The Fairmont Hotel in San Francisco needs to replace its air conditioning system

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:

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)?

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

Explanation / Answer

First we calcatle the NPV and then the equivalent annual cost

The NPV and equivalent annual cost of AC 1

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:

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

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

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