Question

X Company is considering the replacement of an existing machine. The new machine costs $1.8 million and requires installation costs of $250,000. The existing machine can be sold currently for $125,000 before taxes. The existing machine is 3 years old, cost $1 million when purchased, and has a $290,000 book value and a remaining useful life of 5 years. It was being depreciated under MACRS using a 5-year recovery period. If it is held for 5 more years, the machine’s market value at the end of year 5 will be zero. Over its 5-year life, the new machine should reduce operating costs by $650,000 per year, and will be depreciated under MACRS using a 5-year recovery period. The new machine can be sold for $150,000 net of removal and cleanup costs at the end of 5 years. A $30,000 increase in net working capital will be required to support operations if the new machine is acquired. The firm has adequate operations against which to deduct any losses experienced on the sale of the existing machine. The firm has a 15% cost of capital, is subject to a 40% tax rate and requires a 42-month payback period for major capital projects.

5-Year MACRS

Year 120%

Year 232%

Year 319%

Year 412%

Year 512%

Year 65%

1. Should they accept or reject the proposal to replace the machine?

2. What is the NPV?

3. What is the IRR?

4. What is the payback period?

Answer 1

1. they should reject the proposal to replace the machine.

2. NPV = -5516.34

3. IRR = 14.88%

4. payback period = 42.36 months

Calcualtion of the all option are given below -

	Dep. under MACRS		25%	32%	19%	12%	12%
	year	0	1	2	3	4	5
	New machine cost	2050000
	Sold existing machine	125000
	saving in cost by new machine		650000	650000	650000	650000	650000
	increase in net working capital	30000
less	Depriciation		512500	656000	389500	246000	246000
	EBIT		137500	-6000	260500	404000	404000
	Sold of new machine						150000
less	Tax @40%		55000	0	104200	161600	221600
	EAT		82500	-6000	156300	242400	332400
add	Dep. under MACRS		512500	656000	389500	246000	246000
	Earning after depriciation		595000	650000	545800	488400	578400
add	receovered working capital						30000
	Cash flow after tax	-1955000	595000	650000	545800	488400	608400
	Discounting @ 15%	1	0.869565	0.756144	0.657516	0.571753	0.497177
	Present value @ 15%	-1955000	517391.3	491493.4	358872.4	279244.3	302482.3
	Net present value							-5516.34
	Internal rate of return							14.88%

Calculatio of payback period -

cum. Cash flow

595000

1245000

1790800

2279200

2887600

payback period = 3 years + [(2050000 - 1790800)/(2279200 - 1790800)] *12

= 3 years + 259200/488400*12

= 36 months + 6.36 months

= 42.36 months

Note - MACRS dep assumes 25% in first year. reason being the given depriciation rate are based on half year convention. however saving in cost are for full year that why 5% of dep given in last add in first year.

Please comment in case of any clarification required.