Question

The Fairmont Hotel in San Francisco needs to replace its air conditioning system. There are two alternatives, both of which can do the job equally well:

Machine name	AC 1	AC 2
Purchase price	$40,000	$60,000
Operating cost (end of each year)	$17,000	$8,000
Useful life (years)	4	6
Straight line depreciation to zero over (years)	4	6
Salvage value at end of useful life	$0	$0

The relevant discount rate is 10% and the marginal tax rate is 35%.

What is the operating cash flow for AC 1 per year?
What is the equivalent annual cost for AC 1 (in absolute terms)?
What is the operating cash flow for AC 2 per year?
What is the equivalent annual cost for AC 2 (in absolute terms)?

Answer 1

First we calcatle the NPV and then the equivalent annual cost

The NPV and equivalent annual cost of AC 1

Year	0	1	2	3	4
Initial Cost	-40000
Operating cost		-17000	-17000	-17000	-17000
Depreciation tax shield		3500	3500	3500	3500
Operating cash flow	-40000	-13500	-13500	-13500	-13500
NPV at 10%	$ -82,793.18

Equivalent annual cost = NPV*r/1-(1+r)^-n = -82,793.18*0.10/(1-1.10^-4) = -26,118.83

Question 1: Operating Cash flow for AC 1 per year = -$13,500 (the negative sign indicates that this is a cost)

Question 2: Equivalent annual cost in absolute terms of AC 1 = $26,118.83

The NPV and equivalent annual cost of AC 2:

Year	0	1	2	3	4	5	6
Initial Cost	-60000
Operating cost		-8000	-8000	-8000	-8000	-8000	-8000
Depreciation tax shield		3500	3500	3500	3500	3500	3500
Operating cash flow	-60000	-4500	-4500	-4500	-4500	-4500	-4500
NPV at 10%	$     -79,598.67

Equivalent annual cost = NPV*r/1-(1+r)^-n =-79,798.67*0.10/(1-1.10^-6) = -$18,276.44

Question 3: Operating Cash flow for AC 2 per year = -$4,500 (the negative sign indicates that this is a cost)

Question 4: Equivalent annual cost in absolute terms of AC 2= $18,276.44