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 4 years. Do-It-Right sells a sturdier but more expensive system for $13 million; it will last for 5 years. Both systems entail $2 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?

Please answer everything with explanation

Answer 1

Calculation of the Cheap system Depreciation per year :-

Depreciation = Cost of cheap equipment / no of year to be project life = $ 12 million / 4 = $ 3 million

Calculation of the More expensive system Depreciation per year :-

Depreciation = Cost of cheap equipment / no of year to be project life = $ 13 million / 5 = $ 2.6 million

1. Calculation of the equivalent cost of Cheap system :-

Years	Cash out flows	operating cost	Depreciation	total	Tax@30%	Net cash ouflows after tax	PVF@15%	Present value of CF
0	12			12		12	1	12
1		2	3	5	1.5	3.5	0.869565217	3.043478
2		2	3	5	1.5	3.5	0.756143667	2.646503
3		2	3	5	1.5	3.5	0.657516232	2.301307
4		2	3	5	1.5	3.5	0.571753246	2.001136
	Total							21.99242
		Present value of annuity factor at 15% for 4 years						2.854978
		Equivalent Annual cost of Cheap machine						7.703184

2. Calculation of the equivalent cost of More expensive system :-

Years	Cash out flows	operating cost	Depreciation	total	Tax@30%	Net cash ouflows after tax	PVF@15%	Present value of CF
0	13			13		13	1	13
1		2	2.6	4.6	1.38	3.22	0.869565217	2.80000
2		2	2.6	4.6	1.38	3.22	0.756143667	2.434783
3		2	2.6	4.6	1.38	3.22	0.657516232	2.117202
4		2	2.6	4.6	1.38	3.22	0.571753246	1.841045
5		2	2.6	4.6	1.38	3.22	0.497176735	1.600909
	Total							23.79394
		Present value of annuity factor at 15% for 5 years						3.352155
		Equivalent Annual cost of more expensive machine						7.098102

c) Here More expensive system would be selected. Because of the Equivalent annual cost of more expensive system is  lower than cheap system.

Hence more expensive system selected.