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 $16 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 15%. 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 2 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 2 decimal places.)

c. Which system should Blooper install?

Answer 1

a) Statement showing equivalent annual cost of investing in the cheap system

Particular	0	1	2	3	4	5	Total
Cost of cheap purification system	-10000000
Operating cost		-1000000	-1000000	-1000000	-1000000	-1000000
Depreciation		-2000000	-2000000	-2000000	-2000000	-2000000
Total Expense		-3000000	-3000000	-3000000	-3000000	-3000000
Tax savings @ 30%		900000	900000	900000	900000	900000
After tax expenses		-2100000	-2100000	-2100000	-2100000	-2100000
Add: Depreciation		2000000	2000000	2000000	2000000	2000000
Annual cash flow		-100000	-100000	-100000	-100000	-100000
Total Cash flow	-10000000	-100000	-100000	-100000	-100000	-100000
PVIF @ 15%	1.0000	0.8696	0.7561	0.6575	0.5718	0.4972
PV	-10000000.00	-86956.52	-75614.37	-65751.62	-57175.32	-49717.67	-10335215.51
PVIFA (15%,5 years)							3.3522
equivalent annual cost (Total of PV/PVIFA)							-3083155.52

Thus Equivalent annual cost of investing in the cheap system = 30,83,155.52 $

b) Statement showing equivalent annual cost of investing in the expensive system

Particular	0	1	2	3	4	5	6	7	8	Total
Cost of cheap expensive system	-16000000
Operating cost		-1000000	-1000000	-1000000	-1000000	-1000000	-1000000	-1000000	-1000000
Depreciation		-2000000	-2000000	-2000000	-2000000	-2000000	-2000000	-2000000	-2000000
Total Expense		-3000000	-3000000	-3000000	-3000000	-3000000	-3000000	-3000000	-3000000
Tax savings @ 30%		900000	900000	900000	900000	900000	900000	900000	900000
After tax expenses		-2100000	-2100000	-2100000	-2100000	-2100000	-2100000	-2100000	-2100000
Add: Depreciation		2000000	2000000	2000000	2000000	2000000	2000000	2000000	2000000
Annual cash flow		-100000	-100000	-100000	-100000	-100000	-100000	-100000	-100000
Total Cash flow	-16000000	-100000	-100000	-100000	-100000	-100000	-100000	-100000	-100000
PVIF @ 15%	1.0000	0.8696	0.7561	0.6575	0.5718	0.4972	0.4323	0.3759	0.3269
PV	-16000000.00	-86956.52	-75614.37	-65751.62	-57175.32	-49717.67	-43232.76	-37593.70	-32690.18	-16448732.15
PVIFA (15%,8 years)										4.4873
equivalent annual cost (Total of PV/PVIFA)										-3665601.43

Thus equivalent annual cost of investing in the expensive system = 36,65,601.43 $

c) Blooper should install cheap expensive system as it has lower equivalent annual cost