Question

Suppose you need to decide whether to keep a machine or replace it with a new one:

Old machine: The old machine can operate for 5 years with operating cost of $120,000 per year.

New machine: Replacing the old machine with a new one requires a capital cost of $250,000 in year zero (assume that there is zero salvage value for old machine). The capital cost is depreciable from year 0 to year 5 (over six years) based on MACRS 5-year life depreciation with the half year convention (table A-1 at IRS). The new machine has a lower operating cost of $45,000 per year for 5 years (from year 1 to year 5).

Assume both machines produce similar good with similar value that yields similar revenue.

Consider income tax of 35% and a discount rate of 10% annually. In present discounted value terms, how much will you save by replacing the old machine with the new machine?

(Note: What you are being asked to do here is to conduct incremental NPV analysis on the new machine versus the old machine, NPV_{new machine - old machine}.)

Answer 1

From below calculations we can see NPV of new machine is less i.e. $293,220, hence basis incremental NPV analysis we should go with New Machine option. Saving = $2,461

Old Machine	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5
Operating Cost (A)		120,000.00	120,000.00	120,000.00	120,000.00	120,000.00
Tax Benefit (B)		(42,000.00)	(42,000.00)	(42,000.00)	(42,000.00)	(42,000.00)
Net Cost (C = A-B)		78,000.00	78,000.00	78,000.00	78,000.00	78,000.00
Discount Rate (D = 1/[1+r]^n)		0.90909091	0.82644628	0.7513148	0.68301346	0.62092132
NPV (E = Sum of C*D)	295,681.37	70,909.09	64,462.81	58,602.55	53,275.05	48,431.86
New Machine	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Capital Cost - A	250,000.00
Depreciation - (B = A*Dep rate)		50,000.00	80,000.00	48,000.00	28,800.00	28,800.00	14,400.00
Operating Cost - C		45,000.00	45,000.00	45,000.00	45,000.00	45,000.00
Tax Benefit - D = (B+C)*35%		(33,250.00)	(43,750.00)	(32,550.00)	(25,830.00)	(25,830.00)	(5,040.00)
Net Cash Outflow E = A+C+D	250,000.00	11,750.00	1,250.00	12,450.00	19,170.00	19,170.00	(5,040.00)
Discount Rate (D = 1/[1+r]^n)	1	0.90909091	0.82644628	0.7513148	0.68301346	0.62092132	0.56447393
NPV (E = Sum of C*D)	293,220.23	10,681.82	1,033.06	9,353.87	13,093.37	11,903.06	(2,844.95)
MACRS Depreciation Table
Year	5-Year
1	20%
2	32%
3	19.20%
4	11.52%
5	11.52%
6	5.76%