Question

Your firm bought a new sanding machine for its factory floor two years ago for $40,000. The current market value (Year 0) of the machine is $10,000 and you believe that it will last 5 more years (Years 1 - 5). When you're done with the machine, you can sell it for scrap and receive $1,000. However, your firm is now considering buying a more advanced sander for $80,000. The more advanced machine also last 5 more years. The new machine will have a salvage value of $5,000. The more advanced sander will increase revenues by $50,000 a year and save the company $10,000 in labor costs each year when compared to the old machine. The appropriate discount rate for this project is 12% and the company's tax rate is 35%. Use straight-line depreciation (including the appropriate salvage values).

What is the NPV of replacing the old machine? Be sure you take into account the sale of the old machine (including the tax consequences of the sale) in Year 0. This problem is really all about carefully calculating the cash flows associated with this decision each year. Build a mini-income statement for each year and then take that income and turn it into free cash flow by taking into account depreciation.

Answer 1

Book value of old machine= (purchase price)*remaining life/total life
= (40000)*5/7
= 28571.4285714286

Time line		0	1	2	3	4	5
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	6500
Tax shield on existing asset book value	=Book value * tax rate	9999.9998
Cost of new machine		-80000
=Initial Investment outlay		-63500.0002
increase in revenues+savings			60000	60000	60000	60000	60000
-Depreciation	Cost of equipment/no. of years		-16000	-16000	-16000	-16000	-16000
=Pretax cash flows			44000	44000	44000	44000	44000
-taxes	=(Pretax cash flows)*(1-tax)		28600	28600	28600	28600	28600
+Depreciation			16000	16000	16000	16000	16000
=after tax operating cash flow			44600	44600	44600	44600	44600
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)						3250
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							3250
Total Cash flow for the period		-63500.0002	44600	44600	44600	44600	47850
Discount factor=	(1+discount rate)^corresponding period	1	1.12	1.2544	1.404928	1.5735194	1.7623417
Discounted CF=	Cashflow/discount factor	-63500.0002	39821.42857	35554.847	31745.399	28344.106	27151.375
NPV=	Sum of discounted CF=	99117.16