Question

Please show work step by step, NO EXCEL. Thank you!

The investment is $1,000,000, which is depreciated straight line to a zero salvage value over a 10 year life. The asset will be worthless in 10 years. The project will generate, annually, revenues of $800,000, cash operating expenses of $500,000, and depreciation of $100,000. The tax rate is 30%, and the cost of capital is 10%.

a. what are the annual cash flow and the NPV?

b. what would be the annual cash flow and NPV if the tax rate were 0%?

c. what tax rate would result in a zero NPV?

Answer 1

Answer a.

Initial Outflow = $1,000,000
Life of Project = 10 years

Annual Cash Flow = (Revenue - Operating Expenses - Depreciation) * (1 - tax) + Depreciation
Annual Cash Flow = ($800,000 - $500,000 - $100,000) * (1 - 0.30) + $100,000
Annual Cash Flow = $140,000 + $100,000
Annual Cash Flow = $240,000

Cost of Capital = 10%

NPV = -$1,000,000 + $240,000 * PVA of $1 (10%, 10)
NPV = -$1,000,000 + $240,000 * 6.14457
NPV = $474,696.80

Answer b.

Annual Cash Flow = (Revenue - Operating Expenses - Depreciation) * (1 - tax) + Depreciation
Annual Cash Flow = ($800,000 - $500,000 - $100,000) * (1 - 0.00) + $100,000
Annual Cash Flow = $200,000 + $100,000
Annual Cash Flow = $300,000

Cost of Capital = 10%

NPV = -$1,000,000 + $300,000 * PVA of $1 (10%, 10)
NPV = -$1,000,000 + $300,000 * 6.14457
NPV = $843,371

Answer c.

NPV = -$1,000,000 + Annual Cash Flow * PVA of $1 (10%, 10)
0 = -$1,000,000 + Annual Cash Flow * 6.14457
$1,000,000 = Annual Cash Flow * 6.14457
Annual Cash Flow = $162,745.32

Annual Cash Flow = (Revenue - Operating Expenses - Depreciation) * (1 - tax) + Depreciation
$162,745.32 = ($800,000 - $500,000 - $100,000) * (1 - tax) + $100,000
$162,745.32 = $200,000 * (1 - tax) + $100,000
$62,745.32 = $200,000 * (1 - tax)
0.3137 = 1 - tax
tax = 0.6863 or 68.63%

So, NPV will be zero at a tax rate of 68.63%