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

Let us calculate the NPV , IRR and Pay back period, accordingly we can decide whether to go for the project or no.

Initial Investment Outlay--->Cost of the Machine + Installation Cost + Working Capital Requirements - Salvage value of the old machine + Tax( Salvage of Old Machine - Book value of Old Machine)

Therefore,

Initial investment outlay = $1800000 + $250000 + $30000 - $125000 + 0.4($125000 - $290000)

           = $1889000

Lets calculate the Incremental Operating Cash flows for 5 years now.

Change in Cash Flow = (Change in Sales - Change in Costs) (1-T) + Tax savings due to                                                depreciation

Therefore,

CF 1 = [0-(-$650000)](1- 0.4) + 0.4($410000 - $120000) = $506000

CF 2 = [0-(-$650000)](1- 0.4) + 0.4($656000 - $120000) = $604400

CF 3 = [0-(-$650000)](1- 0.4) + 0.4($389500 - $60000) = $521800

CF 4 = [0-(-$650000)](1- 0.4) + 0.4($246000 - $0)       = $488400

CF 5 = [0-(-$650000)](1- 0.4) + 0.4($246000 - $0) = $488400

Old machine has been depreciated to Zero in the 3rd year hence there is no depreciation is charged in the 4th and 5th year.

Terminal year Cash flow :-

Salvage( New Machine):- $150000

Salvage ( Old Machine) :- 0 ( mentioned in the question)

Working Capital Released :- $30000

Profit on sale of new machine = $150000 - $102500= $47500

Profit on sale of old machine = $0

Tax on sale of Machines = $47500*40%= $19000

Therefore Terminal Cash Flow = ($150000-0)+ $30000 - 0.4(47500)=$161000.

As we have all the required cash flows now, Lets calculate NPV

= -$1889000 + $506000*(1/1.15) + $604400(1/1.15)² + $521800(1/1.15)³ + $488400(1/1.15)⁴ +

($488400+$161000)(1/1.15)⁵

NPV = -$46783.94

IRR = 13.96%

PayBack period

Year	Cashflow	Cumulative CF
1	506000	506000
2	604400	1110400
3	521800	1632200
4	488400	2120600
5	488400	2609000

Hence PayBack Period =

3 years + (1889000-1632200) / (2120600 - 1632200) = 3 Years and 6 months = 42 months approx.

As per our calculations ,

The Company X should not accept the Propsal as the NPV is negative (-$46783).

The IRR for the company is 13.96%

PayBack period for the project is 3 years and 6 months i.e. 42 months approx. which is as per the company requirement but company should not accept the project the NPV is negative and will not be profitable for the company.