Question

X Company is considering a new processor that costs $150,000. Shipping and setup costs for the new processor are estimated to be $15,000. X’s working capital requirement is expected to increase by $17,000 when the new processor begins operation and is expected to be fully recoverable at the end of the project. The new processor’s useful life is expected to be 5 years and its salvage value at that point is estimated to be $60,000. The new processor is being depreciated using a 5-year ACRS life. Assume a tax rate of 35% and a cost of capital of 12%.

Estimated incremental revenues and incremental cash operating expenses for the new processor before tax for each year are shown in the table below.

Year	Incremental Revenue	Incremental Cash Operating Expenses	ACRS Depr. %
1	$87,000	$23,000	15
2	$82,000	$25,000	22
3	$93,000	$30,000	21
4	$87,000	$23,000	21
5	$88,000	$29,000	21

Q1.) What is the book value of the new processor at the end of Year 3?

Q2.) What is the total after-tax cash flows in Year 5? Total means incremental cash flows plus terminal cash flows.

Answer 1

Q1.) book value of the new processor at the end of Year 3 = Cost of new processor*(1-sum of depreciation rates of years 1 to 3)

Cost of new processor = purchase price + shipping & set up costs = $150,000 + $15,000 = $165,000

sum of depreciation rates of years 1 to 3 = year 1 dep. rate + year 2 dep. rate + year 3 dep. rate = 15% + 22% + 21% = 58%

book value of the new processor at the end of Year 3 = $165,000*(1-0.58) = $165,000*0.42 = $69,300

the book value of the new processor at the end of Year 3 is $69,300.

Q2.) total after-tax cash flows in Year 5 = [(Year 5 incremental revenue - year 5 incremental cash operating expenses - year 5 depreciation)*(1-tax rate)] + year 5 depreciation + after-tax salvage value + recovery of working capital

terminal cash flows are after-tax salvage value and recovery of working capital.

book value of new processor at the end of 5 years will be zero. so, tax will be applied on entire salvage value because capital gain = salvage value - book value of new processor at the end of 5 years = $60,000 - $0 = $60,000.

year 5 depreciation = Cost of new processor*year 5 depreciation rate = $165,000*21% = $34,650

depreciation is a non-cash expense. so, cash flow calculation it is added back after calculating tax.

after-tax salvage value = salvage value*(1-tax rate) = $60,000*(1-0.35) = $60,000*0.65 = $39,000

total after-tax cash flows in Year 5 = [($88,000 - $29,000 - $34,650*(1-0.35)] + $34,650 + $39,000 + $17,000 = ($24,350*0.65) + $34,650 + $39,000 + $17,000 = $15,827.50 + $34,650 + $39,000 + $17,000 = $106,477.50

the total after-tax cash flows in Year 5 is $106,477.50.