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 $400 for 6 years. Its current book value is $2,400, and it can be sold on an Internet auction site for $4,500 at this time. Thus, the annual depreciation expense is $2,400/6=$400 per year. 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 $8,200, and has an estimated useful life of 6 years with an estimated salvage value of $900. 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 allows for an output expansion, so sales would rise by $2,000 per year; the new machine's much greater efficiency would reduce operating expenses by $1,400 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 the project cost of capital is 14%. Should it replace the old steamer?

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

Answer 1

Solution:

Statement showing annual depreciation and incremental depreciation:

Year	Depreciation(Cost*Rate)	Depreciation of old steamer	Incremental depreciation
1	$8,200*20%=$1640	$400	$1240
2	$8,200*32%=$2,624	$400	$2,224
3	$8,200*19.20%=$1574.40	$400	$1174.40
4	$8,200*11.52%=$944.64	$400	$544.64
5	$8,200*11.52%=$944.64	$400	$544.64
6	$8200*5.76%=$472.32	$400	$72.32

Initial Cash outlay=Cost of Steamer-After tax sale proceeds of old steamer+Increase in working capital

  After tax sale proceeds of old steamer=(Sale price-Book value)(1-tax rate)

= ($4500-$2,400)(1-0.40)=$1260

Initial Cash outlay=$8,200-$1260+($2900-$700)

=$9140

Calculation of cash flows for each year

Year	1	2	3	4	5	6
Incremental sales	$2,000	$2,000	$2,000	$2,000	$2,000	$2,000
Less:Incremental cost	$1,400	$1,400	$1,400	$1,400	$1,400	$1,400
Less:Incremental depreciation	$1240	$2,224	$1174.40	$544.64	$544.64	$72.32
Earning before tax(EBT)	-$640	-$1624	-$574.40	$55.36	$55.36	$527.68
Less:Tax @40%	0	0	0	$22.14	$22.14	$211.07
EAT	-$640	-$1624	-$574.40	$33.22	$33.22	$316.61
Add:Depreciation	$1240	$2,224	$1174.40	$544.64	$544.64	$72.32
Add:Reversal of working capital	0	0	0	0	0	$2200
After tax sale value of old steamer($800*0.60)	0	0	0	0	0	$480
After tax net cash flows(a)	$600	$600	$600	$577.86	$577.86	$3068.93
Present value factor @14%(b)	0.877	0.769	0.675	0.592	0.519	0.456
Present value (a*b)	$526.20	$461.40	$405.00	$342.09	$299.90	$1399.43

Net Present value=Sum of Present value After tax net cash flows-Initial cash outflow

= $(526.20+461.40+405.00+342.09+299.90+1399.43)-$9140

=$3434.02-$9,140

=-$5705.98

Since the NPV of new steamer is negative($ 5705.98 ),hence old steamer should not be replaced.