Question 1 (20 points): Suppose you need to decide whether to keep an old machin

Question

Question 1 (20 points): Suppose you need to decide whether to keep an old machine or replace it with a new one: New machine: If you decide to replace the old machine with a new one, it requires capital cost of $1,000,000 in year zero (and zero salvage value for the old machine). Capital cost is depreciable from year 1 to year 8 (over eight years) based on MACRS 7-year life depreciation with the half year convention (table A-1 at IRS). The new machine can produce income of $450,000 and operating cost of S150,000 per year for 8 years (from year 1 to year 8) and it will have salvage value of 200,000 at the end (with zero book value). Old machine: Old machine can operate only until year 5 with the revenue and operating cost of $350,000 and S200,000 per year (from year 0 to year 5). Old machine will have zero salvage value. Note that the old machine is already in place and operating. However, installing the new machine takes one year and revenue starts from year l. Consider income tax of 40% and minimum rate ofreturn 10%. Construct incremental analysis and conclude which alternative is more economically satisfactory? Please show your work.

Explanation / Answer

For replacement project,
The initial outlay = FCinv = WCinv - Salvage + Tax*(Salvage-Bookvalue)
=1000,000
(as there is no new WCinv and the salvage and book value of old machine is zero)

After tax operating cashflow = (Change in sales - change in cost)(1-tax)+(change in depreciation)*tax
and as the old machine is fully depreciated the change in depreciation is the MACRS deprecitiaon on new machine only

Terminal year cashflow = Change in salvage value + WCinv - Tax*(change in salvage-Change in book value)
As the new machine salvage value is 200,000 (thus change in salavge is 200,000-0 which is 200,000) and there is no book value of new and old machine as they are depreciated to zero
=200,000+0-0.4(200000-0)
=200,000+80000
=280,000
and this will add to the final year ATOCF

Please see below the schedule for NPV:

Initial outlay of 1,000,000

Formula = 450000-350000

Formula = 150000-200000

Formula = 1000,000*MACRS

Change in sales - change in cost)(1-tax)+(change in depreciation)*tax

Year

Change in sales

Change in costs

MACRS

Depreciation

ATOCF

0

-1000000

1

100000

-50000

0.1429

142900

147160

2

100000

-50000

0.2449

244900

187960

3

100000

-50000

0.1749

174900

159960

4

100000

-50000

0.1249

124900

139960

5

100000

-50000

0.0893

89300

125720

6

100000

-50000

0.0892

89200

125680

7

100000

-50000

0.0893

89300

125720

8

100000

-50000

0.0446

44600

387840

NPV at 10%

-$91,504.261

IRR

7.388%

As the NPV of the new replacement project is negative and IRR<Required rate of return we will not accept the project

Initial outlay of 1,000,000

Formula = 450000-350000

Formula = 150000-200000

Formula = 1000,000*MACRS

Change in sales - change in cost)(1-tax)+(change in depreciation)*tax

Year

Change in sales

Change in costs

MACRS

Depreciation

ATOCF

0

-1000000

1

100000

-50000

0.1429

142900

147160

2

100000

-50000

0.2449

244900

187960

3

100000

-50000

0.1749

174900

159960

4

100000

-50000

0.1249

124900

139960

5

100000

-50000

0.0893

89300

125720

6

100000

-50000

0.0892

89200

125680

7

100000

-50000

0.0893

89300

125720

8

100000

-50000

0.0446

44600

387840

NPV at 10%

-$91,504.261

IRR

7.388%

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