Question

One year​ ago, your company purchased a machine used in manufacturing for

$110,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $140,000 today. It will be depreciated on a​ straight-line basis over 10 years and has no salvage value. You expect that the new machine will produce a gross margin​ (revenues minus operating expenses other than​ depreciation) of $60,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $24,000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, and has no salvage​ value, so depreciation expense for the current machine is $10,000 per year. The market value today of the current machine is $60,000. Your​ company's tax rate is 35 %, and the opportunity cost of capital for this type of equipment is 10 %. Should your company replace its​ year-old machine?

1. The NPV of replacing the​ year-old machine is ??? (Round to the nearest​ dollar.)

2. Should your company replace its year-old machine?

Answer 1

Book value old machine = (purchase price)*remaining life/total life
= (110000)*10/11
= 100000

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	39000
Tax shield on existing asset book value	=Book value * tax rate	35000
Cost of new machine		-140000
=Initial Investment outlay		-66000
													100.00%
Profits			36000	36000	36000	36000	36000	36000	36000	36000	36000	36000
-Depreciation	Cost of equipment/no. of years		-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	0	=Salvage Value
=Pretax cash flows			22000	22000	22000	22000	22000	22000	22000	22000	22000	22000
-taxes	=(Pretax cash flows)*(1-tax)		14300	14300	14300	14300	14300	14300	14300	14300	14300	14300
+Depreciation			14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
=after tax operating cash flow			28300	28300	28300	28300	28300	28300	28300	28300	28300	28300
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-66000	28300	28300	28300	28300	28300	28300	28300	28300	28300	28300
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051	1.771561	1.9487171	2.1435888	2.357948	2.593742
Discounted CF=	Cashflow/discount factor	-66000	25727.27273	23388.42975	21262.20887	19329.281	17572.073	15974.612	14522.37475	13202.159	12001.96	10910.88
1. NPV=	Sum of discounted CF=	107891.25

2.

Replace machine as NPV is positive