Economic Income and Total after-tax cash flow

A system purchased:
price = 700,000
shipping, site preparation, and installation cost = 100,000
Δinventory = 50,000
Δaccounts payable = 20,000

sale price = 75,000

Relevant Cash Flows for a Project

Year	1	2	3	4	Total
Sales	750,000	750,000	750,000	750,000
Variable costs	225,000	225,000	225,000	225,000
Fixed expense	75,000	75,000	75,000	75,000
Depreciation	264,000	360,000	120,000	56,000	(*11) 800,000
Earnings before tax (EBT)	186,000	90,000	330,000	394,000
after-tax cash flow	375,600	414,000	318,000	(*12) 292,400
Net income (*1)	(*2) 111,600	(*3) 54,000	(*4) 198,000
Tax rate (*5)	(*6) 40%	(*7) 40%	(*8) 40%	(*9) 40%
A system-related cash flow	(*10) -830,000			75,000
Total after-tax cash flow	375,600-830,000 =-454,400	414,000	318,000	292,400+75,000 = 367,400

WACC = 8%


(*1) Net income = Total after-tax cash flow - Depreciation
(*2) 375,600 - 264,000 = 111,600
(*3) 414,000 - 360,000 = 54,000
(*4) 318,000 - 120,000 = 198,000
(*5) EBT * (1-t) = Net income = Total after-tax cash flow - Depreciation
t = 1-Net income/EBT = 1-(Total after-tax cash flow - Depreciation)/EBT
(*6) t = 1-Net income/EBT = 1-111,600/186,000 = 40%
(*7) t = 1-Net income/EBT = 1-54,000/90,000 = 40%
(*8) t = 1-Net income/EBT = 1-198,000/330,000 = 40%
(*9) given based on the result of (*6), (*7), and (*8)
(*10) Initial investment outlay = (price + shipping, site preparation, and installation cost) + increase in net working capital  = (700,000 + 100,000) + (50,000 - 20,000) = 800,000 + 30,000 = 830,000
(*11) 264,000 + 360,000 + 120,000 + 56,000

(*12) EBT * (1-t) = Net income = Total after-tax cash flow - Depreciation
Total after-tax cash flow = EBT * (1-t) + Depreciation = 394,000 * (1-40%) + 56,000 = 292,400
or
(S-C)(1-t) + D*t = (750,000-225,000-75,000)(1-40%) + 56,000*40% = 270,000 + 22,400 = 292,400

Terminal year after-tax non-operating cash flow (TNOCF) = Sal_T + NWCInv - t * (Sal_T - B_T)
= 75,000 + (50,000-20,000) - 40% * (75,000 - 0) = 75,000
B_T=0 since original (price + shipping, site preparation, and installation cost) = 800,000 = cumulative depreciation at Year 4

Why does NWCInv have positive sign and need to be added back?
You spend some money at the start of the project on NWCInv to start up the capital budgeting project. When the project ends - you get that money back (it gets freed up) and you can sell the NWCInv including inventory, and whatever you procured in the beginning. Since you get it back, you have to add it back and account for it at the end of period cash flow.

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Economic Income = After-tax Operating Cash Flow - Economic Depreciation
Economic Depreciation = Market Value(beginning) - Market Value(ending)
Market Value(time=t) = Present Value of all remaining cash flows discounted at the WACC

Market Value(beginning, Year 3)
= CF₃/(1 + WACC)¹ + CF₄/(1 + WACC)²
= 318,000/(1 + 8%)¹ + 367,400/(1 + 8%)²
= 609,430

Market Value(ending)
= CF₄/(1 + WACC)¹
= 367,400/(1 + 8%)¹
= 340,185

Economic Income(Year 3)
= After-tax Operating Cash Flow (Year 3) - Economic Depreciation (Year 3 to 4)
= 318,000 - (609,430 - 340,185)
= 48,755