Question

•Original Machine

–Initial cost = 100,000

–Annual depreciation = 9,000

–Purchased 5 years ago

–Book Value = 55,000

–Salvage today = 65,000

–Salvage in 5 years = 10,000

•New Machine

–Initial cost = 150,000

–5-year life

–Salvage in 5 years = 0

–Cost savings = 50,000 per year

–3-year MACRS depreciation

•Required return = 10%

•Tax rate = 40%

Based on this information calculate the cash flows generated by replacing the old machine with the new one and the IRR and NPV of doing so.

Answer 1

Time line		0	1	2	3	4	5
Proceeds from sale of existing asset	=selling price* ( 1 -tax rate)	39000
Tax shield on existing asset book value	=Book value * tax rate	22000
Cost of new machine		-150000
=Initial Investment outlay		-89000
3 years MACR rate			33.33%	44.45%	14.81%	7.41%	0.00%	0.00%
Savings			50000	50000	50000	50000	50000
-Depreciation	=Cost of machine*MACR%		-49995	-66675	-22215	-11115	0	0	=Salvage Value
=Pretax cash flows			5	-16675	27785	38885	50000
-taxes	=(Pretax cash flows)*(1-tax)		3	-10005	16671	23331	30000
+Depreciation			49995	66675	22215	11115	0
=after tax operating cash flow			49998	56670	38886	34446	30000
+Tax shield on salvage book value	=Salvage value * tax rate						0
=Terminal year after tax cash flows							0
Total Cash flow for the period		-89000	49998	56670	38886	34446	30000
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331	1.4641	1.61051
Discounted CF=	Cashflow/discount factor	-89000	45452.72727	46834.71074	29215.62735	23527.081	18627.64
NPV=	Sum of discounted CF=	74657.79

Total Cash flow for the period		-89000	49998	56670	38886	34446	30000
Discount factor=	(1+discount rate)^corresponding period	1	1.431742166	2.049885631	2.934907694	4.2020311	6.0162251
Discounted CF=	Cashflow/discount factor	-89000	34921.09206	27645.44477	13249.47973	8197.4643	4986.5155
NPV=	Sum of discounted CF=	0.00
IRR is discount rate at which NPV = 0 =	43.17%