Question

You are considering the replacement of an old machine by a new one. The old machine was bought 5 years ago for $120,000 and is being depreciated (straight line) for a zero salvage value over a 15-year depreciable life. The current market value of this machine is $60,000. The new machine, which will cost $150,000 (with installation cost) will be depreciated (again, on a straight-line basis) over a 10-year life with a $30,000 salvage value.

The new machine will increase revenues by $5,000 per year and decrease operating costs by $15000 per year for the next ten years. An additional amount of $20,000 in working capital will be needed at the beginning of the project life. The tax rate is 30%. The firm’s cost of capital is 10%.

A. The initial investment (t=o) relevant to this project is __________.

B. The after-tax operating cash flows (t=1‑10) for each year is ________.

C. The terminal value of the project is

D. To replace or not to replace, that is the question!

Answer 1

A). Cash flow to start the project at year 0 is $104000

cash flow (year 0) = cost of new equipment + increase in Net working capital - NSV of old equipment

1.cost of cost of new equipment = 150,000

2.increase in Net working capital = 20,000

3.NSV of old equipment

Book value of old asset (BV)	Depreciation basis - Accumulated Depreciation
	= ($120000) - (5 * 8000)
	=$80,000
Market value (MV)	=$60,000
NSV of project old asset	= MV - tax rate (MV-BV)
	=$60,000 - .3 *($60,000- $80,000)
	=$66,000

cash flow (year 0)=( 150,000 + 20,000-66,000) = $104000

B).Yearly after-tax operating Cash Flow for each year is $16,100

Yearly operating Cash Flow

Annual revenue	$5,000
Decrease in Expenses	$15,000
Earnings before tax	$20,000
Taxes (30%)	$6,000
Earnings after tax	$14,000
Add depreciation tax shield	$2,100
Yearly operating Cash Flow	$16,100
Calculation of depreciation tax-shield: - Depreciation of old equipment = $120,000 / 15 = $8,000 Depreciation of new equipment = $150,000 / 10 = $15,000 Incremental depreciation = $15,000 - $8,000 = $7,000 Depreciation tax shield = Incremental depreciation * tax rate Depreciation tax shield = $7,000 * .3= $2,100

C). Terminal cash flow of the project is $41,000

Terminal cashflow = NSV of project assets + Recovered Net working capital

1.NSV of project assets = market value of asset * (1- tax rate)

= $30,000 * (1-.3)

=$21,000

2.Recovered Net working capital = $20,000

Therefore, Terminal cashflow =$21,000 + $20,000 = $41,000

D). Yes, the machine should be replaced because the NPV of the replacement project is positive $10,760.5, which means that the present value of after-tax cash inflows of the project is higher than the outflows by $10,760.5. the replacement of machine will brings further benefits to the company.

NPV CALCULATIONS: -

NPV = after-tax operating cashflows *(PVIFA. 10%,10 years) + Terminal cashflow * (PVIF.10%, year 10)- initial investment

NPV= ($16,100 * 6.145) + ($41,000 * .386) -$104,000

NPV=    $98,934.5 + $15,826 -$104,000

NPV = $10,760.5