Question

One year​ ago, your company purchased a machine used in manufacturing for $ 110 comma 000. You have learned that a new machine is available that offers many advantages and you can purchase it for $ 140 comma 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 $ 55 comma 000 per year for the next 10 years. The current machine is expected to produce a gross margin of $ 20 comma 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 comma 000 per year. The market value today of the current machine is $ 55 comma 000. Your​ company's tax rate is 45 %​, and the opportunity cost of capital for this type of equipment is 12 %. Should your company replace its​ year-old machine?

Answer 1

incremental gross margin
gross margin on new machine		55000
gross margin on old machine		20000
incremental gross margin		35000
incremental depreciation
depreciation on new machine		14000
depreciation on old machine = 110000/11		10000
incremental depreciation		4000
sale value of old machine		55000
book value of old machine (110000-10000)		100000
loss on sale of machine		-45000
tax credit on loss of machine	45000*45%	20250
total cash outlay on new machine
cost of new machine		-140000
sale proceeds of old machine		55000
tax credit on loss on sale of machine		20250
total cash outlay on new machine		-64750
Year	0	1	2	3	4	5	6	7	8	9	10
total cash outlay on new machine	-64750
incremental gross margin		35000	35000	35000	35000	35000	35000	35000	35000	35000	35000
less incremental depreciation		4000	4000	4000	4000	4000	4000	4000	4000	4000	4000
before tax margin		31000	31000	31000	31000	31000	31000	31000	31000	31000	31000
less taxes- 45%		13950	13950	13950	13950	13950	13950	13950	13950	13950	13950
after tax margin		17050	17050	17050	17050	17050	17050	17050	17050	17050	17050
add incremental depreciation		4000	4000	4000	4000	4000	4000	4000	4000	4000	4000
net operating cash flow	-64750	21050	21050	21050	21050	21050	21050	21050	21050	21050	21050
present value of net operating cash flow = net operating cash flow/(1+r)^n r=12%	Q432/1.12^0	R432/1.12^1	S432/1.12^2	T432/1.12^3	U432/1.12^4	V432/1.12^5	W432/1.12^6	X432/1.12^7	Y432/1.12^8	Z432/1.12^9	AA432/1.12^10
present value of net operating cash flow = net operating cash flow/(1+r)^n r=12%	-64750	18794.64286	16780.93112	14982.97422	13377.65555	11944.33531	10664.5851	9521.950983	8501.741949	7590.841026	6777.53663
net present value = sum of present value of cash flow	SUM(Q434:AA434)	54187.19475
Yes old machine should be replaced as net present worth of equipment is positive