Question

The Woodruff Corporation purchased a piece of equipment three years ago for $210,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $86,500. A new piece of equipment can be purchased for $304,000. 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 $79,000 $23,500

2 78,000 17,500

3 71,500 8,500

4 58,250 6,750

5 48,500 5,500

6 44,500 -5,250

The firm has a 25 percent tax rate and a 9 percent cost of capital.

a. What is the net cost of the new equipment?

b. What is the present value of the incremental benefits?

c. What is the NPV of this replacement decision?

Answer 1

1. ADR of 8 years implies MACRS schedule of 5 years to be following for depreciation

2. Net Sales value of old equipment now:

Old equipment purchase price ( 3 years ago)	210,000
Less:
Depreciaion of year -3 (under MACRS schedule) at 20%	42,000	(210,000*20%)
Depreciaion of year -2 (under MACRS schedule) at 32%	67,200	(210,000*32%)
Depreciaion of year -1 (under MACRS schedule) at 19.2%	40,320	(210,000*19.2%)
Total depreciation from year 1 to 3	149,520
Net Book Value	60,480	(210,000-149,520)
Sale of old equipment now	86,500
Profit	26,020	(86,500-60,480)
Tax on profit	6,505	(26,020*25%)
Net Sales value of equipment now	79,995	(86,500-6,505)

3. Yearly Operating Gains

	Operating gains (before tax)	Operating gains (after tax) = (Operating gains (before tax) *(100% - 25%)
Years	New Equipment	Old Equipment	Incremental (New Equipment - Old Equipment)	New Equipment	Old Equipment	Incremental (New Equipment - Old Equipment)
1	79,000	23,500	55,500	59,250	17,625	41,625
2	78,000	17,500	60,500	58,500	13,125	45,375
3	71,500	8,500	63,000	53,625	6,375	47,250
4	58,250	6,750	51,500	43,688	5,063	38,625
5	48,500	5,500	43,000	36,375	4,125	32,250
6	44,500	(5,250)	49,750	33,375	(3,938)	37,313

4. Yearly depreciation and tax shield on depreciation

	New Equipment	Old Equipment
Years	Rate	Depreciation (New equipment cost of $304,000*Rate)	Tax shield (Depreciation * 25%)	Rate	Depreciation (New equipment cost of $210,000*Rate)	Tax shield (Depreciation * 25%)
1	20.00%	60,800	15,200	11.52%	24,192	6,048
2	32.00%	97,280	24,320	11.52%	24,192	6,048
3	19.20%	58,368	14,592	5.76%	12,096	3,024
4	11.52%	35,021	8,755
5	11.52%	35,021	8,755
6	5.76%	17,510	4,378

5. Discount factor at 9%

Year 1 = 1/(100%+9%)^1 = 0.917

Year 2 = 1/(100%+9%)^2 = 0.842

Year 3 = 1/(100%+9%)^3 = 0.772

Year 4 = 1/(100%+9%)^4 = 0.708

Year 5 = 1/(100%+9%)^5 = 0.650

Year 6 = 1/(100%+9%)^6 = 0.596

6. Calculation of Net-Present Value

		Cash-flows		Present value of cash-flows (Cash-flows * Present Value factor at 9%
Years	Particulars	New Equipment	Old Equipment	Present Value factor at 9%	New Equipment	Old Equipment	Incremental (New equipment - Old equipment)
0	Purchase cost	(304,000)	-	1.000	(304,000)	-	(304,000)
0	Sale of old equipment	79,995	-	1.000	79,995	-	79,995
0	Initial Outlay	(224,005)	-	1.000	(224,005)	-	(224,005)
1	Operating Gains (after tax)	59,250	17,625	0.917	54,358	16,170	38,188
2	58,500	13,125	0.842	49,238	11,047	38,191
3	53,625	6,375	0.772	41,408	4,923	36,486
4	43,688	5,063	0.708	30,949	3,586	27,363
5	36,375	4,125	0.650	23,641	2,681	20,960
6	33,375	(3,938)	0.596	19,900	(2,348)	22,248
1	Tax shield on Depreciation	15,200	6,048	0.917	13,945	5,549	8,396
2	24,320	6,048	0.842	20,470	5,090	15,379
3	14,592	3,024	0.772	11,268	2,335	8,933
4	8,755	-	0.708	6,202	-	6,202
5	8,755	-	0.650	5,690	-	5,690
6	4,378	-	0.596	2,610	-	2,610
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