Question

Fairfax Paint operates stores in Virginia. The firm is evaluating the Vienna project, which would involve opening a new store in Vienna. During year 1, Fairfax Paint would have total revenue of 362,000 dollars and total costs of 280,000 dollars if it pursues the Vienna project, and the firm would have total revenue of 310,000 dollars and total costs of 253,000 if it does not pursue the Vienna project. Depreciation taken by the firm would be 65,000 dollars if the firm pursues the project and 45,000 dollars if the firm does not pursue the project. The tax rate is 45 percent. What is the relevant operating cash flow (OCF) for year 1 of the Vienna project that Fairfax Paint should use in its NPV analysis of the Vienna project? What if the project would require an initial investment in equipment of 790,000 dollars that would be depreciated using MACRS where the depreciation rates in years 1, 2, 3, and 4 are 40 percent, 22 percent, 22 percent, and 16 percent, respectively. At the end of the project in 2 years, the equipment would be sold for an expected after-tax cash flow of 12,800 dollars. In year 2 of the project, relevant revenue associated with the project would be 311,800 dollars and relevant costs associated with the project would be 295,600 dollars. The tax rate is 40 percent. What is the relevant operating cash flow (OCF) associated with the project expected to be in year 2?

Answer 1

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. Figures in parenthesis, if any, mean negative values. All financials are in $.

Particulars	Linkage	If Vienna Project is Pursued	Vienna project not pursued
Revenue	A	362,000	310,000
Expenses	B	(280,000)	(253,000)
Depreciation	C	(65,000)	(45,000)
EBIT	D = A + B + C	17,000	12,000
Taxes @ 45%	E = -D x 45%	(7,650)	(5,400)
NOPAT	F = D + E	9,350	6,600
Add back depreciation	G = -C	65,000	45,000
OCF	F + G	74,350	51,600

Hence, the relevant operating cash flow (OCF) for year 1 of the Vienna project that Fairfax Paint should use in its NPV analysis of the Vienna project = Incremental OCF = 74,350 - 51,600 = $  22,750

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If MACRS depreciation is followed on the capex of 790,000 dollars, depreciation in year 1 if Vienna project is pursued = Depreciation without Vienna project + year 1 MACRS depreciation of the new equipment = 45,000 + 40% x 790,000 = 361,000

We repeat the same table as above with the new depreciation figure:

Particulars	Linkage	If Vienna Project is Pursued	Vienna project not pursued
Revenue	A	362,000	310,000
Expenses	B	(280,000)	(253,000)
Depreciation	C	(361,000)	(45,000)
EBIT	D = A + B + C	(279,000)	12,000
Taxes @ 45%	E = -D x 45%	125,550	(5,400)
NOPAT	F = D + E	(153,450)	6,600
Add back depreciation	G = -C	361,000	45,000
OCF	F + G	207,550	51,600

Hence, the relevant operating cash flow (OCF) for year 1 of the Vienna project that Fairfax Paint should use in its NPV analysis of the Vienna project = Incremental OCF = 207,550 - 51,600 = $ 155,950

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For year 2,

If MACRS depreciation is followed on the capex of 790,000 dollars, depreciation in year 2 due to Vienna project = year 2 MACRS depreciation of the new equipment = 22% x 790,000 = 173,800

We make the table again this time with finanacials for year 2:

Particulars	Linkage	Project cash flows
Relevant Revenue	A	362,000
Relevant expenses	B	(280,000)
Relevant Depreciation	C	(173,800)
EBIT	D = A + B + C	(91,800)
Taxes @ 45%	E = -D x 45%	41,310
NOPAT	F = D + E	(50,490)
Add back depreciation	G = -C	173,800
OCF	F + G	123,310

Hence, the OCF for Year 2 = $ 123,310. Please note that cash flow on sale of the asset will not be part of the OCF.