Question

4) Your company is considering a project that will generate sales revenue of $90 million in Year 1. Revenue is expected to be flat for subsequent years. The project requires working capital equal to 16% of sales revenue, and has total operating costs excluding depreciation equal to 50% of sales. The equipment has a 3 year MACRS life and can be purchased and installed for $100 million. The project will end in three years. At that time, the equipment can be sold for $4.2 million. Your company’s tax rate is 25%.

a) Find the initial cash flow (Yr. 0).

b) Find the operating cash flows (Yrs. 1-3).

MACRS Depreciation Tables

Ownership Year	3-Year	5-Year	7-Year	10-Year
1	33.33%	20.00%	14.29%	10.00%
2	44.44	32.00	24.49	18.00
3	14.82	19.20	17.49	14.40
4	7.41	11.52	12.49	11.52
5		11.52	8.93	9.22
6		5.76	8.92	7.37
7			8.93	6.55
8			4.46	6.55
9				6.55
10				6.55
11				3.29
	100.0%	100.0%	100.0%	100.0%

5)   Using the information from Problem 4:

         a)   Find the after-tax cash flow from the sale of the equipment.

         b)   Find the total flow that occurs in Yr. 3.

Answer 1

4)

a) initial cash flow (Yr. 0) = cost of equipment + increase in working capital

increase in working capital will be recovered at the end of the project.

initial cash flow (Yr. 0) = $100 million + ($90million*16%) = $100 million + $14.4 million = $114.4 million

b) Operating cash flow = [(revenue - operating costs - depreciation)*(1-tax rate)] + depreciation

depreciation year 1 = cost of equipment*year 1 MACRS rate = $100 million*33.33% = $33.33 million

depreciation year 2 = cost of equipment*year 2 MACRS rate = $100 million*44.44% = $44.44 million

depreciation year 3 = cost of equipment*year 3 MACRS rate = $100 million*14.82% = $14.82 million

Operating cash flow year 1 = [($90 - $90*50% - $33.33)*(1-0.25)] + $33.33 = ($90 - $45 - $33.33)*0.75 + $33.33 = $11.67*0.75 + $33.33 = $8.7525 + $33.33 = $42.0825 million

Operating cash flow year 2 = [($90 - $90*50% - $44.44)*(1-0.25)] + $44.44 = ($90 - $45 - $44.44)*0.75 + $44.44 = $0.56*0.75 + $44.44 = $0.42 + $44.44 = $44.86 million

Operating cash flow year 3 = [($90 - $90*50% - $14.82)*(1-0.25)] + $14.82 = ($90 - $45 - $14.82)*0.75 + $14.82 = $30.18*0.75 + $14.82 = $22.635 + $14.82 = $37.455 million

5)

a) after-tax cash flow from sale of equipment = Sale value - tax on capital gain

tax on capital gain = (sale value - book value)*tax rate

book value = cost of equipment*year 4 unapplied MACRS rate = $100 million*7.41% = $7.41 million

tax on capital gain = ($4.2 - $7.41)*25% = -$3.21*25% = -$0.8025 million

after-tax cash flow from sale of equipment = $4.2 - (-$0.8025) = $4.2 + $0.8025 = $5.0025 million

b) total flow in year 3 = Operating cash flow year 3 + after-tax cash flow from sale of equipment + recovery of increase in working capital

total flow in year 3 = $37.455 million + $5.0025 million + $14.4 million = $56.8575 million