Question

One year ago, your company purchased a machine used in manufacturing for $100,000. You have learned that a new machine is available that offers many advantages and you can purchase it for $160,000 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 $45,000 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 $9.091 per year. The market value today of the current machine is $60,000. Your company's tax rate is 38%, and the opportunity cost of capital for this type of equipment is 12%. Should your company replace its year old machine? The NPV of replacing the year-old machine is $ (Round to the nearest dollar) Should your company replace its year-old machine? (Select the best choice below.) O A. Yes, there is a profit from replacing the machine. OB. No, there is a loss from replacing the machine

Answer 1

Cash flow for new machine:
Formula	Year (n)	0	1	2	3	4	5	6	7	8	9	10
	Initial investment (II)	160000
	Gross margin (GM)		45000	45000	45000	45000	45000	45000	45000	45000	45000	45000
II/10	Depreciation (D)		16000	16000	16000	16000	16000	16000	16000	16000	16000	16000
	Tax rate (T)		38%	38%	38%	38%	38%	38%	38%	38%	38%	38%
GM*(1-T) + (D*T)	Operating Cash Flow (OCF)		33980	33980	33980	33980	33980	33980	33980	33980	33980	33980
OCF - II	Free Cash Flow (FCF1)	-160000	33980	33980	33980	33980	33980	33980	33980	33980	33980	33980
Cash flow for current machine:
Formula	Year (n)	0	1	2	3	4	5	6	7	8	9	10
	Purchase price (P)	100000
P/11	Depreciation per year (D)	9,090.91
P-D	Book value (BV)	90,909
	Current selling price (SP)	60,000
SP - Tax rate*(SP - BV)	Opportunity cost of not selling the machine today (OC)	71745.45
	Gross margin (GM)		24000	24000	24000	24000	24000	24000	24000	24000	24000	24000
II/10	Depreciation (D)		9,090.91	9,090.91	9,090.91	9,090.91	9,090.91	9,090.91	9,090.91	9,090.91	9,090.91	9,090.91
	Tax rate (T)		38%	38%	38%	38%	38%	38%	38%	38%	38%	38%
GM*(1-T) + (D*T)	Operating Cash Flow (OCF)		18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55
OCF - II	Free Cash Flow (FCF2)	-71745.455	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55	18334.55
FCF1 - FCF2	Incremental cash flow (ICF)	-88254.55	15645.45	15645.45	15645.45	15645.45	15645.45	15645.45	15645.45	15645.45	15645.45	15645.45
	Discount factor @ 12%	1.000	0.893	0.797	0.712	0.636	0.567	0.507	0.452	0.404	0.361	0.322
ICF*Discount factor	PV of ICF	-88254.55	13969.16	12472.46	11136.13	9942.97	8877.65	7926.47	7077.21	6318.94	5641.91	5037.42
Sum of all PVs	NPV	145.76

NPV of replacing the year-old machine = 146

Yes. Since the NPV of the replacement decision is positive, the machine should be replaced as there is a profit from replacing it.