Question

The Woodruff Corporation purchased a piece of equipment three years ago for $247,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $92,250.

A new piece of equipment can be purchased for $305,000. It also has an ADR of eight years.

Assume the old and new equipment would provide the following operating gains (or losses) over the next six years:

Year New Equipment Old Equipment 1............... $78,250 $25,500 2............... 75,250 15,000 3............... 68,750 9,500 4............... 58,500 6,250 5............... 51,000 6,500 6............... 44,250 -8,250

The firm has a 36 percent tax rate and a 9 percent cost of capital.

What is the net cost of the new equipment? Round your solution to two decimal places.

What is the present value of incremental benefits? Round your solution to two decimal places.

What is the NPV of this replacement decision? Round your solution to two decimal places.

Answer 1

A. Calculating net cost of new equipment

Book value of old equipment
(ADR of 8 years indicates the use of the 5-year MACRS schedule)
Year	Depreciation	% Depreciation	Annual depreciation
1	247000	0.2	49400
2	247000	0.32	79040
3	247000	0.192	47424
Total Depreciation rate			$175864

	Purchase price	247000
(-)	Total depreciation to date	175864
	Book Value	71136
	Tax obligation on sale
	Sale price	92250
(-)	Book value	71136
	Taxable gain	21114
(*)	Tax rate	36%
	Taxes	7601.04
	Cash Inflow from the sale of old equipment
	Sale price	92250
(-)	Taxes on sale	7601
		84648.96
	New cost of the equipment
	Purchase price	305000
(-)	Cash inflow from sale of old equipment	84648.96
	Net cost	220351.04

B. Present value of incremental benefits

Depreciation schedule of this new equipment
(ADR of 8 years indicates the use of the 5-year MACRS schedule)
Year	Depreciation	% Depreciation (table 12-9)	Annual depreciation
1	305000	0.2	61000
2	305000	0.32	97600
3	305000	0.192	58560
4	305000	0.115	35075
5	305000	0.115	35075
6	305000	0.058	17690
			305000

Depreciation schedule for the remaining years of the old equipment
Year*	Depreciation rate	% Depreciation (table 12-9)	Annual depreciation
1	247000	0.115	28405
2	247000	0.115	28405
3	247000	0.058	14326
*The next three years represent the last three years of the old equipment

Incremental depreciation & tax shield benefits
Year	Depreciation on new equipment	Depreciation on old equipment	Incremental depreciation	Tax rate	Tax shield benefits
1	61000	28405	32595	0.36	11734.20
2	97600	28405	69195	0.36	24910.20
3	58560	14326	44234	0.36	15924.24
4	35075		35075	0.36	12627.00
5	35075		35075	0.36	12627.00
6	17690		17690	0.36	6368.40

After cost savings
New equipment	Old equipment	Cost savings	(1- Tax rate)	After tax savings
78250	25500	52750	0.64	33760
75250	15000	60250	0.64	38560
68750	9500	59250	0.64	37920
58500	6250	52250	0.64	33440
51000	6500	44500	0.64	28480
44250	-8250	52500	0.64	33600

Present value of the toal incremental benefits
Year	Tax shield benefits from depreciation	After tax cost savings	Total Annuity benefits	Present value Factor %	Present value
1	11734.20	33760	45494.20	0.917	41718.18
2	24910.20	38560	63470.20	0.842	53441.91
3	15924.24	37920	53844.24	0.772	41567.75
4	12627.00	33440	46067.00	0.708	32615.44
5	12627.00	28480	41107.00	0.65	26719.55
6	6368.40	33600	39968.40	0.596	23821.17
Present value of incremental benefits					219884.00

C. NPV of this replacement decision

Net present Value
Present value of incremental benefits	219884
Net cost of new equipment	220351.04
Net present value	-467.04

Based on the Net present value analysis, the equipment should not be replaced.