Question

Pinnacle Custom Home Builders purchased a 40 foot articulating boom lift three years ago for $55,000. The equipment has been depreciated under the 5-year MACRS schedule (20%, 32%, 19%, 12%, 12% & 5%). The old equipment can be sold for $35,000.

Pinnacle is considering the purchase of a new 60 foot articulating boom lift that would allow the company to complete nearly all of its construction projects without the need for costly rental lifts. The new lift could be purchased for $127,000 and would also fall under the 5-year MACRS depreciation schedule.

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

	New Equipment	Old Equipment
1.............	$40,000	$25,000
2.............	38,000	16,000
3.............	35,000	9,000
4.............	30,000	8,000
5.............	25,000	6,000
6.............	22,500	5,000

The firm has a 30 percent tax rate and a 7 percent cost of capital. Should the new equipment be purchased to replace the old equipment? Briefly justify your answer.

All interim calculations (including TVM) must be made using the built-in Excel functions and your submission should be in good form (i.e., neat and easy to follow with descriptive labels, etc.).

Answer 1

Step 1: Calculate Annual Depreciation on Old Equipment Upto 3 Years

The annual depreciation on old equipment upto 3 years is determined as below:

Year	Cost of Old Equipment (1)	MACRS Depreciation Rate (2)	Annual Depreciation (1*2)
1	55,000	20%	11,000
2	55,000	32%	17,600
3	55,000	19%	10,450
Total Depreciation			$39,050

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Step 2: Calculate Book Value of Old Equipment After 3 Years and Gain/Loss on Sale of Old Equipment

The book value and gain/loss on sale of old equipment is arrived as below:

Book Value of Old Equipment After 3 Years = Cost of Old Equipment - Total Depreciation on Old Equipment Upto 3 Years = 55,000 - 39,050 = $15,950

Gain on Sale of Old Equipment = Sale Price of Old Equipment - Book Value of Old Equipment After 3 Years = 35,000 - 15,950 = $19,050

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Step 3: Calculate Net Cost of New Equipment

The net cost of new equipment is calculated as follows:

Tax Loss on Sale of Old Equipment = Gain on Sale of Old Equipment*Tax Rate = 19,050*30% = $5,715

Net Cash Inflow from Sale of Old Equipment = Sale Price of Old Equipment - Tax Loss on Sale of Old Equipment = 35,000 - 5,715 = $29,285

Net Cost of New Equipment = Purchase Price of New Equipment - Net Cash Inflow from Sale of Old Equipment = 127,000 - 29,285 = $97,715

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Step 4: Calculate Annual Depreciation on New Equipment

The value of annual depreciation on new equipment is determined as follows:

Year	Cost of New Equipment (3)	MACRS Depreciation Rate (4)	Annual Depreciation (3*4)
1	127,000	20%	25,400
2	127,000	32%	40,640
3	127,000	19%	24,130
4	127,000	12%	15,240
5	127,000	12%	15,240
6	127,000	5%	6,350
Total			$127,000

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Step 5: Calculate Annual Depreciation on Old Equipment for Remaining 3 Years

The annual depreciation on old equipment for remaining 3 years is arrived as below:

Year	Cost of Old Equipment (5)	MACRS Depreciation Rate (5)	Annual Depreciation (5*6)
4	55,000	12%	6,600
5	55,000	12%	6,600
6	55,000	5%	2,750
Total Depreciation			$15,950

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Step 6: Calculate Annual Depreciation Tax Shield

The value of annual tax shield is calculated as follows:

Year	Depreciation on New Equipment	Depreciation on Old Equipment	Incremental Depreciation (7)	Tax Rate (8)	Annual Tax Shield (7*8)
1	25,400	6,600	18,800	30%	5,640
2	40,640	6,600	34,040	30%	10,212
3	24,130	2,750	21,380	30%	6,414
4	15,240	0	15,240	30%	4,572
5	15,240	0	15,240	30%	4,572
6	6,350	0	6,350	30%	1,905

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Step 7: Calculate Incremental After-Tax Cash Inflow

The value of annual incremental after-tax cash inflow determined as follows:

Year	Cash Inflow (New Equipment)	Cash Inflow (Old Equipment)	Incremental Cash Inflow (9)	(1-Tax Rate) (10)	After-Tax Cash Inflow (9*10)
1	40,000	25,000	15,000	70%	10,500
2	38,000	16,000	22,000	70%	15,400
3	35,000	9,000	26,000	70%	18,200
4	30,000	8,000	22,000	70%	15,400
5	25,000	6,000	19,000	70%	13,300
6	22,500	5,000	17,500	70%	12,250

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Step 8: Calculate Total Annual Benefits

The value of total annual benefits is arrived as follows:

Year	Incremental Cash Flow	Annual Tax Shield	Total Annual Benefits
1	10,500	5,640	16,140
2	15,400	10,212	25,612
3	18,200	6,414	24,614
4	15,400	4,572	19,972
5	13,300	4,572	17,872
6	12,250	1,905	14,155

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Step 9: Calculate Net Present Value

The net present value can be calculated with the use of following formula:

Net Present Value = -Net Cost of New Equipment + Annual Benefit Year 1/(1+Cost of Capital)^1 + Annual Benefit Year 2/(1+Cost of Capital)^2 + Annual Benefit Year 3/(1+Cost of Capital)^3 + Annual Benefit Year 4/(1+Cost of Capital)^4 + Annual Benefit Year 5/(1+Cost of Capital)^5 + Annual Benefit Year 6/(1+Cost of Capital)^6

Substituting values in the above formula, we get,

Net Present Value = -97,715 + 16,140/(1+7%)^1 + 25,612/(1+7%)^2 + 24,614/(1+7%)^3 + 19,972/(1+7%)^4 + 17,872/(1+7%)^5 + 14,155/(1+7%)^6 = -$2,756.91

The new equipment should not be purchased as it results in a negative NPV of $2,756.91.