Question

One year​ ago, your company purchased a machine used in manufacturing for $105,000. 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 $35,000 per year for the next 10 years. The current machine is expected to produce a gross margin of $20,000 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 $9,545 per year. The market value today of the current machine is $65,000. Your​ company's tax rate is 45%​, and the opportunity cost of capital for this type of equipment is 11%. Should your company replace its​ year-old machine?

Answer 1

Time line		0	1	2	3	4	5	6	7	8	9	10
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	35750
Tax shield on existing asset book value	=Book value * tax rate = (105000-9545)*0.45	42954.75
Cost of new machine		-140000
=Initial Investment outlay		-61295.25
Incremental Profits	=35000-20000		15000	15000	15000	15000	15000	15000	15000	15000	15000	15000
-Depreciation	Cost of equipment/no. of years		-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000	-14000
=Pretax cash flows			1000	1000	1000	1000	1000	1000	1000	1000	1000	1000
-taxes	=(Pretax cash flows)*(1-tax)		550	550	550	550	550	550	550	550	550	550
+Depreciation			14000	14000	14000	14000	14000	14000	14000	14000	14000	14000
=after tax operating cash flow			14550	14550	14550	14550	14550	14550	14550	14550	14550	14550
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-61295.25	14550	14550	14550	14550	14550	14550	14550	14550	14550	14550
Discount factor=	(1+discount rate)^corresponding period	1	1.11	1.2321	1.367631	1.5180704	1.6850582	1.8704146	2.07616	2.30454	2.558037	2.839421
Discounted CF=	Cashflow/discount factor	-61295.25	13108.108	11809.1064	10638.835	9584.5357	8634.7168	7779.0242	7008.13	6313.63	5687.955	5124.284
NPV=	Sum of discounted CF=	24393.07576

Replace project as NPV is positive