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 1 20%

Year 2 32%

Year 3 19%

Year 4 12%

Year 5 12%

Year 6 5%

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

Statemnet showing depreciation

Year	Opening balance	Depreciation rate	Depreciation	Closing Balance
1	2050000	20%	410000	1640000
2	1640000	32%	656000	984000
3	984000	19%	389500	594500
4	594500	12%	246000	348500
5	348500	12%	246000	102500

Statement showing NPV

Particulars	0	1	2	3	4	5	NPV
Cost of new machine	-1800000
Installation expense	-250000
WC required	-30000
Salvage value + tax benefit on old machine 125000+40%(290000-125000) 125000+66000	191000
Savings in operating cost		650000	650000	650000	650000	650000
Depreciation		410000	656000	389500	246000	246000
PBT		240000	-6000	260500	404000	404000
Tax @ 40%		-96000	2400	-104200	-161600	-161600
PAT		144000	-3600	156300	242400	242400
Add: depreciation		410000	656000	389500	246000	246000
Annaul cash flow		554000	652400	545800	488400	488400
Salvage value (150000) - 40%(150000-102500) 150000 - 19000						131000
Release of WC						30000
Total cash flow	-1889000	554000	652400	545800	488400	649400
PVIF @ 15%	1.00	0.87	0.76	0.66	0.57	0.50
Present value	-1889000	481739.1	493308.1	358872.4	279244.3	322866.6	47030.48

1) Since NPV is positive project should be selected

2) NPV = 47030.48$

3) IRR is the rate where NPV is 0 at 16.046% NPV is 0

Particulars	0	1	2	3	4	5	NPV
Cost of new machine	-1800000
Installation expense	-250000
WC required	-30000
Salvage value + tax benefit on old machine 125000+40%(290000-125000) 125000+66000	191000
Savings in operating cost		650000	650000	650000	650000	650000
Depreciation		410000	656000	389500	246000	246000
PBT		240000	-6000	260500	404000	404000
Tax @ 40%		-96000	2400	-104200	-161600	-161600
PAT		144000	-3600	156300	242400	242400
Add: depreciation		410000	656000	389500	246000	246000
Annaul cash flow		554000	652400	545800	488400	488400
Salvage value (150000) - 40%(150000-102500) 150000 - 19000						131000
Release of WC						30000
Total cash flow	-1889000	554000	652400	545800	488400	649400
PVIF @ 16.046%	1.00	0.86	0.74	0.64	0.55	0.48
Present value	-1889000	477397.4	484456.2	349256.4	269312.6	308577.1	0

4) Payback period

Year	cash flow	Cummulative cashflow
1	554000	554000
2	652400	1206400
3	545800	1752200
4	488400	2240600
5	488400	2729000

using interpolation method we can find pay backperiod

Year	Cummulative cashflow
3	1752200
4	2240600
1	488400
	136800

=136800/488400

=0.28

Thus payback period = 3+0.48 = 3.48 years