000.00	$154,455.98	$168,223.72	$85,544.75	$62,473.64	$49,018.63	$12,716.73
NPV of new machine =	$12,716.73
As the NPV of the replacement proposal is positive , the firm should invest in new machine.
Working
Calculation of after tax salvage value of old machine
Salvage value of old machine	$400,000.00
Less : Present book value of old machine [$70000*5 years]	$350,000.00
Gain on sale of old machine	$50,000.00
Tax on gain @ 34%	$17,000.00
After tax salvage value [Salvage value - Tax]	$383,000.00
Calculation of depreciation on new machine using 3 Year MACRS
Year	Installed Cost	Depreciation rate	Depreciation
1	$890,000.00	33.33%	$296,637.00
2	$890,000.00	44.45%	$395,605.00
3	$890,000.00	14.81%	$131,809.00
4	$890,000.00	7.41%	$65,949.00
5	$890,000.00		$0.00
Calculation of tax shield on additional depreciation
Year	Depreciation on old machine	Depreciation on new machine	Additional Depreciation	Tax shield @ 34%
1	$75,000.00	$296,637.00	$221,637.00	$75,356.58
2	$75,000.00	$395,605.00	$320,605.00	$109,005.70
3	$75,000.00	$131,809.00	$56,809.00	$19,315.06
4	$75,000.00	$65,949.00	-$9,051.00	-$3,077.34
5	$75,000.00	$0.00	-$75,000.00	-$25,500.00