Question

Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $10 million. The system will last 5 years. Do-It-Right sells a sturdier but more expensive system for $12 million; it will last for 6 years. Both systems entail $3 million in operating costs; both will be depreciated straight-line to a final value of zero over their useful lives; neither will have any salvage value at the end of its life. The firm’s tax rate is 20%, and the discount rate is 14%. Either machine will be replaced at the end of its life.

a. What is the equivalent annual cost of investing in the cheap system? (Do not round intermediate calculations. Enter your answer as a positive value. Enter your answer in millions rounded to 3 decimal places.)

b. What is the equivalent annual cost of investing in the more expensive system? Do not round intermediate calculations. Enter your answer as a positive value. Enter your answer in millions rounded to 3 decimal places.

Answer 1

A

Time line		0	1	2	3	4	5
Cost of equipment		-10
Installation cost		0
Total investment in new machine		-10
-Working capital		0
=Initial Investment outlay		-10
-operating cost			-3	-3	-3	-3	-3
-Depreciation =	Cost of equipment/5		-2	-2	-2	-2	-2
=			-5	-5	-5	-5	-5
-taxes	=(cost- depreciation)*(1-tax)		-4	-4	-4	-4	-4
+Depreciation			2	2	2	2	2
=after tax operating cash flow			-2	-2	-2	-2	-2
Proceeds from sale of assets	=salvage value*(1 - tax rate)
+reversal of net working capital
Terminal year non operating cash flows
Total Cash flow for the period		-10	-2	-2	-2	-2	-2
Discount factor	=(1+discount rate)^n	1	1.14	1.2996	1.481544	1.689	1.9254
Discounted cash flows		-10	-1.75439	-1.53894	-1.34994	-1.1842	-1.0387
NPV=	Sum of discounted cash flows	-16.8662
EAC =	-4.912846552		-4.91285	-4.91285	-4.91285	-4.9128	-4.9128
Discounted EAC			-4.30951	-3.78028	-3.31603	-2.9088	-2.5516
Sum of discounted EAC=NPV=	-16.8662

EAC = 4.913

B

Time line		0	1	2	3	4	5	6
Cost of equipment		-12
Installation cost		0
Total investment in new machine		-12
-Working capital		0
=Initial Investment outlay		-12
-operating cost			-3	-3	-3	-3	-3	-3
-Depreciation =	Cost of equipment/6		-2	-2	-2	-2	-2	-2
=			-5	-5	-5	-5	-5	-5
-taxes	=(cost- depreciation)*(1-tax)		-4	-4	-4	-4	-4	-4
+Depreciation			2	2	2	2	2	2
=after tax operating cash flow			-2	-2	-2	-2	-2	-2
Proceeds from sale of assets	=salvage value*(1 - tax rate)
+reversal of net working capital
Terminal year non operating cash flows
Total Cash flow for the period		-12	-2	-2	-2	-2	-2	-2
Discount factor	=(1+discount rate)^n	1	1.14	1.2996	1.481544	1.689	1.9254	2.195
Discounted cash flows		-12	-1.75439	-1.53894	-1.34994	-1.1842	-1.0387	-0.9112
NPV=	Sum of discounted cash flows	-19.7773
EAC =	-5.085880939		-5.08588	-5.08588	-5.08588	-5.0859	-5.0859	-5.0859
Discounted EAC			-4.4613	-3.91342	-3.43282	-3.0112	-2.6414	-2.3171
Sum of discounted EAC=NPV=	-19.7773

eac = 5.086