Question

Gluon Inc. is considering the purchase of a new high pressure glueball. It can purchase the glueball for $50,000 and sell its old low-pressure glueball, which is fully depreciated, for $8,000. The new equipment has a 10-year useful life and will save $12,000 a year in expenses. The opportunity cost of capital is 10%, and the firm’s tax rate is 21%. What is the equivalent annual saving from the purchase if Gluon can depreciate 100% of the investment immediately.

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)	6320
Tax shield on existing asset book value	=Book value * tax rate	0
Cost of new machine		-50000
=Initial Investment outlay		-43680
													100.00%
Savings			12000	12000	12000	12000	12000	12000	12000	12000	12000	12000
-Depreciation			-50000	0	0	0	0	0	0	0	0	0	0	=Salvage Value
=Pretax cash flows			-38000	12000	12000	12000	12000	12000	12000	12000	12000	12000
-taxes	=(Pretax cash flows)*(1-tax)		-30020	9480	9480	9480	9480	9480	9480	9480	9480	9480
+Depreciation			50000	0	0	0	0	0	0	0	0	0
=after tax operating cash flow			19980.00	9480.00	9480	9480	9480	9480	9480	9480	9480	9480
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-43680	19980	9480	9480	9480	9480	9480	9480	9480	9480	9480
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	-43680	18163.636	7834.7107	7122.4643	6474.9676	5886.3341	5351.2129	4864.738961	4422.49	4020.445	3654.95
NPV=	Sum of discounted CF=	24115.95

Year or period		0	1	2	3	4	5	6	7	8	9	10
EAC			3924.7598	3924.7598	3924.7598	3924.7598	3924.7598	3924.7598	3924.759806	3924.7598	3924.76	3924.76
Discount factor=	(1+discount rate)^corresponding period		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		3567.9635	3243.6031	2948.7301	2680.6638	2436.9671	2215.4246	2014.022356	1830.9294	1664.481	1513.165
NPV=	24115.95
EAC is equivalent yearly CF with same NPV =	3924.759806