Question

Blooper Industries must replace its magnoosium purification system. Quick & Dirty Systems sells a relatively cheap purification system for $12 million. The system will last 6 years. Do-It-Right sells a sturdier but more expensive system for $20 million; it will last for 8 years. Both systems entail $1 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 30%, and the discount rate is 13%. 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 answers as a positive value. Enter your answers in whole dollars, not in millions.)

b. What is the equivalent annual cost of investing in the more expensive system?

Answer 1

Solution:
A.	The equivalent annual cost of investing in the cheap system =$2,401,839
Working Notes:
	The cheap system is Quick & Dirty systems.
	The equivalent annual cost of investing in the cheap system (Quick & Dirty systems) = $2,401,839
		Quick & Dirty systems                   (cheap system)
a	Operating costs	1,000,000
b	Investment	12,000,000
c	Project life	6	year
d=b/c	Annual depreciation	2,000,000
	[investment/project life ]
e=d x 30%	tax shield on Depreciation	600,000
	(tax rate 30% x Depreciation $2,000,000)
f	Cumulative PVF @ 13% for 1 to 6th	3.99755
	[working given below]
g=e x f	Present value of (depreciation tax shield)	2,398,530
h=b-g	Net capital cost	9,601,470
	[Investment - Present Value of (Depreciation tax shield)]
i=h/f	EAC of net capital cost	2,401,838.63
	[Net capital cost / Cumulative PVF @ 13% for 1 to 6th]
	EAC of net capital cost	2,401,839
	The equivalent annual cost of investing in the cheap system (Quick & Dirty systems) = $2,401,839
	Quick & Dirty systems (cheap system)
	Cumulative PVF @ 13% for 1 to 6th is calculated = (1 - (1/(1 + 0.13)^6) ) /0.13 = 3.99755
B.	The equivalent annual cost of investing in the more expensive system =$3,417,735
Working Notes:
	The more expensive system is Do-It-Right systems
	The equivalent annual cost of investing in the Do-It-Right systems (expensive system) = $3,417,735
		Do-It-Right systems                   (expensive system)
a	Operating costs	1,000,000
b	Investment	20,000,000
c	Project life	8	year
d=b/c	Annual depreciation	2,500,000
	[investment/project life ]
e=d x 30%	tax shield on Depreciation	750,000
	(tax rate 30% x Depreciation $2,000,000)
f	Cumulative PVF @ 13% for 1 to 8th	4.79877
	[working given below]
g=e x f	Present value of (depreciation tax shield)	3,599,078
h=b-g	Net capital cost	16,400,923
	[Investment - Present Value of (Depreciation tax shield)]
i=h/f	EAC of net capital cost	3,417,734.65
	[Net capital cost / Cumulative PVF @ 13% for 1 to 8th]
	EAC of net capital cost	3,417,735
	The equivalent annual cost of investing in the Do-It-Right systems (expensive system) = $3,417,735
	Do-It-Right systems (expensive system)
	Cumulative PVF @ 13% for 1 to 8th is calculated = (1 - (1/(1 + 0.13)^8) ) /0.13 = 4.79877
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