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X Company is considering the replacement of an existing machine. The new machine costs $1.8 million...

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?

Solutions

Expert Solution

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


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