Question

Gluon Inc. is considering the purchase of a new high pressure glueball. It can purchase the glueball for $160,000 and sell its old low-pressure glueball, which is fully depreciated, for $28,000. The new equipment has a 10-year useful life and will save $36,000 a year in expenses. The opportunity cost of capital is 11%, and the firm’s tax rate is 40%. What is the equivalent annual savings from the purchase if Gluon uses straight-line depreciation? Assume the new machine will have no salvage value.

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)	16800
Tax shield on existing asset book value	=Book value * tax rate	0
Cost of new machine		-160000
=Initial Investment outlay		-143200
Savings			36000	36000	36000	36000	36000	36000	36000	36000	36000	36000
-Depreciation	Cost of equipment/no. of years		-16000	-16000	-16000	-16000	-16000	-16000	-16000	-16000	-16000	-16000
=Pretax cash flows			20000	20000	20000	20000	20000	20000	20000	20000	20000	20000
-taxes	=(Pretax cash flows)*(1-tax)		12000	12000	12000	12000	12000	12000	12000	12000	12000	12000
+Depreciation			16000	16000	16000	16000	16000	16000	16000	16000	16000	16000
=after tax operating cash flow			28000	28000	28000	28000	28000	28000	28000	28000	28000	28000
+Tax shield on salvage book value	=Salvage value * tax rate											0
=Terminal year after tax cash flows												0
Total Cash flow for the period		-143200	28000	28000	28000	28000	28000	28000	28000	28000	28000	28000
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	-143200	25225.225	22725.4281	20473.359	18444.467	16616.637	14969.943	13486.44	12149.9	10945.89	9861.165
NPV=	Sum of discounted CF=	21698.49631

EAS	3684.43564
Year or period		0	1	2	3	4	5	6	7	8	9	10
EAS			3684.4356	3684.43564	3684.4356	3684.4356	3684.4356	3684.4356	3684.436	3684.44	3684.436	3684.436
Discount factor=	(1+discount rate)^corresponding period		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		3319.3114	2990.37062	2694.0276	2427.0519	2186.5332	1969.8498	1774.639	1598.77	1440.337	1297.601
NPV=	21698.49631
EAS is equivalent yearly CF with same NPV =	3684.43564