Question

The Gilbert Instrument Corporation is considering replacing the wood steamer it currently uses to shape guitar sides. The steamer has 6 years of remaining life. If kept, the steamer will have depreciation expenses of $650 for 5 years and $325 for the sixth year. Its current book value is $3,575, and it can be sold on an Internet auction site for $4,150 at this time. If the old steamer is not replaced, it can be sold for $800 at the end of its useful life.

Gilbert is considering purchasing the Side Steamer 3000, a higher-end steamer, which costs $12,000, and has an estimated useful life of 6 years with an estimated salvage value of $1,200. This steamer falls into the MACRS 5-years class, so the applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The new steamer is faster and would allow for an output expansion, so sales would rise by $2,000 per year; even so, the new machine's much greater efficiency would reduce operating expenses by $1,500 per year. To support the greater sales, the new machine would require that inventories increase by $2,900, but accounts payable would simultaneously increase by $700. Gilbert's marginal federal-plus-state tax rate is 40%, and its WACC is 14%.

Should it replace the old steamer?

The old steamer _________shouldshould not be replaced.

What is the NPV of the project? Do not round intermediate calculations. Round your answer to the nearest dollar.

$  

Should it replace the old steamer?

The old steamer be replaced.

What is the NPV of the project? Do not round intermediate calculations. Round your answer to the nearest dollar.

$  

First determine the net cash flow at t = 0:

Purchase price	($12,000)
Sale of old machine	4,150
Tax on sale of old machine	(230)a
Change in net working capital	(2,200)b
Total investment	($10,280)

^aThe market value is $4,150 – $3,575 = $575 above the book value. Thus, there is a $575 recapture of depreciation, and Gilbert would have to pay 0.40($575) = $230 in taxes.
^b The change in net working capital is a $2,900 increase in current assets minus a $700 increase in current liabilities, which totals to $2,200.

Now, examine the annual cash inflows:

Sales increase	$2,000
Cost decrease	1,500
Increase in pre-tax revenues	$3,500

After-tax revenue increase:

$3,500(1 – T) = $3,500(0.60) = $2,100.

Depreciation:

Year	1	2	3	4	5	6
New a	$2,400	$3,840	$2,304	$1,382	$1,382	$691
Old	650	650	650	650	650	325
Change	$1,750	$3,190	$1,654	$732	$732	$366
Depreciation tax savings b	$700	$1,276	$662	$293	$293	$146

^a Depreciable basis = $12,000. Depreciation expense in each year equals depreciable basis times the MACRS percentage allowances of 0.2000, 0.3200, 0.1920, 0.1152, 0.1152, and 0.0576 in Years 1-6, respectively.
^b Depreciation tax savings = T(ΔDepreciation) = 0.4(ΔDepreciation).

Now recognize that at the end of Year 6 Gilbert would recover its net working capital investment of $2,200, and it would also receive $1,200 from the sale of the replacement machine. However, since the machine would be fully depreciated, the firm must pay 0.40($1,200) = $480 in taxes on the sale. Also, by undertaking the replacement now, the firm forgoes the right to sell the old machine for $800 in Year 6; thus, this $800 in Year 6 must be considered an opportunity cost in that year. Taxes of $800(0.4) = $320 would be due because the old machine would be fully depreciated in Year 6, so the opportunity cost of the old machine would be $800 – $320 = $480.

Finally, place all the cash flows on a time line:

0

1

2

3

4

5

6

	14%

Net investment	(10,280)
After-tax revenue increase		2,100	2,100	2,100	2,100	2,100	2,100
Depreciation tax savings		700	1,276	662	293	293	146
Working capital recovery							2,200
Salvage value of new machine							1,200
Tax on salvage value of new machine							(480)
Opportunity cost of old machine							(480)
Project cash flows	(10,280)	2,800	3,376	2,762	2,393	2,393	4,686

Note: While the calculations above show values rounded to the nearest whole number, unrounded values should be used in all calculations above.

The net present value of this incremental cash flow stream, when discounted at 14%, is $1,433. Thus, the replacement should be made.

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