Question

You must evaluate the purchase of a proposed piece of equipment. The cost of the equipment is $50,000. The installation and transportation cost of bringing the equipment to its location is $6,000. The equipment falls into the MACRS 3-year class. The project is expected to increase revenues by $80,000 each year and increase operating costs (excluding depreciation) by $30,000 each year. This project leads to an increase in net operating working capital by $10,000. You can salvage the equipment for $10,000 at the end of the project. What is the project's cash flow in Years 1, 2, 3, 4? (use MACRS of 33%, 45%, 15%, 7%). Use the NPV and IRR criteria to evaluate this project. Is this project profitable? Use marginal tax rate of 21% and WACC of 10%. (You must show your full work to earn any credit for this question)

Answer 1

Cost of Equipment = $50,000
Installation and Transportation cost = $6,000

Total Capitalized cost = Cost of Equipment + Installation and Transportation cost
                                          = $50,000 + $6,000
                                          = $56,000

Calculation of Depreciation under MACRS and post tax Salvage Value :

Year	MACRS %	Depreciation = Total Capitalized Cost * MACRS %
1	33	18,480
2	45	25,200
3	15	8,400
4	7	3,920

Salvage Value of Equipment = 10,000
Profit on Sale of Equipment = 10,000
Tax on Profit on Sale of Equipment = $10,000 * 0.21
                                                                     = $2,100

Post Tax Salvage Value = Salvage Value – Tax on Profit on Sale of Equipment
                                             = 10,000 – 2,100
                                             = 7,900

a) Calculation of NPV :

PARTICULARS	Year	0	1	2	3	4
INCREMENTAL REVENUES		0.00	80000.00	80000.00	80000.00	80000.00
INCREMENTAL OPERATING COSTS		0.00	30000.00	30000.00	30000.00	30000.00
DEPRECIATION		0.00	18480.00	25200.00	8400.00	3920.00
EBIT		0.00	31520.00	24800.00	41600.00	46080.00
INCOME TAX @21%		0.00	6619.20	5208.00	8736.00	9676.80
UNLEVERED NET INCOME		0.00	24900.80	19592.00	32864.00	36403.20
ADD : DEPRECIATION		0.00	18480.00	25200.00	8400.00	3920.00
LESS : CAPITAL EXPENDITURE		56000.00	0.00	0.00	0.00	0.00
LESS : INCREASE IN NET WORKING CAPITAL		10000.00	0.00	0.00	0.00	0.00
ADD : POST TAX SALVAGE VALUE OF EQUIPMENT		0.00	0.00	0.00	0.00	7900.00
ADD : RECOVERY OF WORKING CAPITAL		0.00	0.00	0.00	0.00	10000.00
POUND FREE CASH FLOW		-66000.00	43380.80	44792.00	41264.00	58223.20
PRESENT VALUE FACTOR @10%		1	0.90909091	0.82644628	0.7513148	0.68301346
PRESENT VALUE @10%		-66000.00	39437.09	37018.18	31002.25	39767.23
NPV = SUM OF PRESENT VALUE AT EACH YEAR					81224.75

Since NPV is positive, the project is profitable.

Present Value Factor have been calculated as = (1/1+r)n

Where
r= Required rate of Return (Discount rate)
n= No of Periods

b) Calculation of IRR :
IRR is the rate at which the PV of Cash Inflows = PV of cash outflows i.e NPV of the project is 0.
Since at discount rate of 10.00% NPV is positive, IRR should be more than 10.00%

ASSUMING IRR TO BE 50.00% AND COMPUTING

PARTICULARS	Year	0	1	2	3	4
POUND FREE CASH FLOW		-66000.00	43380.80	44792.00	41264.00	58223.20
PRESENT VALUE FACTOR @50%		1	0.66666667	0.44444444	0.2962963	0.19753086
PRESENT VALUE @50%		-66000.00	28920.53	19907.56	12226.37	11500.88
NPV = SUM OF PRESENT VALUE AT EACH YEAR					6555.34

Since NPV is positive at discount rate of 50%, IRR should be more than 50%.

ASSUMING IRR TO BE 55.00% AND COMPUTING

PARTICULARS	Year	0	1	2	3	4
POUND FREE CASH FLOW		-66000.00	43380.80	44792.00	41264.00	58223.20
PRESENT VALUE FACTOR @55%		1	0.64516129	0.41623309	0.26853748	0.17324999
PRESENT VALUE @55%		-66000.00	27987.61	18643.91	11080.93	10087.17
NPV = SUM OF PRESENT VALUE AT EACH YEAR					1799.62

Since NPV is positive at discount rate of 55%, IRR should be more than 55%.

ASSUMING IRR TO BE 57.00% AND COMPUTING

PARTICULARS	Year	0	1	2	3	4
POUND FREE CASH FLOW		-66000.00	43380.80	44792.00	41264.00	58223.20
PRESENT VALUE FACTOR @57%		1	0.63694268	0.40569597	0.25840508	0.16458922
PRESENT VALUE @57%		-66000.00	27631.08	18171.93	10662.83	9582.91
NPV = SUM OF PRESENT VALUE AT EACH YEAR					48.75

Since NPV is marginally positive at discount rate of 57%, IRR should be slightly more than 57%.

ASSUMING IRR TO BE 57.06% AND COMPUTING :

PARTICULARS	Year	0	1	2	3	4
POUND FREE CASH FLOW		-66000.00	43380.80	44792.00	41264.00	58223.20
PRESENT VALUE FACTOR @57.06%		1	0.63669935	0.40538606	0.25810904	0.16433786
PRESENT VALUE @57.06%		-66000.00	27620.53	18158.05	10650.61	9568.28
NPV = SUM OF PRESENT VALUE AT EACH YEAR					-2.53

Since NPV is almost zero at 57.06%, IRR is 57.06%.

Since IRR is more than WACC the project is profitable.